Table 2- Factorizations of 2^n-1, n odd, n<1200
n Prime Factors
3 7
5 31
7 127
9 (3) 73
11 23.89
13 8191
15 (3,5) 151
17 131071
19 524287
21 (3,7) 7*.337
23 47.178481
25 (5) 601.1801
27 (3,9) 262657
29 233.1103.2089
31 2147483647
33 (3,11) 599479
35 (5,7) 71.122921
37 223.616318177
39 (3,13) 79.121369
41 13367.164511353
43 431.9719.2099863
45 (3,5,9,15) 631.23311
47 2351.4513.13264529
49 (7) 4432676798593
51 (3,17) 103.2143.11119
53 6361.69431.20394401
55 (5,11) 881.3191.201961
57 (3,19) 32377.1212847
59 179951.3203431780337
61 2305843009213693951
63 (3,7,9,21) 92737.649657
65 (5,13) 145295143558111
67 193707721.761838257287
69 (3,23) 10052678938039
71 228479.48544121.212885833
73 439.2298041.9361973132609
75 (3,5,15,25) 100801.10567201
77 (7,11) 581283643249112959
79 2687.202029703.1113491139767
81 (3,9,27) 2593.71119.97685839
83 167.57912614113275649087721
85 (5,17) 9520972806333758431
87 (3,29) 4177.9857737155463
89 618970019642690137449562111
91 (7,13) 911.112901153.23140471537
93 (3,31) 658812288653553079
95 (5,19) 191.420778751.30327152671
97 11447.13842607235828485645766393
99 (3,9,11,33) 199.153649.33057806959
101 7432339208719.341117531003194129
103 2550183799.3976656429941438590393
105 (3,5,7,15,21,35) 29191.106681.152041
107 162259276829213363391578010288127
109 745988807.870035986098720987332873
111 (3,37) 321679.26295457.319020217
113 3391.23279.65993.1868569.1066818132868207
115 (5,23) 14951.4036961.2646507710984041
117 (3,9,13,39) 937.6553.86113.7830118297
119 (7,17) 239.20231.62983048367.131105292137
121 (11) 727.1786393878363164227858270210279
123 (3,41) 3887047.177722253954175633
125 (5,25) 269089806001.4710883168879506001
127 170141183460469231731687303715884105727
129 (3,43) 11053036065049294753459639
131 263.10350794431055162386718619237468234569
133 (7,19) 163537220852725398851434325720959
135 (3,5,9,15,27,45) 271.348031.49971617830801
137 32032215596496435569.5439042183600204290159
139 5625767248687.123876132205208335762278423601
141 (3,47) 4375578271.646675035253258729
143 (11,13) 724153.158822951431.5782172113400990737
145 (5,29) 2679895157783862814690027494144991
147 (3,7,21,49) 7*.2741672362528725535068727
149 86656268566282183151.8235109336690846723986161
151 18121.55871.165799.2332951.7289088383388253664437433
153 (3,9,17,51) 919.75582488424179347083438319
155 (5,31) 31*.311.11471.73471.4649919401.18158209813151
157 852133201.60726444167.1654058017289.2134387368610417
159 (3,53) 6679.13960201.540701761.229890275929
161 (7,23) 1289.3188767.45076044553.14808607715315782481
163 150287.704161.110211473.27669118297.36230454570129675721
165 (3,5,11,15,33,55) 2048568835297380486760231
167 2349023.79638304766856507377778616296087448490695649
169 (13) 4057.6740339310641.3340762283952395329506327023033
171 (3,9,19,57) 93507247.3042645634792541312037847
173 730753.1505447.70084436712553223.155285743288572277679887
175 (5,7,25,35) 39551.60816001.535347624791488552837151
177 (3,59) 184081.27989941729.9213624084535989031
179 359.1433.1489459109360039866456940197095433721664951999121
181 43441.1164193.7648337.7923871097285295625344647665764672671
183 (3,61) 367.55633.37201708625305146303973352041
185 (5,37) 1587855697992791.7248808599285760001152755641
187 (11,17) 707983.1032670816743843860998850056278950666491537
189 (3,7,9,21,27,63) 1560007.207617485544258392970753527
191 383.7068569257.39940132241.332584516519201.87274497124602996457
193 13821503.61654440233248340616559.14732265321145317331353282383
195 (3,5,13,15,39,65) 134304196845099262572814573351
197 7487.26828803997912886929710867041891989490486893845712448833
199 164504919713.4884164093883941177660049098586324302977543600799
201 (3,67) 1609.22111.87449423397425857942678833145441
203 (7,29) 136417.121793911.11348055580883272011090856053175361113
205 (5,41) 2940521.70171342151.3655725065508797181674078959681
207 (3,9,23,69) 79903.634569679.2232578641663.42166482463639
209 (11,19) 94803416684681.1512348937147247.5346950541323960232319657
211 15193.60272956433838849161.3593875704495823757388199894268773153439
213 (3,71) 66457.2849881972114740679.4205268574191396793
215 (5,43) 1721.731516431.514851898711.297927289744047764444862191
217 (7,31) 5209.62497.6268703933840364033151.378428804431424484082633
219 (3,73) 3943.671165898617413417.4815314615204347717321
221 (13,17) 1327.2365454398418399772605086209214363458552839866247069233
223 18287.196687.1466449.2916841.1469495262398780123809.P24
225 (3,5,9,15,25,45,75) 115201.617401.1348206751.13861369826299351
227 26986333437777017.P52
229 1504073.20492753.59833457464970183.P39
231 (3,7,11,21,33,77) 463.P34
233 1399.135607.622577.P57
235 (5,47) 2391314881.72296287361.P35
237 (3,79) 1423.49297.23728823512345609279.31357373417090093431
239 479.1913.5737.176383.134000609.P49
241 22000409.P66
243 (3,9,27,81) 487.16753783618801.192971705688577.3712990163251158343
245 (5,7,35,49) 1471.P48
247 (13,19) 15809.6459570124697.402004106269663.P34
249 (3,83) 1621324657.P40
251 503.54217.178230287214063289511.61676882198695257501367.P26
253 (11,23) 23*.4103188409.199957736328435366769577.P32
255 (3,5,15,17,51,85) 106591.949111.P28
257 535006138814359.1155685395246619182673033.P39
259 (7,37) 2499285769.P56
261 (3,9,29,87) P51
263 23671.13572264529177.120226360536848498024035943.P36
265 (5,53) 29324808311.197748738449921.P38
267 (3,89) 78903841.28753302853087.P32
269 13822297.P74
271 15242475217.P72
273 (3,7,13,21,39,91) 108749551.4093204977277417.86977595801949844993
275 (5,11,25,55) 382027665134363932751.P40
277 1121297.31133636305610209482201109050392404721.P40
279 (3,9,31,93) 16183.34039.1437967.833732508401263.2034439836951867299888617
281 80929.P80
283 9623.68492481833.P71
285 (3,5,15,19,57,95) 1491477035689218775711.25349242986637720573561
287 (7,41) 17137716527.P62
289 (17) 12761663.179058312604392742511009.P52
291 (3,97) 272959.2065304407.5434876633.P34
293 40122362455616221971122353.P63
295 (5,59) 4721.132751.5794391.128818831.3812358161.452824604065751.P22
297 (3,9,11,27,33,99) 8950393.P48
299 (13,23) 599.9341359.14718679249.13444476836590589479.
.51441563151591093599.260242449712509916159
301 (7,43) 490631.365505823711978039310711.P47
303 (3,101) 607.P58
305 (5,61) 1831.2441.4271.270841.484074637694471.P42
307 14608903.85798519.23487583303.78952752017.P57
309 (3,103) 1953272766780718501831.P40
311 5344847.2647649373910205158468946067671.P57
313 10960009.14787970697180273.3857194764289141165278097.P47
315 (3,5,7,9,15,21,35,45,63,105) 870031.983431.P32
317 9511.587492521482839879.4868122671322098041565641.P49
319 (11,29) 18503.64439.84819793631.P64
321 (3,107) 17866285599391.P51
323 (17,19) 647.7753.39044358788825633753.P61
325 (5,13,25,65) 7151.51879585551.P58
327 (3,109) 20597276734348736647.33157029794959983067039.P23
329 (7,47) 12503.200033.9106063.270447871.P58
331 16937389168607.865118802936559.P72
333 (3,9,37,111) 1999.10657.169831.1238761.36085879.199381087.
.698962539799.4096460559560875111
335 (5,67) 464311.1532217641.P65
337 18199.2806537.95763203297.726584894969.P68
339 (3,113) 10113049.320021624768405574452943847.P34
341 (11,31) 5560125493425335999.126901141805369975317583.P49
343 (7,49) 6073159.1428389887.62228099977.P62
345 (3,5,15,23,69,115) P54
347 14143189112952632419639.P83
349 1779973928671.34720396273212657799920861294559.P62
351 (3,9,13,27,39,117) 446473.29121769.571890896913727.93715008807883087.P21
353 931921.2927455476800301964116805545194017.P67
355 (5,71) 121932688511.P73
357 (3,7,17,21,51,119) 4999.245262248913715001137177.P31
359 719.855857.778165529.65877330027880703.
.370906580744492785430299503112990447.P39
361 (19) 9522401530937.36450568206770608791178096385783.P59
363 (3,11,33,121) 8713.7593961.75824014993.P45
365 (5,73) 8761.13828603741081.82595052745831.P56
367 12479.51791041.78138581882953.301311116540899114446723859201.P56
369 (3,9,41,123) 6376386802464073.P57
371 (7,53) 743.2969.63781899287.204712366597949333831.P57
373 25569151.P105
375 (3,5,15,25,75,125) 751.P58
377 (13,29) 5279.148055441.359661017.P81
379 180818808679.P103
381 (3,127) 2287.15241.349759.P63
383 1440847.7435494593.503823044204581129045587727.
.15174923558680812616818436353130417.P39
385 (5,7,11,35,55,77) 55441.1971764055031.P56
387 (3,9,43,129) 11492353.22763003975641.6834040335349578249140287.P31
389 56478911.4765678679.P100
391 (17,23) 37537.25806248225716242845491832244899635927231330561.P55
393 (3,131) 36093121.51118297.58352641.P55
395 (5,79) 12641.5435488351.16203007441.P70
397 2383.6353.50023.53993.202471.5877983.
.814132872808522587940886856743.1234904213576000272542841146073.P31
399 (3,7,19,21,57,133) 73417.83791.P56
401 856971565399.2136958965524920285681.
.594538100848945223169882301931953.P55
403 (13,31) 45137.8532838289.P94
405 (3,5,9,15,27,45,81,135) 537841.11096527935003481.P44
407 (11,37) 3257.3068001817.1826375940722234754636475033.P68
409 4480666067023.76025626689833.P97
411 (3,137) 823.27261904199932321.647923469936355993348337.P39
413 (7,59) 2006647231.6774027833473375976915021445395839.P62
415 (5,83) 470933694191.3028917598961.130666175908831.
.32367218471375835379289471.P35
417 (3,139) 7606017793609.P70
419 839.903780021613921.5800422716722833271214743.
.10287968884341772230096159036619433593.P47
421 614002928307599.P112
423 (3,9,47,141) 1617189999730415801728461273583.P53
425 (5,17,25,85) P97
427 (7,61) 33282089.P101
429 (3,11,13,33,39,143) 17286204937.1065107717756542892882802586807.P33
431 863.3449.36238481.76859369.558062249.4642152737.
.142850312799017452169.P70
433 22086765417396827057.737748363812546584876297.
.5028667832511715101284999.P63
435 (3,5,15,29,87,145) 256582225885581001782477601.P42
437 (19,23) 3198841.5579617.6203145044672921.P90
439 104110607.127321491658223.122551752733003055543.P90
441 (3,7,9,21,49,63,147) 126127.309583.5828257.4487533753346305838985313.P34
443 887.207818990653657.P117
445 (5,89) 2671.1460384540571001412284141831845453026637206635511.P55
447 (3,149) P89
449 1256303.6871197486841.3578620616468306981503.
.526385733768051189441947168504909159.P59
451 (11,41) 18041.216481.9718704501529.538939720215834697.P80
453 (3,151) 790468905817.P79
455 (5,7,13,35,65,91) 200201.P82
457 150327409.P130
459 (3,9,17,27,51,153) 407770693450231393.24418671951944649151.P50
461 2767.358228856441770927.7099353734763245383.P99
463 11113.3407681.448747600991881.239932071009857681156251129.
.385606580062688087218266143.P62
465 (3,5,15,31,93,155) 2791.103231.P65
467 121606801.1148984537885906196977362003686090739460725564747973734847.P76
469 (7,67) 70321958644800017.1839633098314450447.P84
471 (3,157) P94
473 (11,43) 12853303.133139883512681.4193551379485561391.
.1703616691469833244854254847.P60
475 (5,19,25,95) 4751.18020551.1369738735713888876695951.
.113709467433878120743807151.P48
477 (3,9,53,159) 94447.4879711.242003089.P74
479 33385343.6293443049.
.683481445118041278287416124073722711169070307627777892361.P71
481 (13,37) 138724733805016586033.5800976318060644948970424014255729.P76
483 (3,7,21,23,69,161) 967.18423553.172384633.1186694555374004016103.P41
485 (5,97) 10084875238121.34224064338126003049783351.
.6424414731245950286450458211761.P46
487 4871.P143
489 (3,163) 836191.355307401.116539854237679.619079222361672204943.P48
491 983.7707719.110097436327057.6976447052525718623.
.19970905118623195851890562673.3717542676439779473786876643915388439.P41
493 (17,29) 3616649.10353001.P121
495 (3,5,9,11,15,33,45,55,99,165) 991.334202934764737951438594746151.P40
497 (7,71) 6959.254461617383.P111
499 20959.1998447222711143545931606352264121.P113
501 (3,167) 25129004796912072003423103.P75
503 3213684984979279.12158987054135300783.1873030665061080894263.P96
505 (5,101) 1906785849099933631.P102
507 (3,13,39,169) P94
509 12619129.19089479845124902223.647125715643884876759057.P104
511 (7,73) 15212471.
.144780974187086260903935034761413745643636578290924150417.P67
513 (3,9,19,27,57,171) 57457.35473416481.121323854647.2237717449946593.P56
515 (5,103) 1031.989831.960954217134424245898328814050043401.P78
517 (11,47) 82721.387348809.1292800939332382943.
.270374114136830957955241.26302895729179572365768002599674239.P49
519 (3,173) 1039.P101
521 P157
523 160188778313202118610543685368878688932828701136501444932217468039063.P90
525 (3,5,7,15,21,25,35,75,105,175) 4201.7351.181165951.P57
527 (17,31) 13306086595097866632236752730067629415649399.
.50061214622509969230528187280149191683596667776057.P52
529 (23) 54999142147740840245669969.347916608026315949237260151.
.9114901722266383629807574332217258944092868367.P55
531 (3,9,59,177) 1063.288236359.196629322303.15888898944343.
.8099559410464120708848563721343.P38
533 (13,41) 166297.744487658617.P128
535 (5,107) 12841.95231.879622391.331343920853356078376431.
.23718232032401560617445166686464799001.P49
537 (3,179) 4297.16111.196543.P94
539 (7,11,49,77) 234341789260493933662402728271919.P95
541 4312790327.6115209994009.77146448294831869472151022106713.
.904106555381898703253733254107256591.P73
543 (3,181) 1087.534955385319592511227419175872576025063351.P64
545 (5,109) 3271.213641.18109412991311.2511696210834096991.
.7647513170903349335637401.P65
547 5471.172720604638150729.157552196128597543991.P124
549 (3,9,61,183) 38431.1386525709821079.P89
551 (19,29) 4409.14327.27551.P140
553 (7,79) 166153042787383.P127
555 (3,5,15,37,111,185) 27751.P83
557 3343.21993703.4565508951414453792719.
.22053236096920219270632521586535711.P101
559 (13,43) 3180000071.9215285895065526291256518741915902569.P105
561 (3,11,17,33,51,187) 146983.2009643799642447.P77
563 2815747080256641401887817.13299213974872825932452460424235657.P111
565 (5,113) 185318160171793066961.29444549303703754611026537050435001.P80
567 (3,7,9,21,27,63,81,189) P98
569 15854617.55470673.182602768015690099110572536951.
.110582329556343704552404016904356632250881.P87
571 5711.27409.6969336604531667168509871230100794095801832527002849548226132675916172927.P91
573 (3,191) 32788207.P107
575 (5,23,25,115) 1151.13220653410551.P117
577 3463.132305774316967.P157
579 (3,193) P116
581 (7,83) 798037199.175908273685537.
.15444711420006203351165170879848557117713.P85
583 (11,53) 755569.65780528969.106077807287.P129
585 (3,5,9,13,15,39,45,65,117,195) 2400314671.339175003117573351.
.255375215316698521591.P40
587 554129.2926783.39483330766889.73208283304744901303.
.3728298863422039632638351.P107
589 (19,31) 18083479.36064471.
.2023706519999643990585239115064336980154410119.P103
591 (3,197) 407791.50070703.304292056417.P93
593 104369.3061144307110551703729.
.4027016481761119763553952463965455549881.P113
595 (5,7,17,35,85,119) 34511.199921.69935987114957671.P90
597 (3,199) 5066143.1445406523039.P101
599 16659379034607403556537.
.148296291984475077955727317447564721950969097.P114
601 3607.64863527.
.643390760896826272806925563059612685509039265031067456849993.P110
603 (3,9,67,201) 648168721774409511378116151410898673195879.P78
605 (5,11,55,121) 3631.143448045841.P118
607 P183
609 (3,7,21,29,87,203) 15109165329245515231985834925494692879.P65
611 (13,47) 1223.1609655415875897360904371080437164611501156560743.P115
613 44599476833089207.332817722770314187794325446534549089.P133
615 (3,5,15,41,123,205) 1231.49201.92757531554705041.
.3427007094604641668368081.P48
617 59233.68954123297.
.157751978115225385495647532421006478127229405644601.P120
619 110183.710820995447.
.109378681671075297195692480234213908123642560192251038455204252439.P105
621 (3,9,23,27,69,207) 624456487.93747988411543.P97
623 (7,89) 74383430474532481.
.74716964067758844321661890925503011337830328521.P95
625 (5,25,125) 1277297679372570001.573759820507018639639785001.
.18152902839291497575027462639977160832701118299213751.P54
627 (3,11,19,33,57,209) 11287.12471031.89856878697433.
.8778523027466598416204656058467252273.P47
629 (17,37) 45470534643405479586527115047619453123209.
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631 333628015107245479.474640860193534882628078580680807822523991.P131
633 (3,211) 2399291551.17689153588009.60560850681938908875991.
.9970146666059203361408046051199.P50
635 (5,127) 5081.
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637 (7,13,49,91) 3823.15289.31945881241.153925026222241.8573192048327176271.
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639 (3,9,71,213) 1279.84462210560148142953097.
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641 35897.49999.1173835097.2401258891949526685926151441.745276300734440606226386924312213175677903182797334854064486587296999.P79
643 3189281.22532429052605670225026391054393428833168207234802434915090881303620353.P117
645 (3,5,15,43,129,215) 46441.4175568751.1728221461577944661374351.
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647 303303806129303896428103.11502383762931955619183430785983.P141
649 (11,59) 649001.23952086159.34418203155300430111979265857.P130
651 (3,7,21,31,93,217) 1303.1191622782866437328993110351.P79
653 78557207.289837969.16008527538753578495897.
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655 (5,131) 597361.2576754528566814601.351182936972570824983481.
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657 (3,9,73,219) 73*.10178663167.27265714183.5271393791658529.
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659 1319.11527429277532648241.626564962613678012662146877852049.P144
661 1330270433.3370159489168519.1009157848082361225065617.
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663 (3,13,17,39,51,221) 47737.
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665 (5,7,19,35,95,133) 161517058694951.P117
667 (23,29) 12007.458897.88039999.246270735864387271375789289856617.
.14508653262991734676225669411020750337.P98
669 (3,223) 182224921317852297530287.P111
671 (11,61) 116356769.33491655209.64110547427930873.
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673 581163767.41283139633378645724930694480520226273492263.
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675 (3,5,9,15,25,27,45,75,135,225) 1605151.
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677 1943118631.531132717139346021081.978146583988637765536217.
.53625112691923843508117942311516428173021903300344567.P98
679 (7,97) 6791.59753.93703.
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681 (3,227) 962744903648208108713898832235090314894033.P94
683 1367.434836499112609694795723958417048861299768144283442662402095922180462812746769.P125
685 (5,137) 119191.7084271.83648644144524510111773141111.P123
687 (3,229) 6871.2104809991.175932323679511304414371921.P98
689 (13,53) 135995976143.1067583682127.
.1372617429248257063179636119999552844862152089.P120
691 906642603313.10488160032325844521.2833637724427940664433391497.
.16636201944470267267182958207.P122
693 (3,7,9,11,21,33,63,77,99,231) 289511839.2868251407519807.P85
695 (5,139) 3452778071.3578189431.225797717267637708506527464987314161.
.901584692755427378722839770656354167189649601351.P64
697 (17,41) 16729.P189
699 (3,233) 1401190779823.1917765426328344646895407.
.23482447257772948338207752516264041.P69
701 796337.2983457.28812503.1073825104511.9983923992673.
.15865578195367.40686928318417.P140
703 (19,37) 35284030283053759.1294046302848776287.11931812674076681849.
.167823649475113693461122232089506777.
.59588714597816906383348767955828416209.P69
705 (3,5,15,47,141,235) 157925605323676378629391.P88
707 (7,101) 126729751.128782811543.700553271665826444242790841.
.3598194408030741269333601460682311.
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709 216868921.1391646221255097953.P187
711 (3,9,79,237) 5689.41851365145831.864328108984548257763049805767.
.19573690271784800408214873038427972853220421889.P48
713 (23,31) 68449.335203548019575991076297.
.25302796036126213353739363322307560110912714814142460639.P115
715 (5,11,13,55,65,143) 249602191565465311.598887853030285391.P110
717 (3,239) 40153.12417007.58392032593.55009358369431.
.199987538790826996082414586220862745720625115339053303.P54
719 1439.772207.737572843389436536903316910033561929012829990389769.P157
721 (7,103) 10550281065119153.P168
723 (3,241) 1447.7480159.102072660983478595344638863.P109
725 (5,25,29,145) 448477751.245573800535260692993906074551.
.177457540153273192963355393450351.
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727 17606291711815434037934881872331611670777491166445300472749449436575622328171096762265466521858927.P122
729 (3,9,27,81,243) 80191.97687.379081.
.664728004346558283448724389870269691211809.P90
731 (17,43) 67872792749091946529.
.223192283824457474300157944531480362369858813007.P135
733 694653525743.14399141148866077141941966959399761.
.13948432601001273785699253868326270649.P138
735 (3,5,7,15,21,35,49,105,147,245) 41161.4163041.20147473081.
.2340389488711.27653710336343911.P51
737 (11,67) 4423.12148690313.5157050159173695487.17904041241938148871927.
.1963672214729590922916323781834466879.P108
739 184603056517613273120809.48050683584092004380805463790111.
.2561503388753170490897052206621137620938856555180343258504238260072282185111994663.P87
741 (3,13,19,39,57,247) 83352127.2665675660861389884202429169.P95
743 1487.1219280833.14904366017.118722715461092305629361.
.4721525455401597740684262559.
.4977047949106985392753791512048265888682003683833.P102
745 (5,149) P178
747 (3,9,83,249) 324965201690131831.P131
749 (7,107) 46439.120618551047.227444841245238451591.
.963644196044828188869351734353847.
.4143416085716681490838653625856664863812512904964849.P71
751 227640245125324450927745881868402667694620457976381782672549806487.
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753 (3,251) 4519.12049.220116640729.180797717027593.P117
755 (5,151) 1511.15073467791.286621334502631.P153
757 9815263.561595591.5722137022002067824248227975095857749151312827809388406962346253182128916964593.P134
759 (3,11,23,33,69,253) 1633369.46025761.P119
761 4567.6089.738686421813192728921171408273447.280230266918608239805810556544655376723809198780890337110755962385407.P121
763 (7,109) 2092087318645654859663614111006024142702357805153449558384836836073.P129
765 (3,5,9,15,17,45,51,85,153,255) 16831.3696481.2109936092650831.
.24710462787135943791475548268920478656481.P50
767 (13,59) 38351.297205245433279.6616963204951529.6329588309789019577199.
.756450142211646020278834399577.714106625397559765944265428336645929.P87
769 1591805393.6123566623856435977170641.P198
771 (3,257) 1543.P151
773 6864241.9461521.1165626988664823792549971253972697.
.101625278121114813541046756104385520302531369.
.3102804258869848876949115800490112967822146918598407.P91
775 (5,25,31,155) 3064351.2168815801.1113614148551.P153
777 (3,7,21,37,111,259) 4663.6433561.4750535347861726648681.
.96786396648673403672115546439.P70
779 (19,41) 1559.3142487.21726311.104003232119.164597693569197241.
.202664437974567925010435751833.
.539043252861508730639718553683237826728217905315243065969.P86
781 (11,71) 6511616671913.66232837958133438967.79034734517219615663.
.370549646190282993458807249710605687589893787382049438311221836912017.P90
783 (3,9,27,29,87,261) 1567.602999957032279571271592229136193.
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785 (5,157) 5393364481.135732250385154376731523201.
.2167731870412324810536209829271.
.14488318273595902692706536553684238317387680182551817911.P67
787 9951597611230279.96512008100928793. C204
789 (3,263) 5609685181351.274473195338134592222791.585608533119706764820561.
.748093847626791888666559.20389292512407050043445124186439967.P40
791 (7,113) 1583.7920714887.2549280727345379556480596752292189634269829765250993670402549042422649.P120
793 (13,61) 4759.31721.145211798447.579981948313.557462996944863661915154471811685102632550568013283044249936559839102852607.P111
795 (3,5,15,53,159,265) P126
797 2006858753.54573369937.104757762864135516671.
.747609928190821086986322983.21023711323746974956423747989180911.
.2896793131110864597734842177399739433374955784567182457.P85
799 (17,47) 2957111053582540504996549489605401. C188
801 (3,9,89,267) 3344977.16960539007.1790799748670521.
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803 (11,73) 1607.78366377.1384018681.1533745237729.
.2762339998302448893880313142073.P154
805 (5,7,23,35,115,161) 13816619111.
.368807221314046570921624935038049174011736160751.P102
807 (3,269) 2771239.502502761.P146
809 4148386731260605647525186547488842396461625774241327567978137.P183
811 326023.
.120561845344829717145833822890964664477289164454661659494292322521.
.23119812387308695110542195466723573149999671437304578090473901521408187760986228863.P92
813 (3,271) 24391.2248759.36936217.152948738791.49322756803485314471713.P111
815 (5,163) 180883807440027655212532885072379634915469957001205875201.
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817 (19,43) 81278478804329.1527890378338261467896809.
.503836749763922905688176944079261201.
.7911922734932819371233930194607936241219971448463.P105
819 (3,7,9,13,21,39,63,91,117,273) 2681001528674743.
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821 419273207.109840721427977.286121480219517473. C208
823 1460915248436556406607.1534086200463688788034864584049. C197
825 (3,5,11,15,25,33,55,75,165,275) 702948566745151.9115784422509601.
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827 66161.1637241673.1656489332706171370072190422631.
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829 72953.89654239955972104838901500177.P216
831 (3,277) 1663.3772542223.502746492223.660284006953.679758314119.P118
833 (7,17,49,119) 14821647473599.2394594520709878135254356190088519028761.
.794769178865803830796254438307018567389833.
.16248173432447880508878672460681334430321473.P65
835 (5,167) 18144551.44596548025921.819048171793389082617855311.P152
837 (3,9,27,31,93,279) 1127316245518063.P148
839 26849.138561000316919.377801626929390823.
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841 (29) C245
843 (3,281) 1390916281.2475486361.P150
845 (5,13,65,169) 4493034001.53928095661079461754990292241379839311.P141
847 (7,11,77,121) 42262784685026262370553.P177
849 (3,283) 18679.147727.353712117583777.29940168528270618887118001.P121
851 (23,37) 1530328553290391228929969.11862938913865507127049391.P189
853 2065711807.513740645819473.4727997228805279065233. C212
855 (3,5,9,15,19,45,57,95,171,285) 709018264240844065111.
.158362232618940822526398920291451047671.P72
857 6857. C255
859 7215601.13183242101527799620391251382520507315529510625017. C203
861 (3,7,21,41,123,287) 5167.
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863 8258911.169382737.175642891399. C234
865 (5,173) 526769431.P199
867 (3,17,51,289) 5266159.P158
869 (11,79) 361592639.239506881856626095535121.P203
871 (13,67) 15679.95860519.12708237958354187384010097.
.791926693391795441127294795391450663.
.137403482726882442386895575645854007713.P127
873 (3,9,97,291) 132697.9449353.7969524463.P152
875 (5,7,25,35,125,175) 725688486718330087751.P160
877 35081.1436527.1839699736969340949026772071177.
.4478527345975241075738524755872079528958635991.C178
879 (3,293) 1759.288313.142891999.4010077111.12760970401.
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881 26431.P261
883 8831.63577.258777491057348926546569104663.P228
885 (3,5,15,59,177,295) 2756788662198217256191.P119
887 16173559.139714099995626040378049.2382154297313396649423300881. C210
889 (7,127) 127*.P226
891 (3,9,11,27,33,81,99,297) 1783.12430037668834128259094186647.P132
893 (19,47) 6705767506519.
.1542338292002409373550628606652924602059467660039183.P185
895 (5,179) 21481.6917353530526492681.78961972629651529859281.
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.1696067654151459074824290253436397570222341162468471.P73
897 (3,13,23,39,69,299) P160
899 (29,31) 460289.110521633444549751.
.796968797719178740820037379973406834314737633.C185
901 (17,53) 114684958103.5033986097724889062887.P218
903 (3,7,21,43,129,301) 514711.P147
905 (5,181) 121271.1163487911.
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907 1170031.3256645177.131895016205024767.P241
909 (3,9,101,303) P181
911 1823.26129303.201955048939840841121786425435009.P232
913 (11,83) 35913067887863. C233
915 (3,5,15,61,183,305) 360511.95805951836468022966692945378791.
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917 (7,131) 5503.229268017217.57193908443040877545241.
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919 33554520197234177. C261
921 (3,307) 85724839.1240718764955671.7718960266212068280249289.P137
923 (13,71) 1847.5619297841. C240
925 (5,25,37,185) 27281951.86759605608601233853529454601.P181
927 (3,9,103,309) 46351.2033839.22229194879.312842300671.
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929 13007.340388595097.
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931 (7,19,49,133) 14897.67033.4768748142197177447.P200
933 (3,311) 37321.13129750729.188999403857128746828420806061841.
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935 (5,11,17,55,85,187) 1871.3706347481. C181
937 28111.2419437071. C269
939 (3,313) 1879.995114641.147859967407.
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941 7529. C280
943 (23,41) 9431.39607.21698431.62209711.138325941036565103.
.9280993516297855054039457.57644473457648767005697802783.P171
945 (3,5,7,9,15,21,27,35,45,63,105,135,189,315)
124339521078546949914304521499392241.P95
947 295130657.25749931927.4621646208862937.
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949 (13,73) 22777.78341849.427960745238703.705900082312653909721.
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951 (3,317) 241459659973825303567826493454039.
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953 343081.562070136841.40496650491842199555367.
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957 (3,11,29,33,87,319) 1609806083534335902079374125310994612192903.
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959 (7,137) 23017.531287.12959927.12966664479880063. C213
961 (31) 280651416271709745866686729. C254
963 (3,9,107,321) 14662639.4697382335699080991160439732748977071469258244120906774840307806403019635933401543777637481.P94
965 (5,193) 2184761.204948631.86710817849281.44894058474254631045721.P180
967 23209.549257.1438495818172960049.
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969 (3,17,19,51,57,323) 11726744977.540538609159.
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971 23917104973173909566916321016011885041962486321502513.P240
973 (7,139) 2356070859382001284653313.2166176541500493808960173319. C198
975 (3,5,13,15,25,39,65,75,195,325) 1951.8837728285481551.
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977 867577.1813313.2069655374719577273.49858990580788843054012690078841.C232
979 (11,89) 89*.13815649.7883576248112389199.P237
981 (3,9,109,327) 10341703.499601719.9727892263.128014683020611040553769.
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983 1808226257914551209964473260866417929207023.P254
985 (5,197) 70921.7263391.73518775918537446144887630711. C196
987 (3,7,21,47,141,329) 9585228595374769.512512927677384344303149537.P124
989 (23,43) 31649.36706221574691349767448834021945679.
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991 8218291649.41473350001.231620367206687. C264
993 (3,331) 23833.55609.857491387188810516016046647.
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995 (5,199) 14369791.41735340671.114443156761.
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997 167560816514084819488737767976263150405095191554732902607.P244
999 (3,9,27,37,111,333) 7993.473589937.
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1001 (7,11,13,77,91,143) 6007.6952744694636960851412179090394909207.
.20200567342579527631370455849751729349809657695513.P128
1003 (17,59) 605829388649921.1629239097907113911209.
.2252765682876603539639635308408558411526609.P201
1005 (3,5,15,67,201,335) 68626625145959029951.
.663636889167401354279502795531186216903001.P98
1007 (19,53) 37430191.183802578728708044103. C254
1009 3454817.198582684439.20649907789079.21624641697047.
.30850253615723594284324529.1134327302421596486779379019599.C204
1011 (3,337) 39147943.6853410184776097.P179
1013 6079.71486759597273. C288
1015 (5,7,29,35,145,203) 2154593281.P194
1017 (3,9,113,339) 54919.72386347544037768298632733630815274606848381343.P151
1019 2039.75407.82433230679411141627745147311847388925656728692144689. C246
1021 40841.795808241.51731968308257.
.1866013803867738316856548085894075729799351216503.P232
1023 (3,11,31,33,93,341) 105586579766713.
.91979404475310284038389763276277647.P132
1025 (5,25,41,205) 6151.2252951.2721217151.1330118582061732221401.
.12477521332302115738661504201.519724488223771351357906674152638351.
.177900025086275986080877620282066695098333349981977325551662127751.P72
1027 (13,79) 452599156086559.17560235101945245417825001.
.67545455787839926022098207.C216
1029 (3,7,21,49,147,343) 7*.6896727944023.2714819157586383751.
.3274162442129276091367.
.5878920553871871291270984955318098156844648537.P78
1031 2063.435502649. C299
1033 196271.36913223.88910338973359434076776038119074340716281.
.163771629900828769671363963472861890953631838273.P210
1035 (3,5,9,15,23,45,69,115,207,345) 19616702141919323129388715950912065791.
.647463932206559821122945033207524451183068970139360141681.P65
1037 (17,61) C289
1039 5080711.55853666619936291260749204658315944968646527018488637648010052346319853288374753.P227
1041 (3,347) 24769991104728312891937.P186
1043 (7,149) 2087.100129.3256247.7346919119. C243
1045 (5,11,19,55,95,209) 6271.5972377728166033731379524138706997651075303681.
.2591359432094537078074951131139791193021859439188185801.P114
1047 (3,349) 18063321433.P200
1049 33569.459463.1059099980653317121.P288
1051 3575503. C310
1053 (3,9,13,27,39,81,117,351) 44207047.24295813738965169951447.P166
1055 (5,211) 2111.29257554834707791.
.22798505814116334119485271455401054495620094271.
.307289980970606234686867138691001349037525535679593763081.P130
1057 (7,151) 5318798633.117801297041.6645418768842321985721.P229
1059 (3,353) 18861552481.
.4067055143413119297753219773293999460854231105692799.C150
1061 C320
1063 1485761479.P311
1065 (3,5,15,71,213,355) 14139262262808175798602566204793985440361.
.6252200505559391265660834611730277041893919359311.P80
1067 (11,97) 4884727.32805679003831689475103. C260
1069 17481727674576239. C306
1071 (3,7,9,17,21,51,63,119,153,357) 10711.861229657.52877551231.
.91005071977.5880734007124467829187484937.
.2044333418084691639917563561172180103378559.P69
1073 (29,37) 44197213979727234355841. C281
1075 (5,25,43,215) 4718966201.P244
1077 (3,359) 247711.13759551679.P200
1079 (13,83) 417042099631.1104547173371974879.1234944495181377943.
.112521450818457950210174975426777.C217
1081 (23,47) 47*.3137063.2756059353782849.1248432852603561685630837661279.C251
1083 (3,19,57,361) 14107651849.
.5473015810417967216563512902910681466781133103.
.140183614482450346632384931984512181340021597814186079.P97
1085 (5,7,31,35,155,217) 217001.553351.105254261561.319268480441.P184
1087 10722169.2144921195591.33990250708335239.2105485879475562449.
.421733524843190780249388261839156579767.
.23864222009193938317456687011256092421563991.C192
1089 (3,9,11,33,99,121,363) 141641296831.27306046411338223. C172
1091 87281.551978359.791343585595817.97535130364653673535422113471207017.
.496474000537225566899310934393330825097522839.P221
1093 43721.111487.42565880168703357316051447. C294
1095 (3,5,15,73,219,365) 702595801.
.12687370311710932103729819887748340216531751.P122
1097 980719.4666639.22926719175799.1734492765338661710171833.
.36079584237927411511333522577.205295973898620029528272537868263.P220
1099 (7,157) 11302318217.28617130498420804403756708531447.P240
1101 (3,367) 79273.258977744356523549983.883533090360873723903538281367.P165
1103 2207.4126110275598714647074087.P305
1105 (5,13,17,65,85,221) 7555991.115812024214750631.
.155137816977180947152785562601502526330318743274151.C158
1107 (3,9,27,41,123,369) 7675195491326802969559.472897006006202784083089.P172
1109 30963501968569.85608965982066833903. C301
1111 (11,101) 457892136759270759480793. C278
1113 (3,7,21,53,159,371) 15583.51199.2363026390394916673046830675466863.P146
1115 (5,223) C268
1117 53617. C332
1119 (3,373) 2239.20143.154565233.1100558881.P199
1121 (19,59) 8969.P311
1123 777288435261989969. C321
1125 (3,5,9,15,25,45,75,125,225,375) 213751.150212580033138336342001.
.51833645300329496308097759409726604605029168907048343297938001.P91
1127 (7,23,49,161) C279
1129 33871.833798113. C327
1131 (3,13,29,39,87,377) 1973833390189373292099390923614168779294442399.P158
1133 (11,103) 29237863091999.49785726347323441303511.
.2468805350190760992979935216750635087.C235
1135 (5,227) 132839238602148428191.4503031418785283725652516551. C225
1137 (3,379) 3289098531153894127.
.688979143570616582830070781662622819187353601.C164
1139 (17,67) 138959. C313
1141 (7,163) 301230847.16742221609.14493503199673.628007894034529.
.131380422697420095809.875938090182754292028329.
.106014123028829664722111227465753.P170
1143 (3,9,127,381) 518814559.100342091647341370469161844713.P190
1145 (5,229) 4946401.199439000998738772588908077106387241.
.14555351154393199486009895146040017633961311.P190
1147 (31,37) 100937.9245269025364933413947751633.
.141807120921029844210677840999.C263
1149 (3,383) 2651552381122661167.12917254515820483569633735619111. C181
1151 284278475807.81344898763887260484533897.658622107254745112979229913.
.39146265717288735265327499826695585290297.C242
1153 267497.84755607199. C331
1155 (3,5,7,11,15,21,33,35,55,77,105,165,231,385) 2311.6250631311.
.494224324441.P120
1157 (13,89) 1675125010930879.5519267814834477438497153.
.8835538898098695059049137.15472078121378442801745561.
.7616038569790289017964814010721823388947821809.C182
1159 (19,61) 185441.56256385753. C309
1161 (3,9,27,43,129,387) 6967.5979151.60499150497847. C204
1163 848181715001.337097300570078978047. C318
1165 (5,233) 365106542520646053873234125869250449257912961.P235
1167 (3,389) 60459128773735346116971161647. C205
1169 (7,167) 514361.6020351.7322617.8932786385279.P268
1171 153606920351. C342
1173 (3,17,23,51,69,391) 428417137.18228580446571609.403906782348344599.
.515878737178649880676177.
.920854434270162822283216457951519800254804780099567201431071.P86
1175 (5,25,47,235) 10009431316533167951.1094883804311836270751.
.5170712852551602215753262223559516152087046351.C192
1177 (11,107) 3775817.5960329. C306
1179 (3,9,131,393) 28297.10909426047235017667998633478885601105094202777.P185
1181 4742897.196834168670106625096599487.
.199668911054466914791190422986407.C291
1183 (7,13,91,169) 28393.46655969015605951. C261
1185 (3,5,15,79,237,395) 115150116391.21792652855138681.P161
1187 256393.113603023.1761533117965696212626325049982897.
.766302834531296176581826196660125454171041129.C266
1189 (29,41) 600619547820455607135590639621491727.
.10276876497295959142374278224747317922211821032760703.P250
1191 (3,397) 274404635931475033688839.10712613085162141902489577. C190
1193 121687. C355
1195 (5,239) 270071.10602041.150885481.502862692004168161.
.4925687525543853241.2004186363732465633272613168051655374493121.P187
1197 (3,7,9,19,21,57,63,133,171,399)
122899168808744663588141025320026245511852609957212433417.
.68539098502476500342849178765232476276974878815092900810113.P81
1199 (11,109) 2399.174181129. C314
Table 2{+}(odd) Factorizations of 2^n+1, n odd, n<1200
n Prime Factors
1 3
3 (1) 3*
5 (1) 11
7 (1) 43
9 (1,3) 3*.19
11 (1) 683
13 (1) 2731
15 (1,3,5) 331
17 (1) 43691
19 (1) 174763
21 (1,3,7) 5419
23 (1) 2796203
25 (1,5) 251.4051
27 (1,3,9) 3*.87211
29 (1) 59.3033169
31 (1) 715827883
33 (1,3,11) 67.20857
35 (1,5,7) 281.86171
37 (1) 1777.25781083
39 (1,3,13) 22366891
41 (1) 83.8831418697
43 (1) 2932031007403
45 (1,3,5,9,15) 18837001
47 (1) 283.165768537521
49 (1,7) 4363953127297
51 (1,3,17) 307.2857.6529
53 (1) 107.28059810762433
55 (1,5,11) 11*.2971.48912491
57 (1,3,19) 571.160465489
59 (1) 2833.37171.1824726041
61 (1) 768614336404564651
63 (1,3,7,9,21) 77158673929
65 (1,5,13) 131.409891.7623851
67 (1) 7327657.6713103182899
69 (1,3,23) 139.168749965921
71 (1) 56409643.13952598148481
73 (1) 1753.1795918038741070627
75 (1,3,5,15,25) 1133836730401
77 (1,7,11) 617.78233.35532364099
79 (1) 201487636602438195784363
81 (1,3,9,27) 3*.163.135433.272010961
83 (1) 499.1163.2657.155377.13455809771
85 (1,5,17) 26831423036065352611
87 (1,3,29) 96076791871613611
89 (1) 179.62020897.18584774046020617
91 (1,7,13) 224771.1210483.25829691707
93 (1,3,31) 529510939.2903110321
95 (1,5,19) 2281.3011347479614249131
97 (1) 971.1553.31817.1100876018364883721
99 (1,3,9,11,33) 5347.242099935645987
101 (1) 845100400152152934331135470251
103 (1) 415141630193.8142767081771726171
105 (1,3,5,7,15,21,35) 211.664441.1564921
107 (1) 643.84115747449047881488635567801
109 (1) 104124649.2077756847362348863128179
111 (1,3,37) 3331.17539.107775231312019
113 (1) 227.48817.636190001.491003369344660409
115 (1,5,23) 691.1884103651.345767385170491
117 (1,3,9,13,39) 5302306226370307681801
119 (1,7,17) 823679683.143162553165560959297
121 (1,11) 117371.11054184582797800455736061107
123 (1,3,41) 739.165313.13194317913029593
125 (1,5,25) 229668251.5519485418336288303251
127 (1) 56713727820156410577229101238628035243
129 (1,3,43) 1033.1591582393.15686603697451
131 (1) 1049.4744297.182331128681207781784391813611
133 (1,7,19) 4523.106788290443848295284382097033
135 (1,3,5,9,15,27,45) 811.15121.385838642647891
137 (1) 1097.15619.32127963626435681.105498212027592977
139 (1) 4506937.51542639524661795300074174250365699
141 (1,3,47) 1681003.35273039401.111349165273
143 (1,11,13) 2003.6156182033.10425285443.15500487753323
145 (1,5,29) 7553921.999802854724715300883845411
147 (1,3,7,21,49) 748819.26032885845392093851
149 (1) 1193.650833.38369587.7984559573504259856359124657
151 (1) 18717738334417.50834050824100779677306460621499
153 (1,3,9,17,51) 123931.26159806891.27439122228481
155 (1,5,31) 11161.5947603221397891.29126056043168521
157 (1) 15073.2350291.17751783757817897.96833299198971305921
159 (1,3,53) 6043.4475130366518102084427698737
161 (1,7,23) 8103467492759792327149800361564410265219
163 (1) 11281292593.1023398150341859.337570547050390415041769
165 (1,3,5,11,15,33,55) 415365721.2252127523412251
167 (1) 62357403192785191176690552862561408838653121833643
169 (1,13) 4929910764223610387.18526238646011086732742614043
171 (1,3,9,19,57) 19*.19177458387940268116349766612211
173 (1) 347.4153.35374479827.47635010587.1643464247728189221623609
175 (1,5,7,25,35) 1051.110251.347833278451.34010032331525251
177 (1,3,59) 13099.4453762543897.1898685496465999273
179 (1) 58745093521.4347868190665879373495950562775707707143803
181 (1) 1811.31675363.17810163630112624579342811733978085990447907
183 (1,3,61) 1772303994379887829769795077302561451
185 (1,5,37) 1481.28136651.778429365397887608540618330873281
187 (1,11,17) 2191165825376888084750157716424579062015865776131
189 (1,3,7,9,21,27,63) 379.119827.127391413339.56202143607667
191 (1) 1046183622564446793972631570534611069350392574077339085483
193 (1) 6563.35679139.1871670769.7455099975844049.1280761337388845898643
195 (1,3,5,13,15,39,65) 107251.571403921126076957182161
197 (1) 197002597249.1348959352853811313.251951573867253012259144010843
199 (1) 267823007376498379256993682056860433753700498963798805883563
201 (1,3,67) 2011.9649.6324667.59151549118532676874448563
203 (1,7,29) 596834617.3692022713.252715814615565962418688965855731
205 (1,5,41) 2125820563389437533390243893834597846757304863651
207 (1,3,9,23,69) 6113142872404227834840443898241613032969
209 (1,11,19) 419.3410623284654639440707.1607792018780394024095514317003
211 (1) 4643.9878177.5344743097.199061567251.22481127512575175864234185190299
213 (1,3,71) 5113.17467.102241.203525545766301306933226271929
215 (1,5,43) 9084611.59904608378705661377430182608711698924130721
217 (1,7,31) 16233337.140508608590164280225934233098866842745808905947
219 (1,3,73) 9070197542196643.3278244690156222434135906137
221 (1,13,17) 443.4714692062809.4507513575406446515845401458366741487526913
223 (1) 219256122131.20493495920905043950407650450918171260318303154708405513
225 (1,3,5,9,15,25,45,75) 4714696801.281941472953710177758647201
227 (1) 297371.3454631579714210387.P44
229 (1) 18754643.P62
231 (1,3,7,11,21,33,77) 14323.P32
233 (1) 467.27961.P63
235 (1,5,47) 328006342451.461797907949997211.P27
237 (1,3,79) 647011.13664473.P35
239 (1) 340337.32605142983704221670173899.P41
241 (1) 2411.10411181203.15059828108442641.P43
243 (1,3,9,27,81) 3*.1459.139483.10429407431911334611.918125051602568899753
245 (1,5,7,35,49) 491.15162868758218274451.P29
247 (1,13,19) 207481.10049443.355011619.P45
249 (1,3,83) 9202419446683.P37
251 (1) 238451.P70
253 (1,11,23) 4049.85009.31797547.81776791273.P40
255 (1,3,5,15,17,51,85) 12241.418562986357561.51366149455494753931
257 (1) 37239639534523.518144156602508243009.P43
259 (1,7,37) 1456235596904319041738812533139.P36
261 (1,3,9,29,87) 523.6929826139.3453412901832690553.33563856450515702761
263 (1) 1579.92051.29261114397558193.P55
265 (1,5,53) 593783678966863030035641.P40
267 (1,3,89) 3739.4273.P46
269 (1) 424255915796187428893811.P57
271 (1) 1627.115417966565804897.4635260015873357770993.P40
273 (1,3,7,13,21,39,91) 547.105310750819.P30
275 (1,5,11,25,55) P61
277 (1) 25792643401363.P70
279 (1,3,9,31,93) 26227.119232435043.85384915399027.6444365376140611199022187
281 (1) 563.5203536083.P72
283 (1) 1699.62827.2486265371.67535788803713.P54
285 (1,3,5,15,19,57,95) 1101811.P38
287 (1,7,41) 1723.84413238703660609.4336790831080504259.P34
289 (1,17) 72251.79187.1077971.18360250452977.197766803208315851.P36
291 (1,3,97) 25609.5636963037465601.581546606903256979.99695503427255026561
293 (1) 587.26371.33403.13453890779540632945331892129844577.P42
295 (1,5,59) P71
297 (1,3,9,11,27,33,99) 23761.694387.6215074747201.P32
299 (1,13,23) 2393.834490119087067.P62
301 (1,7,43) 43*.P75
303 (1,3,101) 112102729.P53
305 (1,5,61) 331841.31347559232075126851.P48
307 (1) 1249678499.4315199443523.210708825063558235331.P50
309 (1,3,103) 619.2473.15451.89620507.2400744384937.98277023988499.
.68545852036177507
311 (1) 64067.P89
313 (1) P94
315 (1,3,5,7,9,15,21,35,45,63,105) 1765891.P38
317 (1) 326330579.491981122308467411.P69
319 (1,11,29) 121333341977.169523514238420211.25925516494438382632167017.P31
321 (1,3,107) 154723.20636399209.480625710015394052365153.P25
323 (1,17,19) 17795830908608814443.3211586054639813621611.
.6319957642033539607139.2065255878519475622261353
325 (1,5,13,25,65) 3251.5840251.7812610577851.9860942209386451.P34
327 (1,3,109) 666427.6927735019.P50
329 (1,7,47) 659.762394321774681.P66
331 (1) 5297.2983001129.7520796641.8530674250842274717434530683.P49
333 (1,3,9,37,111) 304363.9853387597819.31031320083857011.P31
335 (1,5,67) 93131.P75
337 (1) 21569.5333388961.964094242760707.P72
339 (1,3,113) 156619.28448881.P55
341 (1,11,31) 647219.1434929.37368615235403.P65
343 (1,7,49) 2513690593.2883580030222424891.P61
345 (1,3,5,15,23,69,115) P53
347 (1) P104
349 (1) 131282633.P97
351 (1,3,9,13,27,39,117) 4247713303224552237738169.P41
353 (1) 3803909572078746837295094051706948091.P70
355 (1,5,71) 15524635883992211.P69
357 (1,3,7,17,21,51,119) 428401.P53
359 (1) 3536450843.1110671633637523.194193974563158088483.P63
361 (1,19) 6874301617534827509350575768454356245025403.P61
363 (1,3,11,33,121) 2179.19488182484739.P50
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701 (1) P211
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769 (1) 36913.77836643.86369467.9401836358059.602141772875227166401.P177
771 (1,3,257) 831139.158530119801167697937.
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775 (1,5,25,31,155) 4651.282519050251.264114740732599186195841745080394055656413965435249440593413845572793896725379051.P86
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787 (1) 942827.5405369360996178738798259049.
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791 (1,7,113) 54112378027.
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793 (1,13,61) 50753.2864285210191809465583254126794859170149406203.P167
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797 (1) 875107.105670649433473243107529297593.
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805 (1,5,7,23,35,115,161) 33035981768945891.
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821 (1) 6569.1037866321911576169081957409.P216
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829 (1) 131147801.3154069493397876555121.2751096190869286949881816932924433.
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831 (1,3,277) 971034308087215866439841492479664676774419087718205580112757800346489383481.P92
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839 (1) 1377062372371126895706481139.P225
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857 (1) 252182368360125289180898199073630970779.
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863 (1) 535070645969.176177196937327118084628312251.
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877 (1) 29819.42355831233323.18969179136276645172100272388219.
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881 (1) 22907.58147.70481.149771.42295049.
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907 (1) 8156908781432775187914049.292694927386576695497498001026561.P216
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937 (1) 1431737.20795779.40172939.1961075885814321323.
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941 (1) 1738969.5062155107501579.1053336016261649316809.P240
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947 (1) 7577.13259.91254170041.212341461377.881206290008086216099.
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967 (1) 440953.103340834172163133609939997710360109744851837737.P238
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971 (1) 495211.3019967621847401.745797773625002825025979.
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1147 (1,31,37) 305771849. C317
1149 (1,3,383) P231
1151 (1) 9209.264731.7183639052011.8057089084163503088491. C302
1153 (1) 27673.3772896236651.1815221738378898021554747. C306
1155 (1,3,5,7,11,15,21,33,35,55,77,105,165,231,385) 9241.18481.
.113571560808091.
.928267859145048237228203439064060384235841167452667731.P69
1157 (1,13,89) 6202223372363094929452168980151819917315301830721. C270
1159 (1,19,61) 117466969. C318
1161 (1,3,9,27,43,129,387) 2779191397441. C216
1163 (1) 59301371.10534255862017.116877740332519011737292886104457. C297
1165 (1,5,233) 179411.9813961. C268
1167 (1,3,389) 9337.97484277202003.45908592787319236096963.
.936622732283266044834451024147.
.3938368118355873575102129530416312021153911608699.P115
1169 (1,7,167) 2339.37409.161323.14608351671572807850092203.
.8414160072705585053393085689.
.23740978495305899888391704714669253618912353.P191
1171 (1) 25763.84313.P343
1173 (1,3,17,23,51,69,391) 236947.647674297.4080494539544536849.
.15477225584568935651447216741685456162338995027.
.352820376398397979265099331984513647290394257293220676543507835019.P68
1175 (1,5,25,47,235) 185651. C272
1177 (1,11,107) 49504078597120643.166419727156424727241892848411.
.18086003974039700834773047458500121168169812493765139.P222
1179 (1,3,9,131,393) 25939.82531.
.358481631294404888613030634349490904280996785041660793.C172
1181 (1) 49603.59051.11403737.67685946763.
.9186599509882727262279760862379532536049.P288
1183 (1,7,13,91,169) 18256533429955747955939. C260
1185 (1,3,5,15,79,237,395) 2371.18859377449506801.P169
1187 (1) 626523937064728884681163. C334
1189 (1,29,41) 28537.306763.9758744379744403.P312
1191 (1,3,397) 1819849.43247593.64339323043.427329609001.
.66809564696120553953329.C180
1193 (1) 324497.6132176836553.
.3830133035529809005604118596180719845719114907654979.P289
1195 (1,5,239) 184087361.1476292474364321072638637843510554375995931. C237
1197 (1,3,7,9,19,21,57,63,133,171,399) 778051.1697347.P183
1199 (1,11,109) 447252559596639611.298257415638476586139.
.794144907494779140961.1996742176615621275047178653063503969.P230
Table 2LM Factorizations of 2^n+1, n=4k-2, n<2400
n Prime Factors
2 5
6 (2) 13
10L (2) 5*
M 41
14L 113
M (2) 29
18L (6) 37
M (2) 109
22L (2) 397
M 2113
26L (2) 1613
M 53.157
30L (6,10M) 61
M (2,10L) 1321
34L 137.953
M (2) 26317
38L (2) 229.457
M 525313
42L (2,14M) 14449
M (6,14L) 1429
46L 277.30269
M (2) 1013.1657
50L (10M) 101.8101
M (2,10L) 5*.268501
54L (2,18M) 246241
M (6,18L) 279073
58L (2) 107367629
M 536903681
62L 5581.384773
M (2) 8681.49477
66L (6,22M) 312709
M (2,22L) 4327489
70L (2,10L,14M) 47392381
M (10M,14L) 7416361
74L (2) 149.184481113
M 593.231769777
78L (6,26M) 13*.313.1249
M (2,26L) 3121.21841
82L 181549.12112549
M (2) 10169.43249589
86L (2) 1759217765581
M 173.101653.500177
90L (2,10L,18M,30M) 181.54001
M (6,10M,18L,30L) 29247661
94L 140737471578113
M (2) 3761.7484047069
98L (14L) 4981857697937
M (2,14M) 197.19707683773
102L (2,34M) 409.3061.13669
M (6,34L) 1326700741
106L (2) 1801439824104653
M 15358129.586477649
110L (10M,22M) 415878438361
M (2,10L,22L) 3630105520141
114L (6,38M) 131101.160969
M (2,38L) 275415303169
118L (2) 1181.3541.157649.174877
M 5521693.104399276341
122L (2) 733.1709.368140581013
M 3456749.667055378149
126L (6,14L,18L,42M) 118750098349
M (2,14M,18M,42L) 40388473189
130L (10M,26M) 108140989558681
M (2,10L,26L) 521.51481.34110701
134L (2) 269.42875177.2559066073
M 15152453.9739278030221
138L (2,46M) 70334392823809
M (6,46L) 5415624023749
142L 4999465853.472287102421
M (2) 569.148587949.5585522857
146L 9444732965601851473921
M (2) 293.9929.649301712182209
150L (2,10L,30M,50M) 63901.13334701
M (6,10M,30L,50L) 1201.1182468601
154L (2,14M,22L) 869467061.3019242689
M (14L,22M) 8317.76096559910757
158L 604462909806215075725313
M (2) 317.381364611866507317969
162L (6,18L,54M) 3618757.4977454861
M (2,18M,54L) 106979941.168410989
166L (2) 13063537.148067197374074653
M 997.46202197673.209957719973
170L (2,10L,34M) 1021.4421.550801.23650061
M (10M,34L) 7226904352843746841
174L (6,58M) 22170214192500421
M (2,58L) 349.29581.27920807689
178L 1069.579017791994999956106149
M (2) 123794003928545064364330189
182L (2,14M,26L) 1093.1093.8861085190774909
M (14L,26M) 4733.556338525912325157
186L (2,62M) 4611545283086450689
M (6,62L) 373.951088215727633
190L (10M,38M) 761.2416923620660807201
M (2,10L,38L) 54721.276696631250953741
194L 389.4657.4959325597.17637260034881
M (2) 3881.5821.3555339061.394563864677
198L (2,18M,22L,66M) 42373.15975607282273
M (6,18L,22M,66L) 235621.8463901912489
202L (2) 9491060093.53425037363873248657
M 809.5218735279937.600503817460697
206L 41201.520379897.473000157711296729
M (2) 17325013.117070097457656623005977
210L (6,10M,14L,30L,42M,70M) 1041815865690181
M (2,10L,14M,30M,42L,70L) 421.146919792181
214L (2) 857.37866809061660057264219253397
M 843589.8174912477117.23528569104401
218L (2) 74323515777853.1746518852140345553
M 5669.666184021.171857646012809566969
222L (6,74M) 1453030298001690873541
M (2,74L) 3109.1398316729.4345052821
226L 10384593717069655112945804582584321
M (2) 58309.2362153.15079116213901326178369
230L (2,10L,46M) 461.5981.359006912765190408181
M (10M,46L) 15096281.1021622741.7834788541
234L (2,18M,26L,78M) 7489.370244405487013669
M (6,18L,26M,78L) 21061.348661.1112388285061
238L (14L,34L) 2381.42841.823481.536296539263941
M (2,14M,34M) 9521.18292898984156916156396101
242L (22M) 3389.91961.4036962584010807014809213
M (2,22L) 1339272539833668386958920468400193
246L (2,82M) 802333429.6027043735173469
M (6,82L) 2953.125965976976392564317
250L (2,10L,50M) 5*.28001.96001.94291866932171243501
M (10M,50L) 7001.3775501.47970133603445383501
254L 509.26417.140385293.90133566917913517709497
M (2) 18797.72118729.2792688414613.8988357880501
258L (6,86M) 5951631966296685834686149
M (2,86L) 17029.46957.96758771543686753
262L (2) 642811237.2745098189.308544695409769427309
M 269665073.810791440841.12450751815271172041
266L (2,14M,38L) 1597.449329386292232535250647435097
M (14L,38M) 2129.126848469231149.679253585011429
270L (6,10M,18L,30L,54M,90M) 541.49681.165041853060421
M (2,10L,18M,30M,54L,90L) 30241.166242935471754241
274L 189061.921525707911840587390617330886362701
M (2) 168434085820849.206875670104957744917147613
278L (2) 1408349.15736774913.492717674609.12763660054721
M 557.1251163891299967635860272509229764287909
282L (2,94M) 1129.1768141.54865357.180846660913
M (6,94L) 5641.270097268484167653999069
286L (22M,26M) 958673.661521349351105339668937661297
M (2,22L,26L) 25741.3426853.9467173.4170165570896115649
290L (10M,58M) 168781.12004541501954811085302214141
M (2,10L,58L) 17401.244716883381.3902095192430070721
294L (2,14M,42L,98M) 540961.40544859693521152369
M (6,14L,42M,98L) 17059410504738323992180849
298L (2) 12961064789.11011808951971745915313242336927641
M 1789.14641916303149.27243386602395588437243602121
302L 2854495385411919762116496381035264358442074113
M (2) 4373689270176379261201.130530323901899210670077
306L (6,18L,34L,102M) 2582029.4260133.12458723489217613
M (2,18M,34M,102L) 613.318194713.238495197879143209
310L (2,10L,62M) 37201.87421.52597081.24865899693834809641
M (10M,62L) 8973817381.57805828745692758010628581
314L (2) 2790467761.5941035366826969.2203942033439148343973
M 182687704666362864775461208552445184771578920961
318L (6,106M) 207973.30007459254393181618012897
M (2,106L) 10177.7971862004867103303293462593
322L (14L,46L) 3221.169373.209160253.27037028118448801270021
M (2,14M,46M) 1933.298817.115927640417.179351574736387915177
326L (2) 653.9781.7807049.4826612561.9716134201585679932947173
M 11692013098647223345629483497433542615764159168513
330L (2,10L,22L,30M,66M,110M) 661.3301.8581.12127627350301
M (6,10M,22M,30L,66L,110L) 391249826881.13379250952981
334L 187072209578355573530071639244871112681892570202113
M (2) 75005713.27395325377910797.18208260781190156536114609
338L (26M) 677.615946323850313.215656329382891550920192462661
M (2,26L) 180201997.1259036730797.408946876729703992293841657
342L (2,18M,38L,114M) 4598533.41435606371227835355919073
M (6,18L,38M,114L) 25309.5675149.39291697.99463730244517
346L (2) 13625405957.175739665310505752968877740350313227534889
M 7152893721041.1673815085186574700322174232069942181681
350L (10M,14L,50L,70M) 701.2430065924693517198550322751963101
M (2,10L,14M,50M,70L) 1038213793447841940908293355871461401
354L (6,118M) 709.12037.2995240087117909078735942093
M (2,118L) 31153.5397793.94789873.20847858316750657
358L (2) 31815461.416115013830990336221.11575709336636595278866333
M 1301260549.588850381287433028279084110474400181861465037
362L (2) 9413.178925762979037.3830538323149121.95016376135553173181
M 28739737348957.106646454159157789533685339377679881781493
366L (6,122M) 5080081.4209508589941.19125556519918081
M (2,122L) 12836737570021.414194958733796530899181
370L (10M,74M) 1392776941.4964166554103541.1258710725115650761
M (2,10L,74L) 29246281.567471221.4299881834172078350686174001
374L (2,22L,34M) 26509131221.35155077044989397.4029292065629191839853
M (22M,34L) 5237.551353793.1819762572673.135322045917118601273437
378L (2,14M,18M,42L,54L,126M) 757.456376431053626339473533320957
M (6,14L,18L,42M,54M,126L) 304832756195865229284807891468769
382L 25212001.5972216269.20844252715379252090938485003447004944677
M (2) 3821.89618875387061.1833085153842665442652283234165143433597
386L 773.635283689603233836449.25564774360363212740382247547878573
M (2) 3089.148997.14402030644704405877.378791300027089635677652285973
390L (2,10L,26L,30M,78M,130M) 2341.723447661.8925278993793241
M (6,10M,26M,30L,78L,130L) 468781.720453772427518446437641
394L (2) 4729.1079423677.152874915601.51480369709170501304394118553664009
M 52009.3862163385805798697201354795194661512726441364448411929
398L 797.1008116715344410461444141839610180239223178503751442552629
M (2) 76554648784441.2099073106303095025303885460879717918033130293
402L (6,134M) 3217.192961.214473433.71848008781.175132692529
M (2,134L) 10453.132661.15704900959651293774270521395753
406L (2,14M,58L) 29*.28474083676894571496726280348891354240661831606009
M (14L,58M) 9810958633253.21597468549493958664902504331670645757
410L (2,10L,82M) 61213422340181.76401557052661070266405340180269721
M (10M,82L) 41*.821.269896441.82777720757144341.758399801407611361
414L (6,18L,46L,138M) 829.853669.26785337149.496817081109150685921
M (2,18M,46M,138L) 3313.18217.318781.6542857.25395382141805460457
418L (22M,38M) 8857714771093.3066290411598855013.27290812893120485231161
M (2,22L,38L) 6689.2039731321.149832750683283097.1937385241416564065603093
422L (2) 95110361.6920400848110359047653995057624941367485834954585997077
M 18455044087121.178325724886188112393573476458482965256782477560753
426L (2,142M) 266677.1396429.18369973.40524027877.20111008087273
M (6,142L) 853.189997.2646185328486854129693169911139349
430L (10M,86M) 129001.1131832377932535124189124787988905860893840561
M (2,10L,86L) 370661.1952201.4538991421.260125854015641.1401345270171101
434L (14L,62L) 867988564747274927163124868127898657976489313137639569
M (2,14M,62M) 31249.776729668507005203702993.139335546032913681584758997
438L (2,146M) 877.1013533.704710824913.142406868765525436670617
M (6,146L) 371335727233.18478609113710122023550126425157
442L (2,26L,34M) 6670914925963435577.2380142106509122200127345885819001687213
M (26M,34L) 1210509821.2291059412513.1118498440898880562062959177194663477
446L 95768689.52016435676012089.2705981985587527191852752325795076108854553
M (2) 11597.6530333.6912010464887165201.P37
450L (6,10M,18L,30L,50L,90M,150M) 413150254353901.3192261504216112476901
M (2,10L,18M,30M,50M,90L,150L) 695701.307116398490301.6269989892198401
454L (2) 4565795412500725128240734773.P40
M 5449.83132849.694512857.5661492593.P39
458L (2) 2749.5523481.84948746297.6211454306149.P35
M 602633653.33074236421.44185520789894155033573.P27
462L (6,14L,22M,42M,66L,154M) P37
M (2,14M,22L,42L,66M,154L) P36
466L 30757.15576974348063186977.25336594975374725568037.P25
M (2) 3108221.P63
470L (2,10L,94M) 941.894434441.3357909154141.38425816980821.722501809616926841
M (10M,94L) 87255998201.3237811125343321.P29
474L (2,158M) 151681.P43
M (6,158L) 18890331057055511701.P28
478L P72
M (2) 77852679293.P61
482L P73
M (2) 2640397.15594629.76119208744309.P45
486L (2,18M,54L,162M) 3333950193493.P37
M (6,18L,54M,162L) 2917.4861.26129603777437.P29
490L (2,10L,14M,70L,98M) 306178659371201.1372226516822701.P22
M (10M,14L,70M,98L) 7439220181.P41
494L (26M,38M) 515737.P60
M (2,26L,38L) 104729.2638949.531455155350809.P40
498L (6,166M) 136453.218166829.41732461753.5791487405427228378717709
M (2,166L) 1993.80485166514184335373.P27
502L (2) 1912621.57762875981.1972386557777.38508212572597.P32
M 5021.45063180240128066017730357.P47
506L (2,22L,46M) 6994042018866541.P51
M (22M,46L) 25301.109297.756550961.2569737193.9623862953.
.156296877661.101027360307659633
510L (6,10M,30L,34L,102M,170M) 51001.2949879781.611787251461.15455023589221
M (2,10L,30M,34M,102L,170L) 15571321.P31
514L 22988734297.P68
M (2) 28564009.360197837.P61
518L (2,14M,74L) 2035259884744589189.P48
M (14L,74M) 6217.P61
522L (2,18M,58L,174M) P51
M (6,18L,58M,174L) 7309.P47
526L 43195464658778477.80181854738775471107692957.P37
M (2) 119929.731141.99972364781.P57
530L (10M,106M) 1061.3181.P56
M (2,10L,106L) 51941.24082141.31213331016701.P38
534L (2,178M) 3401264941.11221454641.P35
M (6,178L) 2137.928574737.P41
538L (2) 2153.3229.5381.4273873.1633401082697.3918695179304214327885157.P27
M 8609.122575221550682354302309961053.P48
542L 10474693.104167755499168696693743867494211841.P40
M (2) 97561.P76
546L (6,14L,26M,42M,78L,182M) 503413.467811806281.P27
M (2,14M,26L,42L,78M,182L) 1948129.P37
550L (2,10L,22L,50M,110M) 12101.35201.698617420601.18735216413769901.P24
M (10M,22M,50L,110L) 1905911178138824081520901.P37
554L (2) 1109.987879984327104437.P62
M 232681.98002601.1093620377.4343215646437.365883785511434081.P31
558L (6,18L,62L,186M) 1117.140617.P47
M (2,18M,62M,186L) 775844757937.P43
562L 91568909.P77
M (2) 3373.3827221.58381440973934522510444290213069.P43
566L (2) P85
M P86
570L (2,10L,30M,38L,114M,190M) 185821.247381.3996146881.P23
M (6,10M,30L,38M,114L,190L) 1457772869697961.P29
574L (14L,82L) 2297.16073.P65
M (2,14M,82M) 10333.3839331472313.17160693383233.P43
578L (34L) 7698961.21886549.113478990853.P57
M (2,34M) 936361.854096275589539341506608949.P49
582L (2,194M) 580837.856752889.P44
M (6,194L) 7570390327211773.69186562412120809.3687531861438052950582913
586L (2) 22396921.12377633813.796088615657.498039116406053.P44
M 5861.12893.60488093.644467520107517023949.P52
590L (10M,118M) 677321.824821.533194801.P49
M (2,10L,118L) 34747599647361961.P54
594L (6,18L,22M,54M,66L,198M) 5292250152949.P42
M (2,18M,22L,54L,66M,198L) 2377.22573.155399494141.4712151755917.P23
598L (2,26L,46M) 6542689297.20825730982886584878330561061323409.P36
M (26M,46L) 20333.956801.15595841.19294368341.6339840806910833.P36
602L (2,14M,86L) P77
M (14L,86M) 4817.18061.2789669.5956189.236344687097.
.26007561155890556369.461291203265457936024109
606L (6,202M) 1213.10838917.482601694398006137569.P29
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1126L (2) P169
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1138L 37690561.
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1154L 2309.92936237.17473219453.13287439049014069.122931731283429211231592321.
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1214L 6391568743817.2366069394177173.
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M 87010881757473495441157.26300074501301139029607543064193681.
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M (2,18M,54L,162M,486L) 15756367092121.2310448606789649285233.
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1462L (2,34M,86L) 3333662945629191088961706760871407975881997.132411637608234702176403937795574265318598971445902740232752192169589.P93
M (34L,86M) 5849.3456169.1105776337262654129.399490631328637643761.
.137012022181393232206253.
.43642955052231388569322806557951798815213926256981.P81
1466L (2) 205726455772006440377818607135775827053674474181634602781.P164
M 627449.P215
1470L (6,10M,14L,30L,42M,70M,98L,210L,294M,490M) 1484701.3298681.
.83468535680255056381.520015769408683617721.744298254317046214381.P28
M (2,10L,14M,30M,42L,70L,98M,210M,294L,490L) 1467061.6793177127101.
.10137296444101.P70
1474L (22M,134M) 5897.32429.61909.29853380696418401.51686732107634400481.
.8069970082210798732538612540391343336685633.P107
M (2,22L,134L) 914450435002519795672193841434619169.
.2638262922012800082690048604667428700453.P124
1478L (2) 523213.170756297.440074501.788092030022183820493369752421.2690689930879440037372552876789965290601761240871891720842427997721986219162721.P91
M 2957.6139613.38076579284342103367042880439853.P181
1482L (2,26L,38L,78M,114M,494M) 8893.P126
M (6,26M,38M,78L,114L,494L) P131
1486L 260683037.P216
M (2) 1126545517.1585883767273046287425657193.
.179473687767485523762057078149.82904514009129973580846869626857.P126
1490L (10M,298M) 12149461.317596431444133301.
.13922047453015798095930702744666309471614785005795919241.P99
M (2,10L,298L) 8941.15472037821.195973382282821775041.P145
1494L (2,18M,166L,498M) 201920077.2024367013.
.255450160174472123250510265381182600544409941.P86
M (6,18L,166M,498L) 842617.456714776565457776947610460261.P113
1498L (2,14M,214L) 32957.4071247577461.P175
M (14L,214M) 8610917449.20882647297.1168781887512373.
.31923290057858087319414543412049.10100617205200540668619445903235817.
.2068214695211281811176768882056531481.P55
1502L 195074519591093.181750785614799949391207816898761374168148975264389.P162
M (2) 9013.3885545486598580976140214349467243582955277.P179
1506L (6,502M) 9421537.70906046209.4376690298097823998048670169409.P102
M (2,502L) 1563229.41432031118658520623317.
.1015015821796377094974033400280350597.P87
1510L (2,10L,302M) 10284066921313719670117464344952798481.
.7646314959368848394486675357078883614676365385821.P96
M (10M,302L) 6731030511001.22524246248701.P155
1514L (2) 83940354459118810481.P208
M 12782703425963929.15546196279794280749075061880957.P181
1518L (6,22M,46L,66L,138M,506M) 3037.6073.9109.176089.13652893.
.80734723637871997.4890980423872252596496536675107089149541.P53
M (2,22L,46M,66M,138L,506L) 407997301669.89841243813164449.
.15555311179383169261.132091523915211513329293.P61
1522L 82189.529657.1567661.407926786285441.1168457387724788393.
.159732666511146601744310161030566437.
.1352634701194560897000646066777989041799189313.
.45835118187315186948237881122511163162916683061.P53
M (2) 9133.9753923125908814024338488617.
.864302875044929823011416054425332009736761.P155
1526L (2,14M,218L) 167861.
.81100940490524995434296633553178345665740792232320957.P138
M (14L,218M) 228901.89585357.1193769557014682568929.
.26949677948560956418555434041273937193.
.58023940775396337496088317549973016234295004562061.P74
1530L (2,10L,18M,30M,34M,90L,102L,170L,306M,510M) 36721.70381.965133181.P98
M (6,10M,18L,30L,34L,90M,102M,170M,306L,510L) 253190737566001.
.358689400191468213568189014966376501.P66
1534L (26M,118M) 2602289873.14878594277.697288564688146289.
.965547036555813950892665424422395130322293.
.27121391735972963364604482493933746021119189.P87
M (2,26L,118L) 32554549.1301673138221.1391657728553.10261059495917413.
.174574320633190844334669825437.
.32370493756031541479030638251403247966716264514809.P84
1538L 1508116661.728725553653.P211
M (2) 487854440461236965376721. C208
1542L (2,514M) 293171209.7752412975359697.340066554311536965308417882742061.P98
M (6,514L) 552218538342469.
.6085412460587930083903553583244932908333069728961100695226000917581.P73
1546L (2) 9277.961613.8979169.28764877.1286673961.6144001889.20680804897.
.72888144455528365833889.101159392465333020291272490553669.P124
M 8950276336541.P220
1550L (10M,50L,62L,310M) 2204849283056077770183700917441626363341403201988701.P130
M (2,10L,50M,62M,310L) 106288917242483907573395401.P155
1554L (6,14L,42M,74M,222L,518M) 15541.P127
M (2,14M,42L,74L,222M,518L) 21757.P126
1558L (2,38L,82M) 65437.2841793.3745809992085397.P191
M (38M,82L) P217
1562L (2,22L,142M) 257068815787496849489.P191
M (22M,142L) 12497.777877.1462033.1668464524433015165835133.
.1072443701632072579384549789.8247505706276398056121502653493.P113
1566L (6,18L,54M,58M,174L,522M) 1005373.900238389553.88293718850941.P120
M (2,18M,54L,58L,174M,522L) 18793.121571536007648069609869.P125
1570L (10M,314M) 1814921.2704723867921.35422803263041.P156
M (2,10L,314L) 762464332510640867293939564541.P159
1574L (2) 26940527389021586346998869.
.50902080564527017360173061387390051814344996542268977221.C156
M 47221.406093.14121929.P220
1578L (2,526M) 104530192048153.89278383816591944174173.
.468320479654392916258882359560461.
.35467094651948541600331422014320230649.P52
M (6,526L) 177592095535805413.
.209464891971049544444372157566739020805493.P99
1582L (14L,226L) 113*.6329.94395483835364237.362648335437701461. C162
M (2,14M,226M) 85429.116163097.P190
1586L (26M,122M) 582049312001.26969455685328761021.
.502340346136939736695391222101.C156
M (2,26L,122L) 179846057.47708294713.3385836026574025144947910893473.
.93491631781994291906413660951010052976306161721305451541.P112
1590L (2,10L,30M,106L,318M,530M) 27087241.1373040346921.5284407007801.
.1210269871632394075226641.683607720175140192010111693752601.P36
M (6,10M,30L,106M,318L,530L) 19081.184441.2422984469411281887781.P95
1594L (2) 2097515909.364129241317395157.P213
M 1131019499249.P228
1598L (34L,94L) 41549.290837.7142332055234648333.6099217213901879740081. C171
M (2,34M,94M) 51137.5394672221.
.2451115619396440849235862100116768648751167995117.C160
1602L (6,18L,178L,534M) 6565668841.1539976855861.72911451369675792637.
.3945245703312222053852257.P93
M (2,18M,178M,534L) 14170974714403144763101597.P134
1606L (2,22L,146M) 50219621.1808418581560889.903888164009442693590288077.
.1482338506032222870906022459128577.
.337779774700456816455577092228603627733197301999086530154776370553.P69
M (22M,146L) 19273.2862083701562715653. C194
1610L (2,10L,14M,46M,70L,230L,322M) 158149013123372670109481.
.457589580500218094330982520525097903344197892931941.P85
M (10M,14L,46L,70M,230M,322L) 6216303835549501.P144
1614L (6,538M) 416413.2621137.962643846199733408565200877781060429.P113
M (2,538L) 16141.30701107729.43932915373.1868171919242953.
.914570427675304311896510460383772935570463409.P77
1618L C244
M (2) 6473.25889.1948073.7660242424577.
.1556583473595126684080853611730128054181078209.P171
1622L (2) 226993790701.120375361925202961.P215
M 5336381.1178063188140768549097.
.155993516049715935315734115302975044254349.P176
1626L (2,542M) 273883482277.2486873948884993.198779717698841035284255913.
.1661993671243438017256281256149910093.P74
M (6,542L) 3253.78049.1593481.1475273053.83478798429270328887973.
.73044219855003574103778189733.
.4713405292661216398984672353497652737173.P47
1630L (10M,326M) 45641.196239297090446416678541.
.3707642406570829114833393150344141.P134
M (2,10L,326L) 9248621.7627588261. C179
1634L (38M,86M) 2091521.15886294883461.5285748520741386282105949513.
.11811951218548871673638976031338702013.
.7900626095422545589371272784733264086865508685709727149.P89
M (2,38L,86L) 382357.6052337.6483713.11637349.17147197.P195
1638L (2,14M,18M,26L,42L,78M,126M,182L,234L,546M) 507781.6224401.P118
M (6,14L,18L,26M,42M,78L,126L,182M,234M,546L) P130
1642L (2) 441085379960554789.356378849959441965290887469317261822121. C191
M 7505293746011641766492467854893261603664038102314712839047907776243712148179748450190533.P160
1646L 19753.17678041.28473240575821815736340752613. C208
M (2) 924509587369596772157.P227
1650L (6,10M,22M,30L,50L,66L,110L,150M,330M,550M)
164342074315726836781988740273689592246064114457301.P71
M (2,10L,22L,30M,50M,66M,110M,150L,330L,550L) 42217104570301.P107
1654L (2) 36389.148861.2312293.130582063447518110584062446171193488957. C195
M 50493458584097.291599907662880149.
.1850744891824232892018330060023474649953.
.118981160680646146541187664972610620871634149.P135
1658L (2) 464235512584146182617.479329249434015760837735948908881.
.9495843085074401617566562609326230101956634470929.
.144369313070047736569001837732936390339888716784191974617519837.P85
M 3825173678485409449.7983838621160200177.12624459932825972330038421.
.286648956293312333537203182607341999451013.
.551411572651197347351047629119823145955983741.P101
1662L (6,554M) 9973.1125470603488333.51689114452666429.
.676569636302657152854889.487914335884174463488431988112971564897.P68
M (2,554L) 171028625446956073.P150
1666L (14L,34L,98L,238L) 16661.46649.1868371709557081.20378049054645577.
.199344004099971410597.
.806048510739185905343984770167131427200553501166861810318477055189.P76
M (2,14M,34M,98M,238M) 73500589.26980673413.440703752018377.P170
1670L (2,10L,334M) 430861.3154569881.7846415030381.22625604968060184427321.
.2262086882766687062334641.P126
M (10M,334L) 2596102992439173192852614756601983822141548332436781.P149
1674L (2,18M,54L,62M,186L,558M) 70309.4081213.1297451663483880043725856297294610187704362366686186248013808494382873.P83
M (6,18L,54M,62L,186M,558L) 789059989.P154
1678L 5564249.2793879899538857933.19338500498002810228771062564557. C197
M (2) 28723493629440097782059388914974037930708633570183584249. C197
1682L (58M) C245
M (2,58L) 366677.3727313.13866300353.213360835453.1127518158768077.P196
1686L (2,562M) 2206057267849.847304927418579057202962063105851800436897604953259070264606037793157.P88
M (6,562L) 5999663863513.P156
1690L (2,10L,26L,130M,338M) 1165339501.333398126078661934421.
.10951196901534534492850755810091411261.
.8500591978242473249929589155637812362821.P82
M (10M,26M,130L,338L) C188
1694L (14L,22M,154M,242L) 29018221.343251023344259430080136457.
.28200299483430955070424820142580026272434397.
.97223612367147967684223013199430303239555535537.P75
M (2,14M,22L,154L,242M) 908695481.6202401437.13560087157. C170
1698L (6,566M) 3830689.53028541.45039969589.2403898139108413.
.96943448874943589381509.P106
M (2,566L) 526381.2212378537.113620361303857.P142
1702L (2,46M,74L) 450395984739049729770917.P216
M (46L,74M) 3466225121.P229
1706L (2) 3413.64007056091437.1122047772459197542365557.
.3670300973252073917081977.P191
M 57568727236201. C244
1710L (6,10M,18L,30L,38M,90M,114L,190L,342M,570M) 110017981.848129221.P113
M (2,10L,18M,30M,38L,90L,114M,190M,342L,570L) P131
1714L 4702664630197.6871169125116761.8859671727690991421.
.51158163991710264101.C191
M (2) 7490495630917903672489.1112610919806658266406382986993.
.37254915681318275345339031340236801161.C168
1718L (2) 82488053.160783317963711097. C233
M 41233.18970157.161362916688885847263044877441415342126713555601. C200
1722L (2,14M,42L,82M,246L,574M) 2675989.P138
M (6,14L,42M,82L,246M,574L) 44773.82657.
.11226524876408775073143033704082858121.P99
1726L 62137.7682681449.12118208029.7636302550869852997. C217
M (2) 12268162909.4190110941193.41734812223623741861146169997.
.46619255366962328167412700221.406766837212504479804114509779153.
.4111798002954124877183397050601213755485272497.P101
1730L (10M,346M) 13841.94672594940509124602676510531741226575772518341.P156
M (2,10L,346L) 3461.297197052517429014237901.
.155239988274216593089164596199061.P149
1734L (2,34M,102L,578M) 3469.38149.11390863043502454932811494176805522322333679313892091082261899485723141.P86
M (6,34L,102M,578L) 83233.67133458080301.15286531841496313.
.76087114479348013.P112
1738L (2,22L,158M) 79976245841124049692014336050829.P204
M (22M,158L) 10429.59093.794450909331238272563227097.P199
1742L (26M,134M) P239
M (2,26L,134L) 482919699751741253.P222
1746L (6,18L,194L,582M) 376885109765881657.P157
M (2,18M,194M,582L) 19181586049511261238746281.4143848071599342832189552657193683851218149055132998865238029290237501.P79
1750L (2,10L,14M,50M,70L,250L,350M) 21001.90984652501.259213867501.
.66769116536501.P141
M (10M,14L,50L,70M,250M,350L) 52501.304501.P171
1754L (2) 136813.16485685958318067491706639165873936208073.P218
M 178909.8045864609.94177931835255001. C232
1758L (6,586M) 3517.17581.98809007760409286120685543691415456350976617.P124
M (2,586L) 70321.3681253.1465751310316457222898312721.
.786189125604290817435554536817956201.P102
1762L 292493.287799987821. C249
M (2) 9908497304929.3070352086706435689. C234
1766L (2) 3533.10597. C258
M 9642835106981.21853773066679313.1397997900714226472761369661333. C207
1770L (2,10L,30M,118L,354M,590M) 941641.112688376490130041.
.13958078871765695340080761.P91
M (6,10M,30L,118M,354L,590L) P141
1774L 1982764321.9982363219299701755701813517.
.2047754087000820349297809443743844453329.
.13231286310635194760975216003886759010777.P151
M (2) 12067954321.154247171201.246306661383223563619590775949. C216
1778L (14L,254L) 394717.2901290617. C213
M (2,14M,254M) 3557.430277.28402945481.
.399127051193796660679495799296414893620857762153.P161
1782L (2,18M,22L,54L,66M,162M,198L,594M) 120726937.212140766502632881.
.126076291066677670603478850918204428036903440615477.P88
M (6,18L,22M,54M,66L,162L,198M,594L) 2170477.168518034037.
.9055086119440404402246938172507702666506358169.P100
1786L (2,38L,94M) 3639869.999648574070171124601432769.
.497403465856372009446461144453.111758423615256944193654963749427567569.
.255421441882647036358581067782818217129321401.
.1039334208152531253984710089202456757484571009.P59
M (38M,94L) 646109108522520037.55737216228051297161494379261805713.P197
1790L (10M,358M) 3581.811893881.4272700190724544357721.
.682862187512541058734549287082001.P147
M (2,10L,358L) 94622981.9818823675183373550041.
.671277176269260334004380493401.C156
1794L (6,26M,46L,78L,138M,598M) 7177.P156
M (2,26L,46M,78M,138L,598L) 10684568857.
.23631648482124605019194916705352421056228717976627497383497516329.P84
1798L (2,58L,62M) 7193.3617439859037.8713454341549.109097329238284141. C207
M (58M,62L) 5886653.20723877457.43875868248089.
.39574364572001586424595746349.C194
1802L (2,34M,106L) 11747392973.91102528862545665457.P221
M (34L,106M) 174044748410668549457.224201551150113268933.P210
1806L (6,14L,42M,86M,258L,602M) 3613.9467360568830697495500595457.
.45757320478618895747604607889547060541.P83
M (2,14M,42L,86L,258M,602L) 44619686161.
.1340323540048991459950036430548177848438612466385636277313.P84
1810L (10M,362M) 1422661.10371301.62984381.2841546437106680644141.
.100673282665910769164456015319401.P142
M (2,10L,362L) 4779887821.284960538160486454165307301.
.1486018607888551051882493975787406621.P145
1814L (2) 36684968468392674349.267301538121080056247956934369.P224
M 2856279634519890658989627576084877545889. C234
1818L (2,18M,202L,606M) 938089.215403913.54459411697.P156
M (6,18L,202M,606L) 3637.11239182354817.89718779799289.P151
1822L 109321.42514235518096149015446235113.
.89978339781600142665771163471628742033256933.C197
M (2) 29153. C270
1826L (22M,166M) 10957.457905185813813.9118425814963735020084050069.
.758984045239765414366290480154514089.
.34334644886182446546273008924242084634327089789559771215864092254849.P97
M (2,22L,166L) 437342857760433461.31722291643604475850861201188341.
.2440105053710133005468894317569383122715715757.P153
1830L (2,10L,30M,122L,366M,610M) 1712881.
.209286094074580318288344692937218868614221.P97
M (6,10M,30L,122M,366L,610L) 61*.358681.602914116781.
.2397096504835438921.89135366684453039762936076301.P79
1834L (2,14M,262L) 18341.73361.106373.337457.602481460214341.
.6274647569487659758609838486398097882441.P161
M (14L,262M) 55021.11142479091341921.96578697208818436822981.
.730039745374219638260113.37447027901314381254512721318017.
.639745584291728863751658159947413.P103
1838L 15174529.1508449364353. C258
M (2) 3677.169097.2703022685717.1071847300685268733.
.2456774736627079417449898904657.P207
1842L (6,614M) 2903157652807014132222997.P160
M (2,614L) 14737.202621.670489.1924167937.20277440672157064961857.P138
1846L (2,26L,142M) 38286041. C246
M (26M,142L) 13837693811900871607717600062424369.
.1064448662217171715112211943132259502103349.P177
1850L (2,10L,50M,74L,370M) 3701.133886258536001.590663067860911343898701.
.866200444503307218246408516520037907601.P137
M (10M,50L,74M,370L) 3760458001.9312718358338301.P192
1854L (6,18L,206L,618M) 401841732395629.10017165502306460200391243108137.P139
M (2,18M,206M,618L) 3709.7417.93097809073.
.15697920117275073486338469567634384633.P129
1858L 11149.319577.551019709753.4609832458707079151039619761.
.1020789673987483714669438485415945837.P195
M (2) 7433.85469.858397.P265
1862L (2,14M,38L,98M,266L) 4639388993.22772885633.114089637061. C197
M (14L,38M,98L,266M) 11173. C224
1866L (2,622M) 3733.17962117.204082834247639533.
.2867134239058725077444870925351109.
.171787846178241745388291751687545359135893624733.P79
M (6,622L) 14929.31582002281292084633680717617.P154
1870L (10M,22M,34L,110L,170M,374M) 706960763753201. C179
M (2,10L,22L,34M,110M,170L,374L) C193
1874L 546289747242387833.102338449889938893229. C245
M (2) 802073.30214971197129.524704862656309.108215387436410988313.P228
1878L (2,626M) 3651421693.153204659721481575760771776889.P150
M (6,626L) 120193.23208500533.484894051077157.479542202751565609741.
.21514288711632793647440840947984309.P103
1882L (2) 3383837.25359946237.20793657827081209534512961080066477973.P229
M 1070913479895698609.6960982604145481063390741994425851833890468577.P220
1886L (46L,82L) 112410858169.36368413831997333.P237
M (2,46M,82M) 2784254414828346243382561. C241
1890L (6,10M,14L,18L,30L,42M,54M,70M,90M,126L,210L,270L,378M,630M) 7561.
.457381.2143261.596526861195233662750200340726624395569101.P73
M (2,10L,14M,18M,30M,42L,54L,70L,90L,126M,210M,270M,378L,630L)
43887888187572165151544641.53557082595126165043094157045628806518641.P64
1894L (2) 189401.1440383213.8204616582857089246514152381.P243
M 6522937.272279643245537.8211191052325823017421025141068065597. C227
1898L (2,26L,146M) 10390402230053.185571869124044164853371079021. C219
M (26M,146L) 3797. C257
1902L (6,634M) 2892776771209447770340654201.P163
M (2,634L) 15217.31877128189.778680603097.3488331309973.
.27069571592372896954201.P130
1906L 20405494957.P277
M (2) 2809306768001. C274
1910L (2,10L,382M) 1443961.92459281.P216
M (10M,382L) 57301.864189637596221.301039635955941955416398544601. C180
1914L (2,22L,58L,66M,174M,638M) 840440400036193222729.
.1085449968759125093329919224369.
.1585333835462829231438151788148865056453.P78
M (6,22M,58M,66L,174L,638L) 15313. C165
1918L (14L,274L) 7673.609014465221.5055546728233.
.13143270612909056636088570135286832260591916100581.P168
M (2,14M,274M) 168388835672177. C232
1922L (62L) 1137450670721.2184269724947805073.
.1208889346570157870280450820286251695464031997.P205
M (2,62M) 252792973.864219613.948729953.37541358506075478258236735332361.
.64570584168627945448109624328792927541.
.172172545512925790802497530112596705980073.P144
1926L (2,18M,214L,642M) P192
M (6,18L,214M,642L) 3853.400877843649997352715160009902239044357801832970765839337907513540064872417.P114
1930L (2,10L,386M) 1246781.1608921341.3568553151401081.
.5955623568140770033895876543735621.P168
M (10M,386L) 232492081623941.8392710322562681. C201
1934L 328781.12056557.P279
M (2) 47054221. C283
1938L (6,34L,38M,102M,114L,646M) 3877.19381.1279081.
.12774353393983945521795713234563738297.
.16750182073211230556310395420299476529.P86
M (2,34M,38L,102L,114M,646L) 926282517007889243128982867521.
.3648011488087216916950150682966398143704581.P101
1942L (2) 5877612181049269.6917838004568007880938360151147285081.P239
M 19421. C289
1946L (2,14M,278L) 38921.87632273.92220941.44849676017189.
.2684356809244885929794686184069.
.4046624378398002211307594382075047504065028449.
.907147414295234719242629807565546337688011292303997378516999456233.P74
M (14L,278M) 218561316364553. C235
1950L (6,10M,26M,30L,50L,78L,130L,150M,390M,650M) 24457095001.P134
M (2,10L,26L,30M,50M,78M,130M,150L,390L,650L) 45984901.
.1131816004801.108792457407671701.P108
1954L 36716449417.415313933724293297909.P263
M (2) C294
1958L (2,22L,178M) 10984381.1749046157.12769069589.
.8540463790853686106162888141.P211
M (22M,178L) 3917.4135297.21467513.57717951413.290857646356157.P222
1962L (2,18M,218L,654M) 109*.17951056093.669657070334773.P168
M (6,18L,218M,654L) 49346313013.1388612680921. C173
1966L 43644426217789.1431746688753709.P268
M (2) 155837128987432356781.1366175048897551662825186361.
.1323103760614147332897213698137697413.P212
1970L (10M,394M) 15761.35461.2214281.464568607149275146234181.
.581887899470864922007450289381.C168
M (2,10L,394L) P237
1974L (2,14M,42L,94M,282L,658M) 57174937.28860857283150817.P142
M (6,14L,42M,94L,282M,658L) 61706836445096809.P150
1978L (2,46M,86L) 7876397. C272
M (46L,86M) 439771371096041.35049840713898433.
.46336564105264156931219140569625359563486333.
.11369308667009289972811369899416497441702608089.P157
1982L 47569.702972273668806189.24108966487910875313.
.44229415926893141209.113447996363645096441.P217
M (2) 27749.63488677307778109.16825619625747922745475011329. C249
1986L (6,662M) 13302229.25430936011753.31614476989231029379232557.
.68905970337561183437462555868709.3973921258176323056321508940165661.
.1314098716175595483898139799716487493.P51
M (2,662L) 183625814209.1018768450523377.74519189014953913.
.18989372631177034732892899753.465177286996430226160539394957.
.617680057559525522778680709413533.P66
1990L (2,10L,398M) 250741. C234
M (10M,398L) 23198204725672081034655436981.
.36016148355139711248940080869144201.C176
1994L (2) 3989.23929.1316041.7905228953.450516200430246120721.
.149156643181299310192264307577506850757.P217
M P301
1998L (6,18L,54M,74M,222L,666M) 72354413161.1222553230560433.
.5735551460378502198796512243143473.
.5497368458116180193233404694623299228824873.P93
M (2,18M,54L,74L,222M,666L) 10126001691430741.382598228266336189.
.799915581937561681389258889697499905881.
.49801579402999682758116547403787291213389808169.P76
2002L (14L,22M,26M,154M,182M,286L) 20021.1849849.690545857.
.41080280592351540541.9215194846651389888428137.
.3969862289663363742872134096701517.
.13628840986604456625675621031891749568696694946387077.P68
M (2,14M,22L,26L,154L,182L,286M) 8009.12039884736627749. C197
2006L (2,34M,118L) 13868109346932001493749981709288184217585361.P237
M (34L,118M) 4013. C276
2010L (2,10L,30M,134L,402M,670M) 1161781.43714589671758035101.
.7202139206809052400714203227736498330521.P93
M (6,10M,30L,134M,402L,670L) 4021.655261.13154273408381894504101.P129
2014L (38M,106M) 23704361089.2345207504177.44598149829737613346817.P237
M (2,38L,106L) 2211373.2743400324920929934072747900058453.P243
2018L 12109.1291942943772106529500099325194662891337468227487983754043873.C240
M (2) 242161.952957298276617.
.1816911194189728629517731150999807102074709889.C238
2022L (2,674M) 8089.3546589.2922737792281.3181075216261429729586653.P156
M (6,674L) 737267931919513717708801.
.397490855733113630613348630003685291009.
.170970754136725722159939805266417998571170101.P96
2026L (2) 33449261.264484004729713012553.399321186049288505641.
.956936627523697040100248003877237301005401.P214
M 564156533186297737660008857018073337721. C267
2030L (10M,14L,58M,70M,290L,406M) 613061.85597365805801531151405792561041.
.87678355175652250615083617929401084618044201.P121
M (2,10L,14M,58L,70L,290M,406L) 36541.357281.P192
2034L (6,18L,226L,678M) 4077850171122577.
.31069150378873790895208046895771360949463293546412105951449429.P126
M (2,18M,226M,678L) 856216369.318132015893843401.
.21147271559400204090224749.454399800958030464217761866249437.
.1065856403671528263525870130273753.P85
2038L (2) 61141.207877.7150897365985729.223030353552686687144432969.P254
M 1862909934566184008482398847661045112399809958601.P259
2042L (2) C307
M 88557457. C300
2046L (6,22M,62L,66L,186M,682M) 4093.10308836566117.909262501760934950641.
.241186415860665003411865101707998523680990567422853.P94
M (2,22L,62M,66M,186L,682L) 431919189109.45982033644093624122893.P146
2050L (10M,50L,82L,410M) 656400720309944201.
.39701639943363232352915408020280101.C189
M (2,10L,50M,82M,410L) 3527365301.P232
2054L (2,26L,158M) 308101.24775349.105748241031224273.
.24187837105009092776233550365107217.P218
M (26M,158L) 4828050703567261.P266
2058L (2,14M,42L,98M,294L,686M) 127597.7687554960386019181.
.52003770991385964409.2258564379815977498898119074673.
.359714423380600478940340236904806333157.P65
M (6,14L,42M,98L,294M,686L) 3346309.5417007821989854721.P152
2062L 181457. C306
M (2) 32993.99370848761184288276203230691281696940392048973. C259
2066L 622097393.1606410037.2302309768953616705880653781. C266
M (2) 4133.78509.764610073.119567616206597388593595587565413062223773.C252
2070L (2,10L,18M,30M,46M,90L,138L,230L,414M,690M)
1899703744314142469016395838361964239321612519501.
.5946756064141975321802721152617946012331105353723221.P60
M (6,10M,18L,30L,46L,90M,138M,230M,414L,690L) 12421.45541.
.284746766418697641868038011821394285860323158881.P103
2074L (2,34M,122L) 8297.4674797.14475794101.9515330527620650472517.
.423082350292474675079511971763937.P215
M (34L,122M) 24889.67591661.19245413381.
.28507675395016426209379265459437.108418776698113814016172668034087889.
.29372667805516620161464001230063579445161.C160
2078L 4157.47577889.25782331522951529761073.507644488024787734242019373.
.144881493240241900269232403148013.C221
M (2) C313
2082L (6,694M) 6071113.42288273231097.920711247257749.56229065675693116237.
.23384866763414531770204088484887647243643341.
.6212208498791522443680860464057886551642074217423393.P58
M (2,694L) 8329.112429.1557337.592686737569.6867574890898053457.P164
2086L (2,14M,298L) 12517.33377.198857827144683169.
.1926620590033512371166117610796118373573.C203
M (14L,298M) C268
2090L (2,10L,22L,38L,110M,190M,418M) 6029645821.P207
M (10M,22M,38M,110L,190L,418L) 1414585500587719775570810281. C191
2094L (6,698M) 2065299637.40562442707197.9617687207378317.P171
M (2,698L) C211
2098L 4640777.83011968817. C299
M (2) 12590854756648551516684021495487769.
.1372098406910139347411473978297737029649599583843164650153.C224
2102L (2) 92489.2030533.207619855320079870004881. C282
M 1513441.77933753.120003217560112501.P286
2106L (2,18M,26L,54L,78M,162M,234L,702M) 511421041. C187
M (6,18L,26M,54M,78L,162L,234M,702L) 150937180544593.
.23640543396721742414157469.P156
2110L (10M,422M) 7313261.1060955698661.8207774689941937459483922881.P206
M (2,10L,422L) 274301.163031261.3518920881831461.
.7798241026129503827660037110146961.C191
2114L (14L,302L) 3646092601989001186525363589.
.46407610276467440780784332348683797989.P206
M (2,14M,302M) 4229.9817417.13093972249.252329098404058364830457653.
.1063976134790213153556087433.C198
2118L (2,706M) 1559123581453.80422923777405534042337. C178
M (6,706L) 27503548942141.2885299533969327285608778291701629.P165
2122L (2) 49459577.2308766446154677.P296
M 43497479736983828850647753.P294
2126L 4253.119057.2351357.118640804957.P294
M (2) 6262064969.51799226966893295289509.51114358532758153182876066459473.
.1603777152900827521607976402498110749.C219
2130L (6,10M,30L,142L,426M,710M) 4261.46861.149101.775548522986795641.
.14434789001414900976541.P116
M (2,10L,30M,142M,426L,710L) 8521.9883201.
.935670834191020341514842275817603083341.
.805863337960228852951520597182877664103305518701.P71
2134L (2,22L,194M) 819457.P284
M (22M,194L) 115237.8670835642148979210715595043749314093.P247
2138L (2) 25657.120995596673449.39769515373402823701741.
.25628302455269700936935750561.P252
M 9900693519731369541341.59623715903776666409686137682448042581.P263
2142L (6,14L,18L,34L,42M,102M,126L,238L,306L,714M)
94655375162339953175243922917053.1678012401109759349697111520625113.
.108843028104327227902725329813334696855127583727517.P58
M (2,14M,18M,34M,42L,102L,126M,238M,306M,714L) 4198321.
.1173210152850615113746646411514378486431017.P125
2146L (58M,74M) 5240533.1179926597.258921638441.6899099304599325137.
.57239645535728805815428122822079940261.C220
M (2,58L,74L) 10554029.17507069.4139856422575882915981.
.4686684675286165749065181429709237342620977.P226
2150L (2,10L,50M,86L,430M) 7480658401.P243
M (10M,50L,86M,430L) 4841801.8395496206695366401. C228
2154L (2,718M) 8193817.P210
M (6,718L) 4133482921.198349540321842343265473158857156629. C171
2158L (26M,166M) C296
M (2,26L,166L) 1281853.4683241262952304822589.1216869644819515145377777.
.47381176963830878991679264698384677605361866148570677.C193
2162L (46L,94L) 12973.1522049.10797029.777589754233.144244914186471029. C258
M (2,46M,94M) 84032617. C298
2166L (2,38L,114M,722M) 108301. C201
M (6,38M,114L,722L) 5716032168945734981112301013351337476653.P167
2170L (2,10L,14M,62M,70L,310L,434M) 156241.3670177421.
.147099130461475017366732184489051451254241.
.27563813842561828696274908802838620374187737481981.P111
M (10M,14L,62L,70M,310M,434L) 34721.399281.16999781.54627581.P192
2174L 18241890517.28221633169.4792343120992181.6215871883210370333. C273
M (2) 4349.182617.887735509. C309
2178L (6,18L,22M,66L,198M,242L,726M) 7692697.158914152241813.
.755084486042964623053695739861.P148
M (2,18M,22L,66M,198L,242M,726L) 4357.1028017.21366181.
.1057452633848904633973879093.P155
2182L (2) 13093.2305837815915297883997398826188721.P291
M 2070456161.1206850555657249.475989046121563895183917.
.115258068376444832585305884399965414081.C243
2186L (2) 13155349.8937940500670340895772341530892104386801. C282
M 4373.2680084093.7650524153545491153109.
.6929589945942729453900732599945559189623922821.C249
2190L (6,10M,30L,146L,438M,730M) 250975213261. C163
M (2,10L,30M,146M,438L,730L) 4890608660294663498626741.P148
2194L 4541645821.87894343384213957. C304
M (2) 114089.79321877.27244396967751097. C301
2198L (2,14M,314L) 4397.35062794955017836596752826831321813.
.2659583415856042053163877781991246706041.C205
M (14L,314M) 30773.3064013.P271
2202L (2,734M) 40201011439837.3831232706825413.374900727248428800313.
.4419878754512078812043658282978507879346813933.P126
M (6,734L) 7170258097.P210
2206L 132361.23687834930522629.1028852979752817834773.
.87406586033870225736205839978450806031138123181.C243
M (2) 525029.37191616185794836393.697490210515755486688501.
.165918875741241072476219693.C256
2210L (10M,26M,34L,130L,170M,442M) 9007961.59234660941.31795116701141.
.323741938065360073352861.P177
M (2,10L,26L,34M,130M,170L,442L) 113850361.4067383975981. C211
2214L (2,18M,54L,82M,246L,738M) 756004316065821564119228881. C190
M (6,18L,54M,82L,246M,738L) 36336169. C210
2218L (2) 13309.3828205897.6295438698503197.
.65811083601260126519272378671163489.
.23775104651520002290075356925975468138328933.P226
M 115337.884194242639628957.435014425521838380022061.
.31278302767943794898000377.C262
2222L (22M,202M) 17353692547269107417712398470333081.
.600642331003578944290343659354472393377.C228
M (2,22L,202L) 679933.10576721. C289
2226L (6,14L,42M,106M,318L,742M) C189
M (2,14M,42L,106L,318M,742L) 347257.286867892221.1057320723649.
.301319905573933.
.148717281078600592954890809105845136311220381815392153537512899309.P79
2230L (2,10L,446M) 16399421.87312813129989707389666674041. C232
M (10M,446L) 829561.1016881.81345941.74926147874622258725821. C225
2234L (2) 67021.250782329104747870229.280207617845230614289.P290
M 40213.71514809.P324
2238L (6,746M) 22381.29576255130269968537. C200
M (2,746L) 998556391921793032142257083493.
.8188933824660612984535850181113325193.C158
2242L (38M,118M) 12041422327407135159361.5152358624818762552412257.
.14614016452161183244796681977286357273.P231
M (2,38L,118L) 341851193.P307
2246L (2) 40429.7224113271397534157.358944225239163622577.
.78644877235130659233562697804336989000673.C253
M 4493.597437.1157722594009.5903190099601.24233759097340549. C288
2250L (2,10L,18M,30M,50M,90L,150L,250L,450M,750M)
106159498187859615558753969965866834587001.
.153697890198639256890056776055121330765387401741771753535238501.P78
M (6,10M,18L,30L,50L,90M,150M,250M,450L,750L) 1799059501.P172
2254L (14L,46L,98L,322L) 22541.108193.270889143560029.
.11969933001079298510777.C233
M (2,14M,46M,98M,322M) 10651266956177.2796521796509427468413.
.177440652731822006259181.P221
2258L 279811361.P332
M (2) 4517.31687253327909.845860743041780788841.
.3168961980027270675772903049581441.
.610169797505852063167912929664486129.P232
2262L (2,26L,58L,78M,174M,754M) 9049.153817.22203793.58775279454393529.
.14208184757236030311549684429380310906195952899285121.P117
M (6,26M,58M,78L,174L,754L) 2232143146107248761501297.P179
2266L (2,22L,206M) 13597.5791897.41143843577.
.10007965273275904867471368225133.C255
M (22M,206L) 90641.1319991045191762036137969.P278
2270L (10M,454M) 3979941061.341947385586795933429891244000271614659521.P221
M (2,10L,454L) 514854161.1852360842230441.
.11854787490285963159654548088590829070481.
.2044691460912167370853215631545447675578681.
.452657293021971150674100530241166787726245423457774561.P113
2274L (6,758M) 245593.P222
M (2,758L) 451942901656777.507017710250042219226541.P190
2278L (2,34M,134L) 82009.2924953.7198481.702133429141. C289
M (34L,134M) 57610621.1026114653093.83181322758949952160061.
.631752406641985228472509909599852426587093.C234
2282L (2,14M,326L) 13693.3340849.1999940237.5021162189.
.1422354638761439563699438766864657591445804014687977.P213
M (14L,326M) 8734996205489.254089910482240077841.
.193162081274292925141302977259421.P227
2286L (6,18L,254L,762M) 68581.30957013.24172568107332159475316053.
.36983739239549519680341811045815130322384077.P147
M (2,18M,254M,762L) 18289.662941.2977460232013.
.108100366556371396909757444126567223975830457614221.C155
2290L (10M,458M) 18967080721.P264
M (2,10L,458L) 9161. C272
2294L (2,62M,74L) 16631501.131289305624138998115419201.
.6020421565341196764351771487948767341068189537.P247
M (62L,74M) 18353.156129641.43944724736733414934459601. C287
2298L (2,766M) 2593247694731387242657.148540834333376678799373.P187
M (6,766L) 20895197788410280731804361141.
.3964735788677720595175372095990165341857.P162
2302L 78960215773801.1739229066659377.14315531938788851695592513. C293
M (2) 36833.58727643349.1332175582691632116991109.P307
2306L 152197.67796401.487690428661.375990376657230739677009027023959553.C287
M (2) 109361035361.1083060417437.1434915902261.8556491520780190213657.
.6313928863515514474051949065037.
.12096757810713964872647191792649783050645864949882197.P207
2310L (2,10L,14M,22L,30M,42L,66M,70L,110M,154L,210M,330L,462M,770M)
407861310781.3276541722830542321.
.2359740183446742670670667665744434142926705478881.P67
M (6,10M,14L,22M,30L,42M,66L,70M,110L,154M,210L,330M,462L,770L) 4621.
.46491061.1701142565107331378341.996393112075334929736912485201.P82
2314L (2,26L,178M) 9257.P315
M (26M,178L) 217517.14647621.
.2611399441339499373329885013353099860731957106781.P257
2318L (38M,122M) 27817.679697869.4375877471939948309.344099814953387082089.
.39099499295517164340521270869.C244
M (2,38L,122L) 4637.152989.580881529.1684427935189. C296
2322L (6,18L,54M,86M,258L,774M) 95851347301.37209645369951841.
.6496073174630179782608508433.P173
M (2,18M,54L,86L,258M,774L) 595788049.10635930289.
.201733784510995734472837.P186
2326L (2) 37217.37453253.1415424616664524411792669.157705304785160725584866573.
.3863307900732427143921088497557815126399849.P245
M 3402398369.12167709806945144034936348279437.P310
2330L (2,10L,466M) 15583496780908814321. C261
M (10M,466L) 511966974989795194817109952829201.
.8565602449358800368653873845874585921.C210
2334L (6,778M) 2319997.2973517.373755179958625706510646037. C194
M (2,778L) C235
2338L (14L,334L) 1122241.12586300846981.21713309717806393531167754789. C253
M (2,14M,334M) 14029.28057.254678341.P284
2342L (2) 13152673.2384970647060589977.P327
M C353
2346L (2,34M,46M,102L,138L,782M) 84457.1468398937.744513968035314938427361.C174
M (6,34L,46L,102M,138M,782L) 416806406641.
.293138785158765167527809171241.P172
2350L (10M,50L,94L,470M) 263201.347801.2431220465777752225890601.
.283401900451417872053764801.6911642791217739195898769605801.P185
M (2,10L,50M,94M,470L) 15012093905101.5216373323605901. C248
2354L (22M,214M) 103577. C314
M (2,22L,214L) 409597.5134243489.2696763541312061983157421198040561. C271
2358L (2,18M,262L,786M) 9433.3051253.78997717.
.7219830728950012537964607935512924568808193.P174
M (6,18L,262M,786L) 80173.29853437573848018732367754264926734261.
.1126022037855281940233176930855453903879451041.
.5140853648305217410902915102611320468253284273.
.247834521954635532745500626340983855795239624057.P55
2362L (2) 8071501966620134876289473357. C327
M 1369961.9178733.7493076529.74682436939657249341097.P310
2366L (14L,26M,182M,338L) 81058592161.6749423878264140893.P253
M (2,14M,26L,182L,338M) 14197.94190461.1591950268614161.P255
2370L (6,10M,30L,158L,474M,790M) 310358259241. C177
M (2,10L,30M,158M,474L,790L) 2678101.3655416608472669202278533979576601.
.230658857263260908581674881336118649784048916403796864221.P91
2374L (2) 9497.151937.19078157209.18049600319059487020771408069. C309
M 383215829.1401980222664869.P334
2378L (2,58L,82M) 71341.989249.19372762237.952283431069. C305
M (58M,82L) 409482089.15666418332748295461.19162921824083567371081.
.59678323107084643519889387415017.338256594766563257848839493358293.P223
2382L (6,794M) 986149.407144053973843038498648693671401041. C197
M (2,794L) 161977.2282227514761573. C219
2386L 55665356141.6192864263277076981.19276031365740866426115587917. C302
M (2) 293731580424649.1624203343961766495413.
.1412810444145553567161915193.P296
2390L (2,10L,478M) 19121.33461.219881. C273
M (10M,478L) 25864061833661.43833713434081. C260
2394L (2,14M,18M,38L,42L,114M,126M,266L,342L,798M) 4789.
.5180922000084027651331204969715053.P158
M (6,14L,18L,38M,42M,114L,126L,266M,342M,798L) 1140784093.
.1901948926639218135030537984965555424870038827309.
.345428744885875799564391656842707702747753419405737.P87
2398L (22M,218M) 23981.3995157450045997881205181480047421.P287
M (2,22L,218L) C326
2^{2h}+1=L.M, L=2^h-2^k+1, M=2^h+2^k+1, h=2k-1.
Table 2{+}(4k) Factorizations of 2^n+1, n=4k, n<=1200
n Prime Factors
4 17
8 257
12 (4) 241
16 65537
20 (4) 61681
24 (8) 97.673
28 (4) 15790321
32 641.6700417
36 (4,12) 433.38737
40 (8) 4278255361
44 (4) 353.2931542417
48 (16) 193.22253377
52 (4) 858001.308761441
56 (8) 5153.54410972897
60 (4,12,20) 4562284561
64 274177.67280421310721
68 (4) 17*.354689.2879347902817
72 (8,24) 577.487824887233
76 (4) 1217.148961.24517014940753
80 (16) 414721.44479210368001
84 (4,12,28) 3361.88959882481
88 (8) 229153.119782433.43872038849
92 (4) 291280009243618888211558641
96 (32) 18446744069414584321
100 (4,20) 401.340801.2787601.3173389601
104 (8) 78919881726271091143763623681
108 (4,12,36) 33975937.138991501037953
112 (16) 449.2689.183076097.358429848460993
116 (4) 59393.82280195167144119832390568177
120 (8,24,40) 394783681.46908728641
124 (4) 290657.3770202641.1141629180401976895873
128 59649589127497217.5704689200685129054721
132 (4,12,44) 7393.1761345169.98618273953
136 (8) 383521.2368179743873.373200722470799764577
140 (4,20,28) 84179842077657862011867889681
144 (16,48) 1153.6337.38941695937.278452876033
148 (4) 20988936657440586486151264256610222593863921
152 (8) 27361.69394460463940481.11699557817717358904481
156 (4,12,52) 84159375948762099254554456081
160 (32) 3602561.94455684953484563055991838558081
164 (4) 13121.8562191377.12243864122465612155106392056552353
168 (8,24,56) 2017.25629623713.1538595959564161
172 (4) 3855260977.64082150767423457.1425343275103126327372769
176 (16) 5304641.275509565477848842604777623828011666349761
180 (4,12,20,36,60) 168692292721.469775495062434961
184 (8) 43717618369.549675408461419937.3970299567472902879791777
188 (4) 1198107457.23592342593.4501946625921233.181352306852476069537
192 (64) 769.442499826945303593556473164314770689
196 (4,28) 7057.273617.1007441.375327457.1405628248417.364565561997841
200 (8,40) 1601.25601.82471201.432363203127002885506543172618401
204 (4,12,68) 8161.40932193.1467129352609.737539985835313
208 (16) 928513.18558466369.23877647873.21316654212673.715668470267111297
212 (4) 1692645313.10920513604018498900801.20946001591429012199281424246257
216 (8,24,72) 209924353.4261383649.24929060818265360451708193
220 (4,20,44) 109121.148721.3404676001.11035465708081.2546717317681681
224 (32) 167773885276849215533569.37414057161322375957408148834323969
228 (4,12,76) 90289.9036489073.29034057164920993379000074993
232 (8) 929.5569.8353.39594977.P50
236 (4) 1889.11329.84961.765373489.P49
240 (16,48,80) 23041.P35
244 (4) 977.37831175201.4889940029309876547089.P37
248 (8) 8929.P69
252 (4,12,28,36,84) 1009.21169.2627857.269389009.1475204679190128571777
256 1238926361552897.P62
260 (4,20,52) 42641.5746001.2400573761.65427463921.P27
264 (8,24,88) 16875081675650881.P32
268 (4) 75041.333808138537249.P61
272 (16) 5441.335631827046798245410603730138717057.P38
276 (4,12,92) 5770338946481798744593.P32
280 (8,40,56) 4481.557761.736961.P43
284 (4) 2273.1433633.P75
288 (32,96) 3457.816769.1562985901350085709953.P28
292 (4) 19602880710043505617.P68
296 (8) 80513.P82
300 (4,12,20,60,100) P49
304 (16) 7798338113.179781388993.84885296460737.643966863870017.
.27362254540091201.237157827243967596481
308 (4,28,44) 13553.74153335873.P58
312 (8,24,104) 4993.94849.P50
316 (4) 504337.994769.P83
320 (64) 286721.446960641.96645260801.3442404051886487041.P34
324 (4,12,36,108) 1297.3889.30433969.1164777409.3718266498433.
.134921168163073.1174029487714513
328 (8) 12239719573537.18093927039368350337.25394524415842506913.P45
332 (4) 11953.14767689550320172808742174828062347720350769.P52
336 (16,48,112) 47886721.P51
340 (4,20,68) 1361.12717361.1392971637361.8088220746627020943841.P33
344 (8) 4129.P98
348 (4,12,116) 82129.10389476529713761.59372021171164475019217.P24
352 (32) 1409.1258753.441995541378330835457.P67
356 (4) P106
360 (8,24,40,72,120) 8369281.P51
364 (4,28,52) 593914915675537.P72
368 (16) 76392570609857.1335570346574631363954390476479681.P59
372 (4,12,124) 1489.29761.22415398357688737.P49
376 (8) 3308801.3853249.487073399939357470433.
.163875530636702837695009.2673989784183378728255297.P30
380 (4,20,76) 3435950210316335724157758000789490561.P51
384 (128) 349621839326921795694385454593.P48
388 (4) 25507121.P109
392 (8,56) 3137.50177.101921.258721.P83
396 (4,12,36,44,132) 311712063697.P61
400 (16,80) 3399426377632056001.4850484222084371979240001.P54
404 (4) 4126631533969610752526181761.P93
408 (8,24,136) P78
412 (4) 454849.667441.40151873.52317884766401.142500609730433.P76
416 (32) 4940417.11342687617.P99
420 (4,12,20,28,60,84,140) 127681.1130641.755667361.P38
424 (8) 1697.P122
428 (4) 4209809.13012913.992005069953996722026755979686303668059315249.P69
432 (16,48,144) 68016300334849.P73
436 (4) 598193.35695338233523972669330604417.
.576694829762330794568961139476826913.P60
440 (8,40,88) 47521.89119361.127886114126296744221796660380215073025601.P43
444 (4,12,148) 92353.126097.532801.854257.85337232196804809313.P46
448 (64) 1489153.P110
452 (4) 9041.30500013280577.P118
456 (8,24,152) 1459574594862075553.320507768196690588004609.P46
460 (4,20,92) 254697295909573204954870539927521.P74
464 (16) 748264961.2245984577.239686663718401.15929619591127520827829953.
.6033312171721035031651315652130497.P44
468 (4,12,36,52,156) 1873.6440452782193.623293182848475361.P53
472 (8) 25342605037666235678081.P118
476 (4,28,68) 94994369.1580019259393.115846651946400929.
.2488196881582734135904733409191377.P45
480 (32,96,160) 26881.4855681.610548481.137603804161.P47
484 (4,44) 209089.33186913.1251287137.
.38608979869428210686559330362638245355335498797441.P61
488 (8) 1035817877926014488587133818491976759389034764353.P97
492 (4,12,164) 62966161.P89
496 (16) 5953.251969.19301855478655894221313.32206359010364528536290817.
.15624307475317816130204755452289007981717441.P45
500 (4,20,100) 4001.1074001.2020001.22624001.1481124532001.P85
504 (8,24,56,72,168) 34273.P83
508 (4) 3108961.17664039857.357319966758824298104849.
.3284305317126808646829056321.78829341974215087229120114369.P55
512 2424833.7455602825647884208337395736200454918783366342657.P99
516 (4,12,172) 328177.359137.52547670996812050561.
.7277473036504760410488618498577.P40
520 (8,40,104) 2081.19868746561.3377549010888001.7580827241843270677601.P65
524 (4) 1271332666556177.36441674155824796521521.
.88628235147538969385874281472055436801.P81
528 (16,48,176) 1632064897.190507963147393.
.44250674269198344200898981420091393.P39
532 (4,28,76) 1692116131441.139065006256539545729.P98
536 (8) 4289.311532723090035002320027134588551176448471666435989092897.P99
540 (4,12,20,36,60,108,180) 2161.21601.201519653761.1117180440577441.P53
544 (32) 15233.143617.443069456129.P134
548 (4) 38226289.15164972751718165538717288739219937057169.P116
552 (8,24,184) 267457249.P98
556 (4) 6673.77764617112817456421627629713.
.1716319040365034397790860195913303021663915471096474850983729.P74
560 (16,80,112) 16824641.86800001.40396092614384641.
.40809065233184155116161.P62
564 (4,12,188) 201777278450257.4409486883238989864703786561.
.38573092257178550307394862497.P41
568 (8) 14254355329.80377573236449.13425464222423304875744449.
.11091113376655556595890990679482099679181989410614081.P68
572 (4,44,52) 145143857.311195251370951377.
.1614501783881444871695814328568586673.P83
576 (64,192) 17047297.628582818817.P97
580 (4,20,116) 6961.9281.167859997042321.P113
584 (8) 32871186029052837857.79778881726281213651073.P131
588 (4,12,28,84,196) 84673.265549217634074770386573489863592827112366481.P52
592 (16) 31474859175390153735107856059776876864094488913562623409377402922304455233.P100
596 (4) P179
600 (8,24,40,120,200) 4801.55201.P88
604 (4) 2417.4363297.730685377.775168188161.P150
608 (32) 14593.671233.620066693671553.
.72957037607516225290419063617993856505649915307620690006389889.P87
612 (4,12,36,68,204) P116
616 (8,56,88) 29569.110881.P135
620 (4,20,124) 6338840521320763912823441.
.8972288213208726237756413079825557066213015494366305516001.P62
624 (16,48,208) 792584833.9155841480185089.P91
628 (4) 7537.118528721.262400181553.992000324534793042722401.
.20605715069815219132625364745038097331729.
.277433242225210532955711783957443819730099281.P56
632 (8) 286297736737.
.471211668918301561515489208246219513333426679953187468148445645729.P111
636 (4,12,212) 12721.239372593.208306541869009.971476396313002897.P81
640 (128) 3288416281349499632641.7771646317471635593256655841281.P102
644 (4,28,92) 53632321.508294185549580458441687901500833.
.187348880910146760908202953046841356170561257966417.P69
648 (8,24,72,216) 10369.259201.1824045366145909775041.
.524833094849624730914401.P76
652 (4) 2609.10433.1322257.28322881.P175
656 (16) 7873.47402561.591100350038949953.1668576469005068046209.
.506060190832207779694850270816882633281.P104
660 (4,12,20,44,60,132,220) 14736481.514210163281.
.649817602852289358605542163521.P48
664 (8) 3508428556083287152033.P176
668 (4) 482851777.670297921.375283446486344365461807838534613233.P147
672 (32,96,224) 494968321.663239809.
.2925384400770993343049563645260155764299463512577.P50
676 (4,52) 210913.47925697.455986337.178077806451169.P152
680 (8,40,136) 496304801.10008321601.33910825580641.
.10146032011084172688350401.18741457027056199460701768016571521.P63
684 (4,12,36,76,228) 12407761.1953842221288628908086845073520488081169.P84
688 (16) 2753.1755145793.18090206003620308180353.
.3374493964203314716755629762689.
.77411329907915702977897669886203158137376728020417.P87
692 (4) P208
696 (8,24,232) 75169.1185335329.2175937261441.3945720769057.
.43420756732422994369.247716071005295731527406385377.P47
700 (4,20,28,100,140) 2801.P142
704 (64) 60299259845689822028046342401.
.3210843755324367119258027752661239735297.P125
708 (4,12,236) 95646885844433203176775508160481.P108
712 (8) 290497.59170049.9497407873.1334056289569.
.25222813432549907120203219752470337287201.P137
716 (4) 94513.10240246321.6249618890312649605712432659622854257.
.22562882829685667659941188646849469227356664645922433.P111
720 (16,48,80,144,240) 37441.170251201.322029272318997936286081.P80
724 (4) 2897.304081.558786628009681.148643100302189793374401.
.3289754668487801751212109418730038529.P134
728 (8,56,104) 145601.9828001.32038310825249.P148
732 (4,12,244) P145
736 (32) 3689800577.6699561451777.428895600365702401.2581126261168515842568515186820240654583079937025463189245875897945938699497995409153.P88
740 (4,20,148) 174463386657191516033932614401.P145
744 (8,24,248) 91556187016478788158721.
.2295529738871686782981597056268590225067747577438438859809.P65
748 (4,44,68) 738395681.16998871173904049.
.199431288499235121583168837778864679060668081.P124
752 (16) 4087873.4810716907835700161.P197
756 (4,12,28,36,84,108,252) P131
760 (8,40,152) 3041.477822284525893121.
.162956550683997466131743371152980332553159745243749491445921.P94
764 (4) 827467009.264476244523458034906978299417485309897059948654792106081.
.2695155945030251018331662354179230226777032634005050325012294828756577662449.P88
768 (256) 212780015855109121.2220842644284984664160257.
.1796602923899342630768062019504577056782884736988571649.P59
772 (4) 43464340002838801.61138085212831760012082560001130966245067663049594184076112874904437731971413080237731822785297556226950049.P108
776 (8) 782209.372454540993.2125457487809.20468009784290989308737. C180
780 (4,12,20,52,60,156,260) 1928161.
.166668825096179161138307580471434399036535876481.P63
784 (16,112) 689921.66308056470365249.P180
788 (4) 72497.3050841968833. C219
792 (8,24,72,88,264) 3169.3665377.12925441.52386049.P120
796 (4) 8214796852906477415899530941807101361.P202
800 (32,160) P193
804 (4,12,268) 209898673.6925799047681.29493338799546784993.
.133304540580175280319733184641.P90
808 (8) 203617.P236
812 (4,28,116) 562943995510177.15902347075274017.
.116248663016701150509115828530608561.P137
816 (16,48,272) 959617.597149752187286607489.47192818771332809681089.
.48734995441023943825153659548266541432641.P65
820 (4,20,164) 141041.11109333761.210085224303959163308751601.
.3017866802599074997815107329034839893699457097851521650341414241.P88
824 (8) 19777.88993.38525979266360291610293571395929675314692801. C193
828 (4,12,36,92,276) 1523521.257952400029937.P139
832 (64) 3329. C228
836 (4,44,76) 2368822395648721.3040124117151617.
.1128504950062383934670257.C162
840 (8,24,40,56,120,168,280) 13441.4841172001.1586308510081.P90
844 (4) 91185761.P245
848 (16) 528209783809.3408818505565834978224383921527937.P206
852 (4,12,284) 13633.31141397544886408722636686759644216932367969.P121
856 (8) 1489441.229634869879668984791701633. C223
860 (4,20,172) 557281. C197
864 (32,96,288) 1718990209.8148919324033.
.672915391135935402269916482777538049.P116
868 (4,28,124) 334853569.71153008417.15174698834406721.922626543715132033.
.1042949211954459511633.P143
872 (8) 17547835073985096343806660481.P232
876 (4,12,292) 45553.52561.241378644784282665724224215269676274193.P126
880 (16,80,176) 32655041.374871146580481.36589369917525430721.
.212669637382198127520411474271156481.P116
884 (4,52,68) 17681.572833.3327377.5882010302757468387457.
.507503808182829478517537.1521590246367016260256977648481.
.9490550620859983699756004482528532989220017.
.459988434780718651547146575150088880586568119521.P49
888 (8,24,296) 1079809.1174047124321.
.129887637532703885175569346500164339384596481.P112
892 (4) 267601.1391521.1345517777.P247
896 (128) 10753.48919385089.39257233394241687553.
.328516339886958171419482857961643272193.
.12914340854285079433782775726161803964147713.
.77338582801985556033595814340666648061420033.P72
900 (4,12,20,36,60,100,180,300)
5807380901690048305970962748462547129404401.P102
904 (8) 3617.65089. C262
908 (4) 83537. C268
912 (16,48,304) 32833.299137.174535138510980012221761.
.107464447084600919847454485663361.P109
916 (4) 24060283912401409.
.9176027840820822557769652003161198049458738352529.P210
920 (8,40,184) 18401.66083546765982085951180190942752889927681.P167
924 (4,12,28,44,84,132,308) 3697.1027489.97374817.39522602650168177.P111
928 (32) 189546985765489533095169829108497477761.
.4971141705173876156149290559555016352907777.
.37655062972389867990357372885125574412752388332039169.P137
932 (4) 74561.85458417577408481.
.24702666841918364091482253393576619555300632286283423601713.C200
936 (8,24,72,104,312) 26391457.54573491387218500862753537.
.174989678972338341728544129375449953.P105
940 (4,20,188) 13885681.56287943657879761.P198
944 (16) 33803203708913089579238660220728641.P245
948 (4,12,316) 3793.2707489.P178
952 (8,56,136) P232
956 (4) 765459043457.8806289643641483412983387861556412577. C238
960 (64,192,320) 49921.P150
964 (4) 1602657713.442593060923913234007268894869422114481.
.23623969993379158557066131313305487489116369.C198
968 (8,88) 30977.2555521.204452543956321.5588918964965108257.
.3254976976165960099872801486011429794721.P182
972 (4,12,36,108,324) 26232337.13655624113.
.1581214773543289355763694808184205062516817.P136
976 (16) 361526017.21251836487537653646842236161.P253
980 (4,20,28,140,196) 7841.35281.141121.4653041.60893281.4387897103521.C162
984 (8,24,328) 349107457.628217089.30220180022953160453457856387777914721.
.738313998235889565301599572531640626810525425999201.P87
988 (4,52,76) 189697.167659649.1482371489.6450973392449.9931868988289. C212
992 (32) 5201080300033.3085397990461441.53497190411184131713.
.243889001786361258243254488269457409.P206
996 (4,12,332) P198
1000 (8,40,200) 76001.42144001.293543676001. C217
1004 (4) P302
1008 (16,48,112,144,336) 423319681.494077391563970390335488001.
.7201935329692363728844274296784241409.
.1006545610655423007817780018765739801419395841.P57
1012 (4,44,92) 14405614244209.924278616131729.3693169819477873192220694097.
.120332962388310414552825393007131887467525410881.C163
1016 (8) 131101681409.53428165972513.8431309118401633.581367694924545281.
.313033168856062878953819009.P219
1020 (4,12,20,60,68,204,340) 171664686650370481.1230412270786066204321.P116
1024 45592577.6487031809.4659775785220018543264560743076778192897.P252
1028 (4) 2685107860437307121.266473139971248960398417.
.39268438158946581131254913.C241
1032 (8,24,344) 242193739165634585377.702389334730574219713.
.13298428572991424840707017555082369.
.3662668785050561460441277306761003321502356238369.P79
1036 (4,28,148) 136753.16208182530992884848445503478656332461639153. C212
1040 (16,80,208) 201219077319973441.1493088790381629762730439505281. C184
1044 (4,12,36,116,348) 11514589201.10094533349991037489.
.337138190889530707009.
.25582121116971797723434440295709382794690160485178612721.P98
1048 (8) 1211489.45529313.454261889.410515107056935291714767361.
.5546025484206613872527377154544456740766039233.P219
1052 (4) 22625271329336833. C300
1056 (32,96,352) 155852929.15747624837121.46714408868623938817.
.3046044023647117265076766795424257.P119
1060 (4,20,212) 4241.22625755121.378827137612775441.
.23678936375488328669921.P197
1064 (8,56,152) 3404801.35868448673.477170373761089.7802057668861532450977.
.1053871639906983063115212651361.4708253967270778823533486411429633.9641617775435904042941328754047791354041387354346049144727138420456673.P73
1068 (4,12,356) C212
1072 (16) 107201.5028065709856661529105121236692752636100161. C271
1076 (4) 4037153.4326200033.707374699665617.208611133232063053649.
.10342980458599601976190587017511281.C238
1080 (8,24,40,72,120,216,360) 6281281.148759201.4518776161.
.30263419164953868175425499201.P121
1084 (4) 4337.13009. C318
1088 (64) 544001.76138241.19632633765734319603254407700647195022608373249.P249
1092 (4,12,28,52,84,156,364) 26209.279553.404284148686608554495041.
.1580204575585229261365153.
.69864226063509680379988083391904586415696439739773112049.P60
1096 (8) 457024161409.63074817527233.1188755858465841569.P284
1100 (4,20,44,100,220) 567601.277173601.333742931196401. C213
1104 (16,48,368) 26497. C208
1108 (4) 13297.476041121.2550041661553.
.7910906581519939367772674324430352577.C271
1112 (8) 934309676929.P321
1116 (4,12,36,124,372) 1093681.P211
1120 (32,160,224) 8539067456641.101750737670401.1146946484544001.
.5344315494149074932607669859871361.
.43824827636716143409491817541084379878753281.P112
1124 (4) 205107521.1496800817300278753. C311
1128 (8,24,376) 1078369.7341898433044801. C200
1132 (4) 275814838289.362073730366785443780868881.P302
1136 (16) 9168689293924594269435012699390053650369. C298
1140 (4,12,20,60,76,228,380) 4561.P170
1144 (8,88,104) 25744577.377140193. C274
1148 (4,28,164) 30645407522290070293105505369518259537.P252
1152 (128,384) 18433.27733723987969.87706468640521797294901519524699649.
.24616619374763459476215125737554777509377.
.154271541316301150598792104029544235059675368229377.P88
1156 (4,68) 17*.41617.295937.83736716905921.31148444724976529.
.2428691128313288513.P268
1160 (8,40,232) 977403570406117601.841464143582829714489281.
.57281536092725157009193935521.P200
1164 (4,12,388) 5106360913.265523238370190187626688601808496584295502513.P178
1168 (16) 4673.1137948235396559809. C326
1172 (4) 9377.1345457.91433799750097436823339479719705770866646653617. C295
1176 (8,24,56,168,392) 3040410389842561.5091542821206332688289.
.21566694047156190030012960957098417375263164101421409.P113
1180 (4,20,236) 89681.141601.1250801.13083841.106827761. C249
1184 (32) 9473.1202741777537.414581855009107748596797028667339521.P296
1188 (4,12,36,44,108,132,396) 427681.59008134786334273. C195
1192 (8) 255373980342366346612993.P334
1196 (4,52,92) 38273.14536633697.36919357139916161.
.14755410932634657950998395089.1757744807679263833464910204577.
.122255024596887310384016956082161.C197
1200 (16,48,80,240,400) 9601.57601.17963653814841601.P168
Table 3- Factorizations of 3^n-1, n odd, n<600
n Prime Factors
1 2
3 (1) 13
5 (1) 11.11
7 (1) 1093
9 (1,3) 757
11 (1) 23.3851
13 (1) 797161
15 (1,3,5) 4561
17 (1) 1871.34511
19 (1) 1597.363889
21 (1,3,7) 368089
23 (1) 47.1001523179
25 (1,5) 8951.391151
27 (1,3,9) 109.433.8209
29 (1) 59.28537.20381027
31 (1) 683.102673.4404047
33 (1,3,11) 2413941289
35 (1,5,7) 71.2664097031
37 (1) 13097927.17189128703
39 (1,3,13) 13*.313.6553.7333
41 (1) 83.2526913.86950696619
43 (1) 431.380808546861411923
45 (1,3,5,9,15) 181.1621.927001
47 (1) 1223.21997.5112661.96656723
49 (1,7) 491.4019.8233.51157.131713
51 (1,3,17) 12853.99810171997
53 (1) 107.24169.3747607031112307667
55 (1,5,11) 11*.1321.560088668384411
57 (1,3,19) 229.248749.1824179209
59 (1) 14425532687.489769993189671059
61 (1) 603901.105293313660391861035901
63 (1,3,7,9,21) 144542918285300809
65 (1,5,13) 131.3701101.110133112994711
67 (1) 221101.441019876741.475384700124973
69 (1,3,23) 277.2461243576713869557
71 (1) 3754733257489862401973357979128773
73 (1) 11243.20149.15768033143.9460375336977361
75 (1,3,5,15,25) 601.9601.2098303812601
77 (1,7,11) 51457561.7151459701.76831835389
79 (1) 432853009.392038110671.145171177264407947
81 (1,3,9,27) 3889.1190701.12557612956332313
83 (1) 167.12119.1036745531.950996059627210897943351
85 (1,5,17) 2663568851051.862970652262943171
87 (1,3,29) 74821.32234893.150224123975857
89 (1) 179.1611479891519807.5042939439565996049162197
91 (1,7,13) 4011586307.3745603812007166116831643
93 (1,3,31) 1117.26273701844015319144827917
95 (1,5,19) 191.78958087694609321439660131899631
97 (1) 76631.2549755542947.48845962828028421155731228333
99 (1,3,9,11,33) 3186217.12812432238302009985937
101 (1) 33034273.465092326319.50316775668019759306202964023
103 (1) 6957596529882152968992225251835887181478451547013
105 (1,3,5,7,15,21,35) 421.6301.1616161.26751945361
107 (1) 50077.229837.48965028505045123993421250406516036571557
109 (1) 1091.521402591.3499901929.239789806103.10624346875389299603
111 (1,3,37) 18702169.119779213.6962353413269964253
113 (1) 227.1583.2172539.526256453012063980796131127321354599535039
115 (1,5,23) 1975931.6273542442241.52370346649565455417091
117 (1,3,9,13,39) 4162861.1846794457.2821964307371847613
119 (1,7,17) 239.44626806191326911791.397881837642577477902049
121 (1,11) 11617.3981923614021.657890411545272648205502849240259841
123 (1,3,41) 51169.1999827817517387044561568810795329
125 (1,5,25) 251.358291751.14781691751.391632555001.989947158849251
127 (1) 5843.681229.21520151.76082653.301515315752300874236564235591357673
129 (1,3,43) 4129.2199072289.912851565662857110894244969
131 (1) 263.605199588591144003100881306574406851660288427740394885828171
133 (1,7,19) 8757948941961838067.257513776243156826379279929309507
135 (1,3,5,9,15,27,45) 541.53825041.773618132427345151923061
137 (1) 4933.217629707.108081809773839995188256800499141543684393035450350551
139 (1) 1669.5430731.P57
141 (1,3,47) 161969595577.2031161085853.165301473942399079669
143 (1,11,13) P58
145 (1,5,29) P54
147 (1,3,7,21,49) 47041.P36
149 (1) 7451.177941761.P59
151 (1) 1511.6263783.64745079361.P51
153 (1,3,9,17,51) 6213394261.35106034213.P26
155 (1,5,31) 311.3586225081.P46
157 (1) 9421.3381925092493.9891109125337566719.P40
159 (1,3,53) 712550912937217.P35
161 (1,7,23) P63
163 (1) 5227348213873.8882811705390167.P49
165 (1,3,5,11,15,33,55) 50821.P34
167 (1) 58451.88177.1767863.10063060897082377.P48
169 (1,13) 2029.163264150141.P60
171 (1,3,9,19,57) 119701.P47
173 (1) 347.762239.2125048865543.P62
175 (1,5,7,25,35) 109201.1430128198787051.P38
177 (1,3,59) 709.2224898159852613649.P34
179 (1) 359.56207.100957.19510643.291066066130451.6779963644378513811.P33
181 (1) 90863.890159.P76
183 (1,3,61) 733.97806913.2421854958301.P34
185 (1,5,37) 2221.17761.35521.146891.228082801.49804972211.
.87841814842081.1654235911196704741
187 (1,11,17) 6359.1272753542934479.3411926755457243.P42
189 (1,3,7,9,21,27,63) 49888641454623789553.P32
191 (1) 383.311713.9593931911.P73
193 (1) 6563.29723.2346066378779.218246094772601642186973037.P45
195 (1,3,5,13,15,39,65) 2341.39838501.P35
197 (1) 9851.741019334164502879.11472574961994477441469621.P47
199 (1) 1360648969.293366430131930353811221418233.P57
201 (1,3,67) 1089421.P57
203 (1,7,29) 2843.735673.P71
205 (1,5,41) 6971.31981.P68
207 (1,3,9,23,69) 829.1657.4969.P54
209 (1,11,19) 419.2927.99381983898121.340838185560681043030809047.P40
211 (1) 2111.962188370639.54046656969013.5676687374958905209.
.1695949409060064182746451.P29
213 (1,3,71) 5113.22716867932413.115264393627813.3613512804721129.
.89665588664737776553
215 (1,5,43) 8477881.14491125481091320910774351.P48
217 (1,7,31) 20399.24040333283.20545698698839917414079969.P46
219 (1,3,73) 135781.P64
221 (1,13,17) 443.P89
223 (1) 54473097204950819531444809.P81
225 (1,3,5,9,15,25,45,75) 116101.875701.286870274711101.
.515009259868501.119634969443826601
227 (1) 19907051929.86695423725589885803695742296342497463.P60
229 (1) 8047106008391.32356561399076305309.284663996630519253661.
.634538541879036040523.P36
231 (1,3,7,11,21,33,77) 3697.73155606217.P43
233 (1) 467.27599172691870182517.6354979252162209284471.
.38247482016765032274959.P45
235 (1,5,47) 5171.11321831.1287586151.30168205545535224185322498361.P40
237 (1,3,79) 37520893.52802131282482966001751707837.P38
239 (1) 479.17209.43301964055635533333945745533106128044213.P67
241 (1) 553788718707122198751861425724478919.P79
243 (1,3,9,27,81) 70957.6627097.21835473162448454819220238921.P38
245 (1,5,7,35,49) 32341.P76
247 (1,13,19) 14327.50427403417.85336889516918333646696709.P63
249 (1,3,83) 35882730354181.P65
251 (1) 503.5894996162509148852365257446042626007.P80
253 (1,11,23) 23*.38636905168680714294388463.P78
255 (1,3,5,15,17,51,85) P62
257 (1) 120277.1329772662933524112502310453951741137.P82
259 (1,7,37) 2591.18131.P96
261 (1,3,9,29,87) P81
263 (1) 53653.78901.2750510656513.65397307474141.153572905037740933.
.352436749324038579121.P52
265 (1,5,53) 3181.18474777940736174884324451.3449313707942322494318140511.P43
267 (1,3,89) 850666273.2270061722000879968839976583683542421.P39
269 (1) 10223.262007.116075653.76305384036997.299470647963251.P83
271 (1) 3253.8916443.490543245624181.2709600825365281117.P86
273 (1,3,7,13,21,39,91) 30577.1636991658121.2148920356182437964673.P31
275 (1,5,11,25,55) 121083372541491664042201.P73
277 (1) 15801743.478803193369.P113
279 (1,3,9,31,93) P86
281 (1) 563.3373.422063.434989.1000081249.38012519036699.
.124205327610431.543615007915184215523.2397212236344676495763.P38
283 (1) 133227911.1830824353.306487563493.1257602943398454563.P88
285 (1,3,5,15,19,57,95) 5731756981.P60
287 (1,7,41) P115
289 (1,17) 44507.1088953.P120
291 (1,3,97) 189733.1693621.80640757.184812684901540537.P55
293 (1) 587.64911612051881874971.P117
295 (1,5,59) 739861.311834125441.1243704975397142761851514391.
.15800757982738113728531939755751.P35
297 (1,3,9,11,27,33,99) 1182737161.7899901813.370231459035769.P53
299 (1,13,23) 599.10997221.2886381073947332989.8661965714512154562493.P76
301 (1,7,43) 8127001.921928537909.31575110690775101163983809.
.2954696283347370339434959009.P49
303 (1,3,101) 1213.464114346100971670261030354878981449019613.P51
305 (1,5,61) 65881.4919054377091.
.46229214937048975901175732207117334435811.P57
307 (1) 10610542242923144869.1209358403350153553775181.P104
309 (1,3,103) 1237.16069.P90
311 (1) 3733.12460588823.873069502041694941443.
.2241207330424850668586082361185081412667449.P72
313 (1) 2370037.3759897752153653302941126019779.
.2714675534408576046409316982151068303918417599.P67
315 (1,3,5,7,9,15,21,35,45,63,105) 1571221.P63
317 (1) 3493595928049.199057440042898163364095413.P113
319 (1,11,29) 3191.113164935467.26425387421490471188793734763177943613329.P79
321 (1,3,107) 3853.6421.1276775957917.P82
323 (1,17,19) 647.1600789.39039719.29134285181591.P108
325 (1,5,13,25,65) 217520261488056211634951.
.27612401161496267925537524217847751.P57
327 (1,3,109) 122953.1340701.55471745029.
.714322353831283890903559265735120995717.P43
329 (1,7,47) 659.16451.94041956807.P114
331 (1) 1581832451.16312845121.
.530654464353667468092169451245888744365152829791.P91
333 (1,3,9,37,111) 1179099721.2628354173876461837.P76
335 (1,5,67) 2791110259168381.P111
337 (1) 8089.338861091937.736092762241.P134
339 (1,3,113) 51017244973.283274887324515433.P79
341 (1,11,31) 4093.9484546040170844481070590623.P112
343 (1,7,49) 24697.385540919.4551588049.8465728310029191083.
.23451446896560788630183.32312015265609073916797.P54
345 (1,3,5,15,23,69,115) 1381.9661.31741.6784081.76675561.P58
347 (1) 291481.1150057146229.185498348145073.328003153456707623.
.20912010800475074747.33844448484642846054095202148071217.P63
349 (1) 94042850889984510998289152320438541798532018021653956283741193211654025280185459.P87
351 (1,3,9,13,27,39,117) 244297.503457454452889.P83
353 (1) 509027.4088777503007.P150
355 (1,5,71) 734346611.66824157595186257988571.P102
357 (1,3,7,17,21,51,119) 20001459491011594009.P73
359 (1) 719.169998846011.470920899227107034926837.
.41996290825582863451929997.278252468335029499500820080150443.P76
361 (1,19) 103969.930643561.1544679802763873663.
.212442076518129661950839.675873510595715629396212612371.P78
363 (1,3,11,33,121) 1453.49369.312284816501197.46007931271317089317.
.1377783168921566387641.P42
365 (1,5,73) 1030031.1472874512323892527561.
.154738943915325955520331463109617606098450974126281.P60
367 (1) 11665463.667804211.137673218986445617.189120585817572803.
.41234466042798529583.
.1511495257840070716998865694022937935039928231350493.P54
369 (1,3,9,41,123) 1767210188478589.P100
371 (1,7,53) 743.18485797607002442471500555321.
.17177672994159234619140207492038707631055212708408339.P66
373 (1) 2985102182914331046162839597551944594782446234875693326246633144966957389.P106
375 (1,3,5,15,25,75,125) 8788416011598893375808561717543001280896024501.P50
377 (1,13,29) 4338169506098819.1726610752347421021849.P124
379 (1) 210917324869.1518049814692403.
.2011339669987253732917345076957200061377270925662226533.P100
381 (1,3,127) 597409.2896724388952980361.P96
383 (1) 23747.2835733.263172186419.428039526143.999607767985979.
.1085363716480624115399141696533.P104
385 (1,5,7,11,35,55,77) 225611.868561.
.10758904556355084920587039558086313081.P67
387 (1,3,9,43,129) 308842594561.269123363760531549673.P89
389 (1) 51349.19404514058063.
.15573016748048048503912224242515798000782107281721099399054521.P107
391 (1,17,23) 17987.94214579.2837442021361921.1136310624674027548741.
.1720132331768569247939.72643760507536226775553.
.947813454284697545292967550627029.P42
393 (1,3,131) 2083574227432941258356498327796750385623056105089493677.P70
395 (1,5,79) 5531.231040361073709413931057501.6434943291436769366927146921.
.15726644297407162541884251721.5478828409328216056558228587181.P32
397 (1) 366829.2233523.163396728220907574918050165329759467394476719555940685707819382394752434296939.P100
399 (1,3,7,19,21,57,133) 49279693.1068595417.89076199828580322541.P67
401 (1) 90932896832200086926891164728383761.
.5865500973936060729431154988451238023.P120
403 (1,13,31) 121674645534469.14392455313096812239313539411.P130
405 (1,3,5,9,15,27,45,81,135) 155521.285121.2820618974881.P80
407 (1,11,37) 18354073.1862400449807666627.P147
409 (1) 20720759.145724851390704755159.149201935333301250525828683.P142
411 (1,3,137) 2115829.634432753.685934341.
.113938829134880224954142892526477.P74
413 (1,7,59) 827.4957.48301177.366438032528092142507.
.3721114359214874154231319889680078283.
.37698754823547437188883025448675820051387027651.P48
415 (1,5,83) 363541.1333811.223210122334888198292034419263747875011.P107
417 (1,3,139) 43302949.2016598657.201360112381724767096677592621.P86
419 (1) 839.596113491371.2151506053058735838822709777.
.654885891476141016165461375447.1593204794095231348491880857761413.
.496097134087521646396618935298341361.P59
421 (1) 1206587.6804488281.129208238531.30289645235740564742379791.
.4635694062476599636809044531.10722271475553804482227981559844589.P87
423 (1,3,9,47,141) 55837.57529.27115993.35675821.P108
425 (1,5,17,25,85) 49354957842491569509980274834655501.
.445538977312957153485923190322961189401.P80
427 (1,7,61) 98386025627.562686760931.84404570448444086183953.
.3556068841871225054499505739.P99
429 (1,3,11,13,33,39,143) 2175889.64139087689249.103304599144666396621.P75
431 (1) 863.31033.5327475339364876749276709275805059852090562839012167.P147
433 (1) 218233.7945316512501413421855357.6152250713758461148996890901.
.3336469615060863393363305195427888169.P112
435 (1,3,5,15,29,87,145) 34118036879281.221485711052594564349712441.P68
437 (1,19,23) 4400140239259780643.15627149386345831933.
.76907777590720989373489360682236534152419285175538746028263539.P90
439 (1) 32983465912566571821412548179.P181
441 (1,3,7,9,21,49,63,147) 2204277929951182849.
.407888431426111186599600583446287711634101230416829.P52
443 (1) 887.298583.44457709.213177803.39035565972229475013089333692179660570470638499946800742936602098518439852516325639.P105
445 (1,5,89) 477126751861.2912333801178961.P141
447 (1,3,149) 17881.P137
449 (1) 14112071.88173395548188366438189921318359.
.430763314083559275178358410713636609779704909657.P128
451 (1,11,41) 47807.6704567.5295342260891.
.9183412117682309234428195579372695474479792771904536038283293309153.P100
453 (1,3,151) 2689557037.20851551949.8824691215488669109.
.2210252986790978093597221.P80
455 (1,5,7,13,35,65,91) 911.386134706231.2478098909059595945200318151.
.1435809872133506127696992748549282318301.P57
457 (1) 176540143789.10976741555411.790112768389761097.
.44526916528666152642757247913322427.P141
459 (1,3,9,17,27,51,153) 3673.230736771829.889501314241.
.11786772814775877294179029.122217754676326531200106433310349.P54
461 (1) 11987.118164568780375261.
.1203473922272303966282236445337792145487543.
.1869566096395282675969776108567405541557601722844515411421.P100
463 (1) 11113.83341.155569.1767202459333.P195
465 (1,3,5,15,31,93,155) 146941.4307761.6184582891232396881.P85
467 (1) 27836167022857.P210
469 (1,7,67) 1306456857231927329331341682365113787.P153
471 (1,3,157) 95232991961590105161615580822336892311998189163571236402837.P90
473 (1,11,43) 947.1815542308537.1261183235795048844037.
.201972084490941146836006403755873.P132
475 (1,5,19,25,95) 2057701.4490080243969653901.P147
477 (1,3,9,53,159) 39365302681.954458120492216837136711901.P112
479 (1) 2017549.52133736060349.257620598280719473.
.10332092185328194888766505728921146249.P154
481 (1,13,37) 709957.772164427380203166258004598008121532652933.P159
483 (1,3,7,21,23,69,161) 696032619727190918566594730968478467309.P88
485 (1,5,97) 971.145501.22836387874896451734446934241.
.163135411964857917127880147033711.P115
487 (1) 12364016389.870250716374636481172397688250744935344421236524471557980004227913123906687196026086432880299.P130
489 (1,3,163) 107581.P150
491 (1) 983.24551.844124016018569089.155447385335258570051.P189
493 (1,17,29) 135769072957854733.
.24461879114558805437371311641297107167592931037239137.P145
495 (1,3,5,9,11,15,33,45,55,99,165) 35669701.
.37073055770742955860149669357943581889942083408919721.P55
497 (1,7,71) 3984424151.432547838166529.1309567972706389369.
.428692823469180744251.13872998573921896220953.
.785010913523701739507985671014620709.P80
499 (1) 1919016277.716332093275045781.114551315779689543877.
.32242867762626707702019834661.1242829528432779408196747984311772979.P126
501 (1,3,167) 218437.4769521.777324624268955461.12015367658187607573.P110
503 (1) 7043.12073.30311006351.41692265961952424506975231211.P193
505 (1,5,101) 205031.3732938536661701.
.276878587446880592989075966008807841.P135
507 (1,3,13,39,169) 13*.2624233.580460684077.13956160423453.
.5242148588473376340853.P95
509 (1) 1019.7127.54973.97729.14495303.324927277.
.59561824373572167761652488341.
.1408323592065265621229603282020508687.P146
511 (1,7,73) 16347913.2429424817.2126913191482456609.P172
513 (1,3,9,19,27,57,171) P155
515 (1,5,103) 1031.13904017381.
.81390061154901040915047190963509493467072953179621.P132
517 (1,11,47) 18121754584561.11564421035953127.
.195823481748025157463422904654781.
.439353102824911497759602166124705290731.P120
519 (1,3,173) 4153.78539233.5907694552891069.P137
521 (1) 394004822498482103.1113152871547083276871904557.P204
523 (1) 8321977.4613832781. C233
525 (1,3,5,7,15,21,25,35,75,105,175) 81901.2181094346193283895070901.P86
527 (1,17,31) 592116121.60805701944219890543261.
.35323611400399730994438310886415603767.C160
529 (1,23) 259211. C237
531 (1,3,9,59,177) 3030949.318413423593.52482008124253.
.179197588057109824392880988379522349.P100
533 (1,13,41) 218531.13847341.1930037901921949. C202
535 (1,5,107) 5351.18191.467591.12476029871.1357991694228074281.P161
537 (1,3,179) 4297.749352523284764318713.8568932552695444750981.
.475397205540953687028104590513677195842929.P82
539 (1,7,11,49,77) 20483.
.20179225620456881076565285297998895427104238023763.P147
541 (1) P258
543 (1,3,181) 926328015235949414291418541.
.463363430282411974100538913890658610885126169932893.P94
545 (1,5,109) 4186691.35190503941.84366737811375632628503563923652151.
.99797555942653388706432640777540240541708135578117354589424604772651.P86
547 (1) 30706393.558494059583. C242
549 (1,3,9,61,183) 7121629.
.220257342188626832493266960690843824669780354485938649638296830097.P100
551 (1,19,29) 1103. C238
553 (1,7,79) 317093519.240780364415138273081833.
.87342335082383885287816699213.C163
555 (1,3,5,15,37,111,185) 3867972842907961.
.2802413728088191273163920691908084325126644440764112648781.P65
557 (1) 876719.738062910427842529349814970162431779.
.31212257157054463252180370125069868081029.P184
559 (1,13,43) 5591.363424907.246489783634693.2335335318506881393.
.481462259966792434510742876635621.
.547743001660321354161077319158425694627.
.5564687761959436217109524353035918465205794740817325357931.P67
561 (1,3,11,17,33,51,187) 462734945368154372497.P133
563 (1) 14639.833967397.3232624393.2417050476241.
.41052191913815517786897602917577867.C199
565 (1,5,113) 44584191057421.25980807832750689658262178521983417527371.C160
567 (1,3,7,9,21,27,63,81,189) 26369913549996278516269.
.45111196029657508252387343389.
.48750358213862475070428657195079499092364689.P60
569 (1) 677111.171320564838201511904772549355954093. C231
571 (1) 890761.P267
573 (1,3,191) 1395829.15228049.191767493773.1494750313938269233.
.52279762365721011661.3388194620796866088519622669.
.14392074847295204526143504797565870269.P54
575 (1,5,23,25,115) 1151.1147615958647770851.
.243100818052550571272923886250428813459958001.
.18704988023033955131884066803385914940043877116522417022997906375751.P78
577 (1) 1758616206671.320535087664410947.21124577988954378706562426699.
.2883042291035918919488259490805466705119.
.477350833522476258826705274670317082147893737193497151.P124
579 (1,3,193) 26337570509291567389.480713392276365718072808464510304281.P128
581 (1,7,83) 1163.15405080652360541860434857813626384150523357.P189
583 (1,11,53) 96779.228527014581832693.480232466488974827.P208
585 (1,3,5,9,13,15,39,45,65,117,195) 692641.5953777759294129441.P113
587 (1) 466079.13152323.645446916044561004799825839125327.
.1048103888628429160984645776606224045032081.
.65654207366367155415201780117119460885628511.
.10994467441005798959066699751380077376871526520617.P100
589 (1,19,31) 7069.127167457.188002714453.15211987064329401478201. C213
591 (1,3,197) 31453021.5587380752269.3263687409355178360703349.P143
593 (1) 1187.694542949.1350773353.
.1115284110713736819943648961041196747319825421489.C214
595 (1,5,7,17,35,85,119) 81010441.3200519281.52864515971.
.20036793671274541049376611411.115460168265259575622411758906553741.P92
597 (1,3,199) 73783203733.6630293477484412123587586871701728361.
.8845057746607360101578544062042919811228803419862160327100045773.P78
599 (1) 15214538903.1666033953246993576905689.11621341565257598111021473.
.463863815296317703220841922489739.
.230941609196548964668124778957274786501.
.116299206023397239536920319253925869667382606684529884846610766493.P90
Table 3+ Factorizations of 3^n+1, n<=600
L,M for n=6k-3<=1197
n Prime Factors
1 2.2
2 2*.5
3 (1) 7
4 2*.41
5 (1) 61
6 (2) 73
7 (1) 547
8 2*.17.193
9 (1,3) L.M
L 19
M 37
10 (2) 5*.1181
11 (1) 67.661
12 (4) 6481
13 (1) 398581
14 (2) 29.16493
15 (1,5) L.M
L (3) 31
M 271
16 2*.21523361
17 (1) 103.307.1021
18 (2,6) 530713
19 (1) 2851.101917
20 (4) 42521761
21 (1,7) L.M
L (3) 7*.43
M 2269
22 (2) 5501.570461
23 (1) 23535794707
24 (8) 97.577.769
25 (1,5) 151.22996651
26 (2) 53.4795973261
27 (1,3,9L,9M) L.M
L 19441
M 19927
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M P78
490 (2,10,14,70,98) 10781.11139181433126881.42616540594017306841.
.1939897538167586914233386033412974841301862291509811887541.P64
491 (1) 60892643104482757573306223567662688740985969197465290654173842691745096014633691396823.P148
492 (4,12,164) P153
493 (1,17,29) 11833.10460016289198147545294753955830327500027581.P167
494 (2,26,38) 3131049661742425528068232396297.P176
495 (1,3,5,11,15L,15M,33L,33M,55,165L,165M) L.M
L (9M,45L,99M) P58
M (9L,45M,99L) 2971.650229042030120136981.P33
496 (16) 135752657940481.29572149681736256801.14697881508142957864698198881.
.72829931572241882463585913265633971549921127240417.P118
497 (1,7,71) 23857.1010899.
.13220422274071910215876252468819242538756902481.P145
498 (2,6,166) 15937.6623401.7160040632843551703449.
.216620436604313043566475914989777.
.3827781058655183126205789289853376790116016057.P46
499 (1) C238
500 (4,20,100) 150001.292503690001.36502594199089001.P158
501 (1,167) L.M
L 8017.44089.P72
M (3) P79
502 (2) 1017977689.P230
503 (1) 3019.36217.148601137514445965937491402579869.P200
504 (8,24,56,72,168) 2017.3340002808701217.P119
505 (1,5,101) 13692562779434643730988640327490622722291.P151
506 (2,22,46) 1013.163383816509. C196
507 (1,13,169) L.M
L (39L) 1123288921.P66
M (3,39M) 2004679.23944746073.57337058923.677975281092877.P33
508 (4) 54093886887062230599082516017052647105427126977713417. C188
509 (1) 39115633.1644550169868135799.
.19724128725821325379688781664270351435664812399.C171
510 (2,6,10,30,34,102,170) 1221260165462288630183115844288801.
.28035931589952039775691912430255721.P55
511 (1,7,73) 3067.14980477.118595256151.595010167626673.
.811585543251277560120467057191.3865306830584167073127171461490704904967.
.10793217203542650706249328961410064151855304581.P55
512 2*.134382593.22320686081.12079910333441.100512627347897906177. C193
513 (1,3,9L,9M,19,57L,57M,171L,171M) L.M
L (27M) 13339.2370225727729.18922857792733.P48
M (27L) 2053.796177.36441469.366009862219342685069818843.P34
514 (2) 149789881.13910135119037034721.
.5440162865009261024414945198670366357712554963673.P169
515 (1,5,103) 3490445461.
.77104115792306847773969759123947639401032809855965933396877513801.P121
516 (4,12,172) 30783585638170665502302948775733553745441793307097626003633282161500251889.P87
517 (1,11,47) C220
518 (2,14,74) 1230769.979486201.34380007061.
.1223967211946315524725505592278476748023592868457900490298056129.P118
519 (1,173) L.M
L (3) 1039.89269.3420017971.480647111193166117297.P44
M 16420688749.P73
520 (8,40,104) 121848815628062263103880401.10462398853448190277892819673521.
.125866583264034588195744509082241.
.8122589491866480893725693444173991689595601.P52
521 (1) 162553.8421451860752373577.
.51165684502959756249678612643377203741178823.C181
522 (2,6,18,58,174) 2089.579519470436095816296129.
.1166719221359482022233853557270249.
.27380528417882557686112275647129461671050857.P57
523 (1) 1146386713.P240
524 (4) 1049.177113.49553133408503725483772128111721395851817067100721.P191
525 (1,5,7,25,35,175) L.M
L (3,15L,21L,75M,105M) 12571651.368748451.10926062701.52316163901.P21
M (15M,21M,75L,105L) P58
526 (2) 36821.P246
527 (1,17,31) 619753.853101913964277975211.P203
528 (16,48,176) 2113.592070831406883027811373793806890294756873473.
.262707337319860778256426594724354117232793156673.P58
529 (1,23) P242
530 (2,10,106) 1061.2660013821.3976724621.7254137274841765833361.P155
531 (1,3,59,177L,177M) L.M
L (9L) 19538371812403.P70
M (9M) 1063.59473.174169.P70
532 (4,28,76) 56708009.573459238801.P187
533 (1,13,41) 187959269942189179513.42142122253902558090112972368111079.
.516469933130631687266967194982169414626403685360388146231581267.P112
534 (2,6,178) 46993.741193.2706313.15733777.42487177.
.120512015532869945521.891451372846431848735162460907849.P84
535 (1,5,107) P203
536 (8) C252
537 (1,179) L.M
L 2592169385514147730111519261.P58
M (3) 16111.556332001.2192254171.501846712686893762203.P42
538 (2) 2621920730595608239277.
.4424817286530482826420459992414631518016054430795822455701.C177
539 (1,7,11,49,77) 782525804283438601.28217734621389695902213.
.540324884800234472172474265352251.P128
540 (4,12,20,36,60,108,180) P138
541 (1) 71413.147842923003.306306876284281205126803290163.P213
542 (2) 7589.26017.18484369.926085049.1362124198068961.
.3970395385882420438589.1694156924687062004467070149488256157.P161
543 (1,181) L.M
L 1087.551689.19200481.51815235259.P60
M (3) 16617973.33643789547415373.13705675299301440100413601.P37
544 (32) 3649153.22590274733794400005119041.
.39992943232822333333109885414590913.
.41059640536030373858233736700354817.
.258768655908138617716174465552256367225580398337.P96
545 (1,5,109) 55586252581.222094774181491.
.762658977787211242107442855719555201241.
.359724730688548839284429979569498755479269797028602258574692740391.P77
546 (2,6,14,26,42,78,182) 106919748110822278633.20331397066267412031817.P96
547 (1) 357739.343661503.9998905729658756438442605226431814823.P210
548 (4) 1097.6217786649.205605612252656107662337.
.1688132433503810557364924441.C197
549 (1,3,61,183L,183M) L.M
L (9L) 6685697047209949.P71
M (9M) 22273394581666022203950859117.P58
550 (2,10,22,50,110) 276355201.6194196537071004001.P164
551 (1,19,29) 3196903.19442587.12156353749.433530461509609.
.5513389920148472663664331.11685042184199374835527472009419491917385043.
.57611874727884489362275168075966226905107431227.P88
552 (8,24,184) 1329217.14968033.10517455983432702721.
.1355934381451153256620998071713.P106
553 (1,7,79) 3319.6637.234363784537.
.1154021679827974602378869280423716945140873.P163
554 (2) 1109.7757.353453.1370597.45713469553.138224186669.697798351849.
.16939393542765939529.1702499228515647866519998734119027924624597.
.113108446589272373679314126747449776560428449341.P103
555 (1,5,37,185) L.M
L (3,15L,111M) 4441.1487523211.1202795300401566511.P39
M (15M,111L) 1107781.17939821.7970539859298388628345851.P30
556 (4) 579353.5067709817.322415479537.P237
557 (1) 3343.495738992209.95038110117395158295809864435076885251.P212
558 (2,6,18,62,186)
337944030532390049133239607747158234348370173256068275584939697.P110
559 (1,13,43) 6709.2858823573451. C225
560 (16,80,112) 7841.571201.1130081.14582401.1599365090041528321.
.12313028928129353461145843498245441.P109
561 (1,11,17,187) L.M
L (3,33M,51L) 1123.P74
M (33L,51M) 1184904535775852187955082288041.P46
562 (2) 3751695056761. C255
563 (1) 13513.46901369347503080003230459. C239
564 (4,12,188) 378380976729169.2661122837511375697.63242317817361890497.P123
565 (1,5,113) 1905181.29430434051521.6511198304862822004141.
.41137621042151315777486573761.P144
566 (2) 34523737.59287369.49809099173.P244
567 (1,3,7,9L,9M,21L,21M,27L,27M,63L,63M,189L,189M) L.M
L (81M) 28408969.P70
M (81L) 23054587993795681.P61
568 (8) C268
569 (1) 10243.37400371.6108324565058656226827.P238
570 (2,6,10,30,38,114,190) 227486230155721.285624459420362072231818320481.
.19563591976917681250519957752816158641.P57
571 (1) 1346419.1942543.3230959355675389279.
.34632863850238633929356979151.9902409776002501575427276068949.P182
572 (4,44,52) 3758814696232211617.P211
573 (1,191) L.M
L 2293.7744669.36128797.18216735472439781167890822031947.P43
M (3) 515701.472343383.2860788451.29182386445021501.
.1971688819139946257137.P29
574 (2,14,82) 7893649.P223
575 (1,5,23,25,115) 593401.203739751. C196
576 (64,192) 96769.2742235226781697.80329587759500549712086601217.
.358294686971605247257324400220810330552461569.P90
577 (1) P275
578 (2,34) 82081781.P252
579 (1,193) L.M
L P93
M (3) 12739.251287.P82
580 (4,20,116) 41761.661201. C204
581 (1,7,83) 10459.42837229933.925726166919048803358499. C197
582 (2,6,194) 304197120772507903298833.30085941527949966019986217.P135
583 (1,11,53) 3499.34981.35662111.69802591. C225
584 (8) 1017329.361454863814403857.241534941436263184720740713528257.P219
585 (1,3,5,13,15L,15M,39L,39M,65,195L,195M) L.M
L (9M,45L,117M) 40763971.134825306053231.P48
M (9L,45M,117L) 16381.P65
586 (2) 292106875057.P268
587 (1) 235085219994159229.P263
588 (4,12,28,84,196) 35281.993540468213734224019741430591793.P123
589 (1,19,31) 28176583.323164794187953820273424568081687845767. C212
590 (2,10,118) 812008114170481.699252037103152246228501801.
.4462341932240217419644566476266934959661.2278778428224885338388821602515615817605475626225677346287478598452941.P71
591 (1,197) L.M
L (3) 10639.195036838514113748972287141.P63
M 430503804021162564249547.P71
592 (16) 165699617.3806479489.65975951252407411592256725153262330209. C220
593 (1) 211197634469030854488137501976187207.P248
594 (2,6,18,22,54,66,198) 2377.23761.28513.5716279934982996193.
.1432504508430034508204758969.20587702622139319137357302758154737.P80
595 (1,5,7,17,35,85,119) 454494430583206275164377352644259431.
.1718744650754182976202528603042164953120336270744134393913100855221.P82
596 (4) 1193.20804671181218580689181693883121473121. C243
597 (1,199) L.M
L (3) 11941.188653.33475617898267731167713.P63
M 29851.13192248510319.663447176016922740823.P57
598 (2,26,46) 163853.115852981037.10907098969729.350530770356853529.
.351220238258463351865281969766903601936378570569.P158
599 (1) 27263461551898213. C269
600 (8,24,40,120,200) 64575767537215201.
.227831060593285510425519277644775297708801.P95
-------------------------------------------------------------------------------
603 (1,3,67,201L,201M) L.M
L (9M) 14592601.419046409.574307266483.2960693160319.P55
M (9L) 19932769.6134598978931.458674586623531.P60
609 (1,7,29,203) L.M
L (21M,87M) 1012563218857.P68
M (3,21L,87L) 2437.99877.2951329832776462049641.P51
615 (1,5,41,205) L.M
L (15M,123M) 113161.18428901811.20737470706861.P48
M (3,15L,123L) 1231.15910442371.24299529451.370521558779523271.P36
621 (1,3,9L,9M,23,69L,69M,207L,207M) L.M
L (27L) 601686824239.P83
M (27M) 352381483.17692787399887.3738085960401704053.P55
627 (1,11,19,209) L.M
L (3,33M,57L) 21319.150368908141.388863219568252900988590466647.P42
M (33L,57M) 140449.237150211.P72
633 (1,211) L.M
L (3) 103813.501655861343941.263592416413242632502019.P57
M 210157.10443674741443.11449168292738643406007298913.P55
639 (1,3,71,213L,213M) L.M
L (9L) 83071.24780475516004633995023031589350084985539501303.P50
M (9M) 1279.378747033568494391.P80
645 (1,5,43,215) L.M
L (15M,129M) P80
M (3,15L,129L) 1291.2186551.33530971.46914743951431.P50
651 (1,7,31,217) L.M
L (21M,93M) 4085677.90012469.724905427.2042545894999.P50
M (3,21L,93L) 3907.5209.219072259055583303411259.P56
657 (1,3,73,219L,219M) L.M
L (9L) 550246699.177530280013.1058918094477900492958354359420721.P51
M (9M) 502839510741577.116942368867889110665870097.
.2492873545646565038715607009.P35
663 (1,13,17,221) L.M
L (3,39M,51L) 2943226818125892905544757.P68
M (39L,51M) 1327.5779328325617809.22740289380659761.
.576476186885145538438910347.P30
669 (1,223) L.M
L (3) 3710391883796434048417989052519.P75
M 393373.2208436016030508499618943893.134921949641246929842999472177.P45
675 (1,3,5,9L,9M,15L,15M,25,45L,45M,75L,75M,225L,225M) L.M
L (27L,135M) 28351.33751.270001.2443501.166148551.P57
M (27M,135L) 7373701.47317973274744751.10052296641904080110450401.P38
681 (1,227) L.M
L 44816172799.6465119944406394614327660870683.P67
M (3) 5449.13439720233.88086411863544059401.1310040527962707397387.P53
687 (1,229) L.M
L 2749.72823.10218493614783823.P85
M (3) 374813879071.5085687079494603710866459.P73
693 (1,3,7,11,21L,21M,33L,33M,77,231L,231M) L.M
L (9M,63L,99M) 34651.9412658641.16811532739.533440753503058171.
.1974059964778769407.P26
M (9L,63M,99L) 347887.450451.6296599.32684071566486927734971544953.P40
699 (1,233) L.M
L (3) 205507.216644478591019.
.4335257933548061295968935256413888403027203.P49
M 4131567084277.58423463723552958571.P79
705 (1,5,47,235) L.M
L (3,15L,141M) 8461.1694821.P79
M (15M,141L) 6635218360523583511.49787475447478272436561.P46
711 (1,3,79,237L,237M) L.M
L (9M) 1030190696075822904523.37104626883041865086339016005581.P59
M (9L) 1423.63155614359749727228914496979.P80
717 (1,239) L.M
L P115
M (3) 48757.270813940325189568943.P89
723 (1,241) L.M
L 4822318324289817291969211.P91
M (3) 1447.55781050264403179.98154562384116674301868417.P69
729 (1,3,9L,9M,27L,27M,81L,81M,243L,243M) L.M
L 2917.10021812319.74789972644573.
.128802173701412100299505707658931451317.P51
M 1459.P113
735 (1,5,7,35,49,245) L.M
L (3,15L,21L,105M,147M) 145531.498331.514758172908631.P55
M (15M,21M,105L,147L) 14926003681.74791772471622991.P54
741 (1,13,19,247) L.M
L (3,39M,57L) 1483.31737434851689997.P84
M (39L,57M) 38621483576071092940921575769.P74
747 (1,3,83,249L,249M) L.M
L (9L) 4483.303283.113702119066171.6783049792575948870710879779.P67
M (9M) 80677.32521393.35602595168256401435752912921434267983606166613.P59
753 (1,251) L.M
L 5423922557089335747765967970338216706551100947.P75
M (3) 2789170090026586683751.4730372605863138117902461.P73
759 (1,11,23,253) L.M
L (33L,69L) 3037.579877.12798259.34480068373143557889186331.P63
M (3,33M,69M) 40844827.42062263.P91
765 (1,3,5,15L,15M,17,51L,51M,85,255L,255M) L.M
L (9L,45M,153M) 3061.9181.42841.3246751801.40013904871.P60
M (9M,45L,153L) 279991.P87
771 (1,257) L.M
L (3) 9135897736885657805029.571122649743809813904227350343296963.P65
M 13879.78643.141034621423.165254121698644537736573602249.P74
777 (1,7,37,259) L.M
L (3,21L,111M) 83414059.1779148183.165773949223.2133010034304073.P60
M (21M,111L) 1740481.127076001907.P86
783 (1,3,9L,9M,29,87L,87M,261L,261M) L.M
L (27M) 13002499.203824620975729575719.P93
M (27L) 1567.356921882778817.593973884916708178275496891.
.2486830332101401520473942574497.P46
789 (1,263) L.M
L 1043280019867.32974341269754568228469618932542542372707492068847.P64
M (3) 1579.42840043160337151.13661893881209539237410778809936721.P71
795 (1,5,53,265) L.M
L (15M,159M) 2519110141.219155971856761.358752636951732211.
.3620474240298805411.P39
M (3,15L,159L) 21945325612504650106384598423521.P69
801 (1,3,89,267L,267M) L.M
L (9M) 309344599.231121501201.144441230687236477.
.1005106048692711751.209193899135109381487.P51
M (9L) 95665033.24071705219862678529.
.817576445040642684875975963157408264856921.P57
807 (1,269) L.M
L (3) 5191863397940689668569933101.P100
M 54877.25588357.93494549298854768677.
.1667434534078422877501816329924811.P64
813 (1,271) L.M
L (3) 1627.58537.2230873.8475830822135212338398067962551832652525613.P72
M 13863159773521.62014564661966845526233585639.P88
819 (1,3,7,13,21L,21M,39L,39M,91,273L,273M) L.M
L (9M,63L,117M) 3018697947220411.39685911678305092747.P69
M (9L,63M,117L) 7754293.P97
825 (1,5,11,25,55,275) L.M
L (15M,33L,75L,165M) 3301.2113651.12932701.
.282136916401854566106640313673268951.P44
M (3,15L,33M,75M,165L) 42888451.1020438840301.3961066561651.P64
831 (1,277) L.M
L 1663.114679.1630423.11765644789597.
.119504555178871023268983534947447527269739.P64
M (3) 44076407438191.P118
837 (1,3,9L,9M,31,93L,93M,279L,279M) L.M
L (27M) P129
M (27L) 65324650043539.P116
843 (1,281) L.M
L (3) 5059.20233.172911911281.1375848322657.14303058265301079714689773.P77
M 35407.5590415520155419.329926320009546557993324157253.
.93889530611687790784978792499340162064561.P44
849 (1,283) L.M
L (3) 25471.
.8301611466314080069549501904096798647209210526843211654301019.P69
M 1699.6793.2312677.1597501142432086574210778580316694710747482879.P77
855 (1,3,5,15L,15M,19,57L,57M,95,285L,285M) L.M
L (9L,45M,171M) 669698075470951.311642677077889231.P71
M (9M,45L,171L) 46343064339361.P90
861 (1,7,41,287) L.M
L (21M,123M) 49939.65437.40412782566432403.
.237114113888408583765557191645881523849.P50
M (3,21L,123L) 1723.454609.121776397.1719933601.
.91763484684142928487860846109974647.P54
867 (1,17,289) L.M
L (51M) 1279693.2795209.5673649.834225827263.37071429676781111221.
.44345272375637763996684787.P54
M (3,51L) 494191.P125
873 (1,3,97,291L,291M) L.M
L (9L) 1747.19207.408099356737585867477.P110
M (9M) P138
879 (1,293) L.M
L (3) 70321.2297707.56267724103.416629385310769.
.167751946286921312488219891880427162376891986493.P56
M 17581.1625466728689.9956126099416515198337.P102
885 (1,5,59,295) L.M
L (3,15L,177M) 11966355914190302880887590274169088432923151.P69
M (15M,177L) 3541.153991.3239558431.6846630811.1233993275550631.P67
891 (1,3,9L,9M,11,27L,27M,33L,33M,99L,99M,297L,297M) L.M
L (81L) 4269572953837417792609635043.P102
M (81M) 106921.P124
897 (1,13,23,299) L.M
L (39L,69L) 52027.129169.71610909064105842601.205388305725186615253.
.1451925916588584927958371446332297.P43
M (3,39M,69M) 19109689.302504188071570951181107121549176773073635506699.P72
903 (1,7,43,301) L.M
L (21M,129M) 6045855901.8396466037.P101
M (3,21L,129L) 43*.3613.26628205801.38473551584154787339.
.620858350010958430897.P65
909 (1,3,101,303L,303M) L.M
L (9M) 1072218223.875878760011500587604133.P111
M (9L) 34543.89083.301789.8814142206721.
.2115245411381559866287397735509425577692165007.P71
915 (1,5,61,305) L.M
L (3,15L,183M) 7321.402601.
.11680290833436277523654510517818365661993128293160111.P54
M (15M,183L) 1831.23821111.P104
921 (1,307) L.M
L (3) 5527.12435343.94037544541.41544366292130993379842581.P99
M 1839136588897.P135
927 (1,3,103,309L,309M) L.M
L (9M) 16378714333.248791041001.2460603909422278394029.P103
M (9L) 3709.7417.667441.14962044180614665681.
.15140038547438480400123764651003503396345909.P71
933 (1,311) L.M
L 11197.6126079.57673461824953153.P121
M (3) 2375632591.15789599377.
.2403609388542331863112187538138617537886829.P86
939 (1,313) L.M
L 5865193850703540120141889.P125
M (3) 37561.477013.P139
945 (1,3,5,7,9L,9M,15L,15M,21L,21M,35,45L,45M,63L,63M,105L,105M,315L,315M) L.M
L (27L,135M,189M) 273909322011876278491.P83
M (27M,135L,189L) 17297447591971.622244499968071.P76
951 (1,317) L.M
L (3) 454579.36324397.4242031875148351.110636908354198084399.
.549512115983126575855924649876601277813687417.P57
M P152
957 (1,11,29,319) L.M
L (3,33M,87L) 170347.63889321.1073843959.2062565445871789.
.1289483195503733143.P79
M (33L,87M) 28909057.P126
963 (1,3,107,321L,321M) L.M
L (9L) 75319350121.2727870992921938573.12019580563813427953015581187.
.38530727715140134780820983363.P66
M (9M) 616321.1147982842062882883.130120720999646859863046577.
.1018903915374204583869487996244315736990815281.P57
969 (1,17,19,323) L.M
L (51M,57M) 3877.475441789.P125
M (3,51L,57L) P138
975 (1,5,13,25,65,325) L.M
L (15M,39L,75L,195M) 1951.P112
M (3,15L,39M,75M,195L) 5851.12641851.91467329665270032489740651551.P75
981 (1,3,109,327L,327M) L.M
L (9L) 2063874889.91755041113.P135
M (9M) 45127.38767159.33992611927399.259351671880027.
.8939748369206359.3043186199715894155713.P77
987 (1,7,47,329) L.M
L (3,21L,141M) 26755907602439184337475848551837359355828727.P89
M (21M,141L) 34519339.553998931060051.634553779763610143347.
.18452857936885202842977571159.P60
993 (1,331) L.M
L (3) 1987.617647.478405756968549949554133.P125
M 91036793334049.
.15690438092853039519623397570358428793135659828199624606933.P86
999 (1,3,9L,9M,37,111L,111M,333L,333M) L.M
L (27L) 2615383.
.792615901665390921359533539904938817776371948323522457540677.P89
M (27M) 1999.7993.48366655669261.P134
1005 (1,5,67,335) L.M
L (15M,201M) 2011.739828812361.2709644468095958739571.
.396067351989170036074128364869717451081.P51
M (3,15L,201L) 1648757425261.114930794313903734467877618236500915404671.P74
1011 (1,337) L.M
L 10111.475422088807.
.40017666590749974337826438228229397342408512612651846790009.P87
M (3) 296768007466640363281.118311296994193648484589397.P114
1017 (1,3,113,339L,339M) L.M
L (9M) 8342589313.915099621078019541370469051218219809941501498141.P103
M (9L) 258319.4759561.423195294979.249504620848655097819331.
.16211062842493949016958272244358278685152181951173.P65
1023 (1,11,31,341) L.M
L (3,33M,93L) 19174858828306360645533450526720857649051.
.19337980565378171534889993094421861389450501.P60
M (33L,93M) 82325575332463.916226106737897927533.
.1575155207429963661696683189664217.P75
1029 (1,7,49,343) L.M
L (3,21L,147M) 7*.48517052647620607.P123
M (21M,147L) 374557.596821.43130485963642981.9062940254538824227819939.
.3354356969043817266850856322523231704213187.P45
1035 (1,3,5,15L,15M,23,69L,69M,115,345L,345M) L.M
L (9M,45L,207M) 20544192840232981974341524541641114431739055519477161.P74
M (9L,45M,207L) P126
1041 (1,347) L.M
L 6892793323373912358814239820687.
.254139660710314265859242122277843290934557.
.2027489666453382580690006167619461409824120037.P49
M (3) 2083.5377807.62778629657763042467737492867348937820421529565882574678483317963541237.P84
1047 (1,349) L.M
L 6271848287482534909.P148
M (3) 60727.77479.898327.2770820587.460776856808846708848573192891152036252965685853508369019636063025441.P72
1053 (1,3,9L,9M,13,27L,27M,39L,39M,117L,117M,351L,351M) L.M
L (81L) 381350269.828864739.14770982235456815760466328504017.
.23879893447642484359783138389093155014728859.P63
M (81M) 21061.365426184943.P139
1059 (1,353) L.M
L (3) 79615621.2367719063763857822934247.
.195570061420579042031041088952820573.
.500258793716411748689797558450829549801989.P59
M P169
1065 (1,5,71,355) L.M
L (3,15L,213M) 4261.22362247200781.P118
M (15M,213L) 63901.432391.153492061.P115
1071 (1,3,7,17,21L,21M,51L,51M,119,357L,357M) L.M
L (9L,63M,153M) 2143.402777955417573.36954556187808421.
.64876583110042176390667.808469860665849095653200462979.P51
M (9M,63L,153L) 736437756465937.P123
1077 (1,359) L.M
L 318793.409261.3668263.1276578871.60311487349.127112425273.P123
M (3) 803443.518094843517.1205494272636831421987.
.44779485581193256543637836329731095292692846473629922755299.P74
1083 (1,19,361) L.M
L (57M) 21694657.8099144023.
.22828720873262330503325108479824493034448606761137807585784451157.P82
M (3,57L) 165219033390738118332292179232147915902737269.
.3568834663422179977171480813036610383328917129.P74
1089 (1,3,11,33L,33M,121,363L,363M) L.M
L (9L,99L) 224462503.156441397046089226264659108360279.
.4789533577787722153663685529580118155897.P78
M (9M,99M) 68080872565310442682643322747747949652359837857769.P108
1095 (1,5,73,365) L.M
L (3,15L,219M) P138
M (15M,219L) 15331.30661.159871.421228655258062410033653011.P97
1101 (1,367) L.M
L (3) 30829.17858221.41809050307.8396582951528257.
.134749475083956907205486512513.
.8666916629965482510964850398830114343085488527676513.P55
M 509503144616650455503996339457594409.
.264193080736619186575079537844126610922023.
.3531705268360585891927961325305093393548926979.P53
1107 (1,3,9L,9M,41,123L,123M,369L,369M) L.M
L (27M) 50923.294765319.13791897770970942680535455432563.
.9432555424486966319627392760832640039.
.1055115277879332623881428695105269317991.P52
M (27L) 1442768599.3039999121.
.40354730433306829441509327784357516287682106779.P107
1113 (1,7,53,371) L.M
L (21M,159M) 36924889.38112674467477620617176194290527.P110
M (3,21L,159L) 18035053.10395399967.P132
1119 (1,373) L.M
L 2239.44838882787.557848953547.32885806849221579450136161458340408001.
.3946461488572658967696073707447590491657.P76
M (3) 6037564587283.241305707598530173.319357751072156851.P130
1125 (1,3,5,15L,15M,25,75L,75M,125,375L,375M) L.M
L (9M,45L,225M) 11251.P140
M (9L,45M,225L) 139160448001.608322810746251.15395456686740751.P102
1131 (1,13,29,377) L.M
L (3,39M,87L) 33931.20997779557.1685960157180749122543193233.
.429799925110471135868536930564099991316083221.P74
M (39L,87M) 477426769.411432653347.26673569340297259349908069.
.673936252988940025236706095937800943722160198360658521.P61
1137 (1,379) L.M
L (3) 4549.2881159.3043833139.
.29515549254398209225874406335593365027179323.P117
M 15919.48604477.472451297377.P158
1143 (1,3,127,381L,381M) L.M
L (9M) 25147.564643.14843675190367934329303984224806061782112721.
.559813558907477788828824742131148220203759108013390354857710889.P65
M (9L) 989839.1546605334493611687.335666830931171561323468264590217.
.32898190462493372969237618399233766551837.P84
1149 (1,383) L.M
L 254601325861.223598667809830895887.
.308065186446746401305805565391533648719087.P110
M (3) 4597.4276579.117713139221326092919.
.3989312721215157653235728892586256757888727.
.7998959914577646744146936767408412879563117.P67
1155 (1,5,7,11,35,55,77,385) L.M
L (15M,21M,33L,105L,165M,231M) 2311.164011.239902949263975525353211.P84
M (3,15L,21L,33M,105M,165L,231L) 4621.1836451903532401.P96
1161 (1,3,9L,9M,43,129L,129M,387L,387M) L.M
L (27M) 6967.1661072887.203283251641.349060141531.3946231636939.P132
M (27L) 401707.3352969.6396630351427.6587554895924096809739238055210098776104755624225403298527439376440348329.P83
1167 (1,389) L.M
L (3) 9337.90121360236991.11630010100238599287067.
.664895970649041600038389.143188658495499597709982916815768458561.P83
M 20117172706549.25494187496341.271578092384041.382599816259332655502611.
.13978789464758904293057280795184889726963506615759.P72
1173 (1,17,23,391) L.M
L (3,51L,69M) 354247.6314742277.816858571368627283.P136
M (51M,69L) 2347.2414275181974182801433.P143
1179 (1,3,131,393L,393M) L.M
L (9L) 28352547568921790651747638524393003422138037231571.P137
M (9M) 6032311057.114364589293.3224395563158620487627301979.
.634192808066964130084356885435428340601.
.1584994109212772740649132634823292175704137.P57
1185 (1,5,79,395) L.M
L (15M,237M) 47192805093847040521.
.20164963601406293102055186569464341960751.P89
M (3,15L,237L) 2371.P146
1191 (1,397) L.M
L 13115766186228547772332771.701457075383373677285061251153227.P132
M (3) 92899.542867329.323850582802486898673680349766993.
.2723107444337684264671357032400412204920503919.P97
1197 (1,3,7,19,21L,21M,57L,57M,133,399L,399M) L.M
L (9L,63M,171M) 4789.3922616881.572479271659.
.449561206200996995233570693777.7372498813842828927303424845982122157.P63
M (9M,63L,171L)
38225866405490489875912283507646527829742078214496872839.P100
3^{3h}+1=(3^h+1)L.M, L=3^h-3^k+1, M=3^h+3^k+1, h=2k-1.
Table 5- Factorizations of 5^n-1, n odd, n<450
L,M for n=10k-5<=895
n Prime Factors
1 2.2
3 (1) 31
5 (1) L.M
L 11
M 71
7 (1) 19531
9 (1,3) 19.829
11 (1) 12207031
13 (1) 305175781
15 (1,3) L.M
L (5M) 181
M (5L) 1741
17 (1) 409.466344409
19 (1) 191.6271.3981071
21 (1,3,7) 379.519499
23 (1) 8971.332207361361
25 (1,5L,5M) L.M
L 9384251
M 101.251.401
27 (1,3,9) 109.271.4159.31051
29 (1) 59.35671.22125996444329
31 (1) 1861.625552508473588471
33 (1,3,11) 199.386478495679
35 (1,7) L.M
L (5M) 85280581
M (5L) 211.631.4201
37 (1) 149.13971969971.8737481256739
39 (1,3,13) 79.608459012088799
41 (1) 2238236249.5079304643216687969
43 (1) 1644512641.172827552198815888791
45 (1,3,9) L.M
L (5L,15M) 1171.169831
M (5M,15L) 297315901
47 (1) 177635683940025046467781066894531
49 (1,7) 227376585863531112677002031251
51 (1,3,17) 90271.317731.654652168021
53 (1) 5960555749.17154094481.27145365052629449
55 (1,11) L.M
L (5L) 11*.103511.190295821
M (5M) 511831.65628751
57 (1,3,19) 11735415506748076408140121
59 (1) 21180247636732981.2047572230657338751575051
61 (1) 8419.918585913061.140194179307171898833699259
63 (1,3,7,9,21) 280729.2161279.23792163643711
65 (1,13) L.M
L (5M) 20986207825565581
M (5L) 131.1034150930241911
67 (1) 269.1609.26399.2454335007529.604088623657497125653141
69 (1,3,23) 139.6211.598761682261.8868050880709
71 (1) 569.18607929421228039083223253529869111644362732899
73 (1) 4853479.5729041.9519524151770349914726200576714027279
75 (1,3,5L,5M,15L,15M) L.M
L (25M) 151.3301.183794551
M (25L) 1989151.49892851
77 (1,7,11) 527093491.8090594434231.162715052426691233701
79 (1) 205367807127911.58523123221688392679.344120456368919234899
81 (1,3,9,27) 4861.11419697846380955982026777206637491
83 (1) 20515111.1431185706701868962383741.88040095945103834627376781
85 (1,17) L.M
L (5M) 8198241112969626815581
M (5L) 1531.34563155350221618511
87 (1,3,29) 5569.6961.28870194250662203210437116612769
89 (1) 179.9807089.14597959.834019001.8157179360521.231669654363683130095909
91 (1,7,13) 9680647790568589086355559.17499733663152976533452519
93 (1,3,31) 31*.148429.878851.172974812463239310024750410929
95 (1,19) L.M
L (5L) 2851.11600321878916922053491
M (5M) 4113691.1245576402371959291
97 (1) 389.264811.P60
99 (1,3,9,11,33) 143551.1731511.22542470482159.153560376376050799
101 (1) 5937018283241.3434487311396589821473854121.P30
103 (1) 3709.28429.59117897713198738371603984809.P35
105 (1,3,7,21) L.M
L (5L,15M,35M) 21226783250214361
M (5M,15L,35L) 1736701.119461537021
107 (1) 6421.5486016363791.35411885288978941.172163150940018661.P24
109 (1) 1091.1007161.1528399.P61
111 (1,3,37) 3109.P47
113 (1) 2939.6329.129499.308491.304247586761.2084303944451.
.620216264269531.8237123176890810696379
115 (1,23) L.M
L (5M) 689081.29028071.100062970166640331
M (5L) 461.691.2855911.824480311.17223586571
117 (1,3,9,13,39) 223963741.P42
119 (1,7,17) 239.1429.4999.7497182681291140146079.P36
121 (1,11) 12101.486179.P68
123 (1,3,41) 739.960139.1785961.9025583299.P31
125 (1,5L,5M,25L,25M) L.M
L 3597751.P29
M 28707251.4032808198751.767186663625251
127 (1) P89
129 (1,3,43) 18471511.43955934961951833386625799.P26
131 (1) 2621.23928199.34720241.16815642611861.P60
133 (1,7,19) 9311.65171.281429.3257947519.152317058321.P41
135 (1,3,9,27) L.M
L (5M,15L,45M) 11071.1312315694449748688331
M (5L,15M,45L) 541.26941244373060650224561
137 (1) 20551.603349.48102071.121719631478506669.7851027307722624763151.P39
139 (1) 21521602057721.6789441546024769741462601111.P56
141 (1,3,47) P65
143 (1,11,13) 24615836446631.53130566763791958299.P51
145 (1,29) L.M
L (5L) 1461311.P34
M (5M) P39
147 (1,3,7,21,49) 24556351.5071357999.2035895040229.P30
149 (1) P104
151 (1) 1175989.2237519.389439261961.12799319666401.
.2843809592323334251225153490677489.P35
153 (1,3,9,17,51) 4591.26481241.360143672909416579.P39
155 (1,31) L.M
L (5L) 11161.257611.31473312961.21783999170235219053011
M (5M) 311.5624951.P33
157 (1) 32029.5129819.2107089779.8616314452100494153901371725720169.P55
159 (1,3,53) 1775305720077559.P58
161 (1,7,23) P93
163 (1) 4599209.40100609.675775181.6582151087844246659.
.102556399583828574447011133455059.P40
165 (1,3,11,33) L.M
L (5M,15L,55M) 2311.P26
M (5L,15M,55L) 331.9867165115635267180926131
167 (1) 18371.53441.P108
169 (1,13) 13859.784646826705980283039372085276899721.P70
171 (1,3,9,19,57) 19*.P75
173 (1) 1039.3461.1708272343265311.P99
175 (1,5L,5M,7,35L,35M) L.M
L (25M) 28001.200201.8894201.P26
M (25L) 12601.50051.22661801.1657309151.38105263380318401
177 (1,3,59) 198241.340863370420651571324835367261.P47
179 (1) 359.3581.75539.17315029.100894073362387242965129.P84
181 (1) P126
183 (1,3,61) 38431.P80
185 (1,37) L.M
L (5M) 2591.P47
M (5L) 30810641.21829321837586441.P27
187 (1,11,17) 4200769.1202338040280510524134632541097924516136661.P64
189 (1,3,7,9,21,27,63) 305921358183421.P62
191 (1) 112691.60426671.P121
193 (1) 749154725101.406875383561091922623241829.P96
195 (1,3,13,39) L.M
L (5L,15M,65M) 14821.P29
M (5M,15L,65L) 933692761.P26
197 (1) 470323176131.362204827770839.P111
199 (1) 53731.P134
201 (1,3,67) 1248228732195063112609361470351.P63
203 (1,7,29) 493291.4978655062910170670969991331.P84
205 (1,41) L.M
L (5L) 15991.1256950067521.P40
M (5M) P56
207 (1,3,9,23,69) 10047916621.P83
209 (1,11,19) 419.56431.P119
211 (1) 5594292675731.37973612258438259769.2047676978710884689089.
.144115393066310961947385445876092809.P59
213 (1,3,71) 156309592445437909.P81
215 (1,43) L.M
L (5M) 1291.P56
M (5L) 431.144982241.1273316896028212631.P31
217 (1,7,31) 8681.1828916514769.P110
219 (1,3,73) 439.429241.2183431.239701757320911389817996792709.P57
221 (1,13,17) 351391.231452141519.183276094190104631834639.
.1436003589550079403417985191612889433318011249.P49
223 (1) 355909.P150
225 (1,3,5L,5M,9,15L,15M,45L,45M) L.M
L (25L,75M) 1274851.1390332823651.489346511141264975761501
M (25M,75L) 1086749551.P33
227 (1) 863773591.17408515139.107857890714179.154907695140797990849.
.239976686263858506551.16831369699997499687405534401.P57
229 (1) 2749.53129.63785116081353654247759.25703365361608909110896940589.P101
231 (1,3,7,11,21,33,77) 13920748381.267859557529209897722406319386619.P42
233 (1) 1318781.412500871.208771951788632309319091684496790985222571.
.122893706196784651098718052024745515496783278694509.P57
235 (1,47) L.M
L (5M) 20885861.68308861.P49
M (5L) 941.4231.96766610646500911.P42
237 (1,3,79) 12799.657439.447298617719114285037649.P76
239 (1) 479.40093613041379.P151
241 (1) 79531.578401.882061.464913101.128338427949683383916242111.
.23296571833941039118079506609079.1054929344030207429836604785995221.P53
243 (1,3,9,27,81) 1459.14001661.P103
245 (1,7,49) L.M
L (5L,35M) 491.8821.10781.P49
M (5M,35L) 16650328910366149531471.P37
247 (1,13,19) 29641.893134065430622331883159985777080426121.
.73264607998188798376620748253610482190769.P67
249 (1,3,83) 499.12451.169321.64613577662440706821.
.486307761332920261532701.P60
251 (1) 8325671.31005529.P161
253 (1,11,23) 215556321311.4586605887769406257148888900423581.
.75458741165755163938354406143932160485170968091.P62
255 (1,3,17,51) L.M
L (5L,15M,85M) 1021.1445377105917001.P27
M (5M,15L,85L) 236641.782302186051.38385602257801.263420722813531
257 (1) 10081392432072125477404185330039079.P146
259 (1,7,37) 1483253451821989.12331512430205535516641371.P111
261 (1,3,9,29,87) 6717619.81131329.420610743056505018221215111.P77
263 (1) 1523516701711.P172
265 (1,53) L.M
L (5M) 488094322309591.1335618937071191.P43
M (5L) 1061.43347650492220877561107611.P45
267 (1,3,89) 1069.1133149.1652731.18484574880511.369718501929859.
.92358800604937937130124908509003639071.P42
269 (1) 3229.4016171.32785719659723694619.P158
271 (1) 64993931.12987902099.P171
273 (1,3,7,13,21,39,91) 376909369155066379919582224252183771.P66
275 (1,5L,5M,11,55L,55M) L.M
L (25L) 23785874550224051.29881163609373451.43877290026688801.P21
M (25M) 233201.1234133939501.354655233566701.P38
277 (1) 37095841.14075563135476669013895019180975816431.P149
279 (1,3,9,31,93) 247114592858611.P112
281 (1) 631100202961413821.P179
283 (1) 1699.451669.113334709.416742821994932569.33926661157694104397239.
.1503555624642039390353881.8717585253517894966154284413195420314854559.P73
285 (1,3,19,57) L.M
L (5M,15L,95M) 30211.260930841421.P35
M (5L,15M,95L) 571.P48
287 (1,7,41) 10690751.203375089.1038891585945814650631.P132
289 (1,17) 17341.81053519.27605542907603789.9027110169772242694759.P140
291 (1,3,97) 8731.15247819.65482996292971.425798685220729.P95
293 (1) 1759.520369.224108738217451.88957588316686547560127731.P155
295 (1,59) L.M
L (5L) 842521.6264826343527027047964986594326671.P42
M (5M) 1448181445390051.485704102682442915241.P45
297 (1,3,9,11,27,33,99) 1049599.1730583185128108939.
.101367829967676409195407966079.P73
299 (1,13,23) 599.71761.1076401.7752619982267966542535041531665354400879.
.4483622187767180916663396803931609479674368941155912707479.P74
301 (1,7,43) 66221.3595452428681.453098474981964966729037498128705243871.P121
303 (1,3,101) 126463111.
.897449797190508611732321830427288714681382628177991026939.P75
305 (1,61) L.M
L (5L) 1884901.P78
M (5M) 1831.2441.1786560207910631.117369445599178322177831741.P36
307 (1) 30093907237519.41907329770349.3707465989826721707843621775363101765344082634099897042729510565487681100579030907337171.P100
309 (1,3,103) 619.8934148519.42173111702521341940416989340041084225191.P90
311 (1) 263729.1649908341047346424876131429988519619911.38695455401981313830913060474530524458380779268946879355849020686413069.P102
313 (1) 229651231.21428622089774767159447145142284385968882142917892658511907216761741.P143
315 (1,3,7,9,21,63) L.M
L (5M,15L,35L,45M,105M) 11971.23311.34651.P38
M (5L,15M,35M,45L,105L) 1732501.P45
317 (1) 34871.29048967458203698934091. C194
319 (1,11,29) 95701.533942839.103842769598157852780123277204006116809062929798301541558844883634526221.P111
321 (1,3,107) 35311.80251.3482851.
.204438681420686525733014991351502624422714996979.P85
323 (1,17,19) 3247691391126251. C186
325 (1,5L,5M,13,65L,65M) L.M
L (25M) 1659451.142816611356873351.P61
M (25L) 1641395317366745868848220671801.P54
327 (1,3,109) 3900606421.2570834326384926058220919782123933663342371.P99
329 (1,7,47) 659.6581.15957217104409233285978673415179.3625663221570350634568091041714437127962087908478575591859134630145357912199.P80
331 (1) 67440292875072467734808551587718580464816759. C187
333 (1,3,9,37,111) 15319.344145511.
.11071665290671449530331408923856186107268916092023773607149.P81
335 (1,67) L.M
L (5M) 126631.11494162725571360186894779691.P59
M (5L) 1148552280514941389076611.P69
337 (1) 242550562936636678266163293887551.P203
339 (1,3,113) 7459.234303241.22628763748399.204867325883294509.
.24528557597575188455414632667311.P83
341 (1,11,31) 109121.10161119.192446105281.609146164309. C175
343 (1,7,49) 245723963580715350733457214075196517831719729.P162
345 (1,3,23,69) L.M
L (5L,15M,115M) 21391.31741.1715341.27875688121.P36
M (5M,15L,115L) 37951.5347963681.2351881115374174051.P30
347 (1) 34911671.9060198312365106899848549. C210
349 (1) 465248728728895394653153888943818531375975270853944206732179708325578302943996260672261958710669770611963071.P136
351 (1,3,9,13,27,39,117) 7655311.
.6475711850365695029787483033056414199292785571.
.1489161023006154219903790225805356280792802449809.P51
353 (1) 235099.5451190499.205504553260781.34785215885504832719. C198
355 (1,71) L.M
L (5L) 8499626476216091.8558727566683804731617356972960527829841.P43
M (5M) 71*.17041.7484111.P85
357 (1,3,7,17,21,51,119) P135
359 (1) 719.41785692653578003162849.6677881008782967997903339939.
.837248571667848555569202584041.P168
361 (1,19) 129422865652104096162599.6417463808715658282089494909. C189
363 (1,3,11,33,121) 3631.P151
365 (1,73) L.M
L (5M) 1077334433621.11219338425853865221726037921.P61
M (5L) 6571.1328865721.650916499741.22354588958731.33735961890251.
.560294380367699191.P32
367 (1) 1047157937929.645658411286666140609459.
.52862043959452141411641760543741.P189
369 (1,3,9,41,123) 127551580041880421988556534595464339049133992744450750874579570996690409.P97
371 (1,7,53) 2969.11131.35922655704041.226578241537144915139.
.11014814494800487352604755748091574916119.
.22524108177157511856531387268450126765714109909640309103811550689.P73
373 (1) 2239.4350204259.1368671486390599.437284546695919489287780329.
.132287615591619115060073063073355132265371.
.993814769723013038733622579709248518485779.
.2634696095973127246023496488851214554377085833500724085471.P65
375 (1,3,5L,5M,15L,15M,25L,25M,75L,75M) L.M
L (125M) 751.317286001.527559073501.P47
M (125L) 281057814001.38033863525621501.P42
377 (1,13,29) 13076016539.1267005005969.2778318756799.
.72952844755822287959.7913584118074610352277451069398306909.P144
379 (1) 15919.19709.154593500445308877590595293456916511.P221
381 (1,3,127) 17365824770202511.2146271536375625882474712607488854837881.
.12882995722731844746940951540119250212241259630747509.P69
383 (1) 525692477729.2948582111117607147637161465549027541.
.4260621080011732733351177066528303869.C183
385 (1,7,11,77) L.M
L (5M,35L,55M) 33411357084712191971.P65
M (5L,35M,55L) 2471701.927476143441.134234460550630441.P49
387 (1,3,9,43,129) 27091.42571.237619.591570397114510975382037276803611.
.2656120768584457773885517433083338243991.P90
389 (1) 179719.138068549.3391732755856086401282016931. C231
391 (1,17,23) 2568871.74708371.311250747739.416079604348810289.
.787775103387484980951811308682438561347569.C161
393 (1,3,131) 344313589.
.3275262323842759491144568903593811836020835083160675552849533185921.P107
395 (1,79) L.M
L (5L) 104449388937445035371.P90
M (5M) 190391.68175421.38701052851841.6440862401422039384631.P61
397 (1) 1043801929.7768438039. C258
399 (1,3,7,19,21,57,133) 93174481.P144
401 (1) 58161041.P272
403 (1,13,31) 1892489.688730186119.311447631608357947354270996859.
.5031770563367301370277089549186021905732092831.C159
405 (1,3,9,27,81) L.M
L (5L,15M,45L,135M) 811.1621.6481.921737881.P57
M (5M,15L,45M,135L) 2332368714077641.279151346689444799703543961.P34
407 (1,11,37) 24421.P248
409 (1) 4909. C282
411 (1,3,137) 1758306499.13509261751.3501243666084542114634292493431.P141
413 (1,7,59) 1677756178117368440322458992363311946171.P204
415 (1,83) L.M
L (5M) 116201.90045041.167674286348441.20498545382037148227331.
.84340842933027824154067061.P39
M (5L) 1209311.P109
417 (1,3,139) 5839.1446646439677126258978503447303571.
.2463633633449688423900024936785360355054079.P114
419 (1) 839.3676736043047175259.
.72898712900545938884496308172168836533702575641.C224
421 (1) 14894981.31410466159536169.73688412163867840421869.
.2510106373340528083960492234939.
.6226633359276226469107090691434236881.C180
423 (1,3,9,47,141) 5844169.39572332202385740741222289075450046633403426658269930807344301678241999541.P113
425 (1,5L,5M,17,85L,85M) L.M
L (25M) 5101.3609101.P102
M (25L) 4878161432677729051.P94
427 (1,7,61) 4271.18978978300104368967581806916192652565860081. C205
429 (1,3,11,13,33,39,143) 859.17885869.300128401.P150
431 (1) 3449.494789.598229.47689015695989309431. C266
433 (1) 25981.P298
435 (1,3,29,87) L.M
L (5M,15L,145M) 22621.646325611.81097049492978072251.P46
M (5L,15M,145L) 5931661.195347093735677589850742253611.P42
437 (1,19,23) 48398105719.59147335579.P256
439 (1) 1031865461192099.677725117273121779.
.1567744952609398205028484317631.C244
441 (1,3,7,9,21,49,63,147) 29989.78818666779584504109.
.6667457715286125980193380399931785881.
.1326741989101977002310909280900124438213535612865860634471.P58
443 (1) 649538175793866829.616533026379726629232183581257435377049529.P250
445 (1,89) L.M
L (5L) 26701.26698816301.103738789930024471.P92
M (5M) 8011.15131.101232724284574681.14542112049750708402496286411251.P67
447 (1,3,149) C207
449 (1) 8786607424180750985373917154782538355992341. C271
-------------------------------------------------------------------------------
455 (1,7,13,91) L.M
L (5L,35M,65M) 252009190957922611927192988424665484581951479831.P53
M (5M,35L,65L) 911.4914911.6481021.P85
465 (1,3,31,93) L.M
L (5M,15L,155M) 18918352942471114958730682051.P57
M (5L,15M,155L) 2791.6084353978581.385988764693732689151104968796091.P35
475 (1,5L,5M,19,95L,95M) L.M
L (25L) 1954151.P120
M (25M) 11360856146437080511603913201.
.11971699680363533589698621027808346660430201.P55
485 (1,97) L.M
L (5M) 971.2387171.286948574407858827947671.
.4064396828893513244260225706548054644512772987091.P53
M (5L) 3881.12611.5829701.11401381.4588270721.P104
495 (1,3,9,11,33,99) L.M
L (5L,15M,45L,55L,165M) 578259991.P76
M (5M,15L,45M,55M,165L) 991.19801.14300545887541.
.123624849246637675534237287451.P35
505 (1,101) L.M
L (5L) 205031.520151.656821011757186571.
.36690330713871434099552140344241171.P77
M (5M) 5051.671651.119524411.9476228324821.
.22556231631518418786932381290161151.P75
515 (1,103) L.M
L (5M) 1031.96821.326493403069610501.87332225947582956902696341.
.8693112016386012208667474531956646459249501.P48
M (5L) 41201.236985509596761461.56727322344599853862293969440589550231.P84
525 (1,3,5L,5M,7,15L,15M,21,35L,35M,105L,105M) L.M
L (25L,75M,175M) 1051.P81
M (25M,75L,175L) 37815352051.P74
535 (1,107) L.M
L (5M) 618691336713427778212600657181.277267461900868216455231985933091.P86
M (5L) P149
545 (1,109) L.M
L (5L) 232171.21519871.222583733401.P128
M (5M) 1102582961.2392268400751445411411.197279999499978473755531.
.2602111035179418475927861.P73
555 (1,3,37,111) L.M
L (5L,15M,185M) 12211.154402111.9202869825377571330816454640823938251.P51
M (5M,15L,185L) 156511.834721.19852351.P83
565 (1,113) L.M
L (5M) 81119810875491958307893501.P131
M (5L) 17317559621.578904334643163991518185302373441.P114
575 (1,5L,5M,23,115L,115M) L.M
L (25M) 201781301.59383718252771389151.31766207470090423211256551886690151.
.8681684850386430151422007197514419601.P55
M (25L) 1151.173651.1069501.40231601.26135496851.
.3190505517374665681595009461154083852963479431101993034851.P64
585 (1,3,9,13,39,117) L.M
L (5M,15L,45M,65L,195M) 5648761.945078093181.1016644491721.P70
M (5L,15M,45L,65M,195L) 2497240172701.7845827291641.P76
595 (1,7,17,119) L.M
L (5L,35M,85M) 23801.25970709103346701.9538501024577801535193513460771.P83
M (5M,35L,85L) 3597764176982506745587150886060717612102325001.P90
605 (1,11,121) L.M
L (5L,55L) 11*.
.187582679253889692817030220745179165323721206561986278625943751.P91
M (5M,55M) P154
615 (1,3,41,123) L.M
L (5M,15L,205M) 1231.2908888501.1788582600145862687626441.P76
M (5L,15M,205L) 62731.248461.18383372131.226073665516341068071.P71
625 (1,5L,5M,25L,25M,125L,125M) L.M
L 637043435256965381251.887918028727761332501.P133
M 1122853751.P166
635 (1,127) L.M
L (5M) 39371.1291779384590714829718240121.
.16676977654171910567446311966822846252082621.P101
M (5L) 702206150831.5598493819552929453451.
.12318542415046443477661711361.P115
645 (1,3,43,129) L.M
L (5L,15M,215M) P117
M (5M,15L,215L) 1269509641.4144987978415039132191.
.3118954401781386053150022153343306501.P51
655 (1,131) L.M
L (5L) 14411.592121.601291.2304799900471.
.9401087165312249425680125005501.P124
M (5M) 18341.51703081.799726387996561.
.18890996177400050445796057359872326454156186975971421.P103
665 (1,7,19,133) L.M
L (5M,35L,95M) 197093734279293731287445626494587381600438850930731.P102
M (5L,35M,95L) 347131.426361515667769851699539882056479395496411.P104
675 (1,3,5L,5M,9,15L,15M,27,45L,45M,135L,135M) L.M
L (25M,75L,225M) 14851.71551.
.224491256466428912635990400917424912842296807654322501.P64
M (25L,75M,225L) 1357803001.8227149935929283044132471512207436501.P80
685 (1,137) L.M
L (5M) 18025611971.535569744943399716958855013333971.P147
M (5L) 497478532938871159260123601.5276583832843396532095802023230871.
.1056664240671504816947479204045440388475071602248489506201.P74
695 (1,139) L.M
L (5L) 10170631.460503727624584883373804093554831.
.6361052470423138945814073705227461.P120
M (5M) 822881.28927420661.9807083838590469822562651.
.8652435908097010399434328826426397220701136561.P106
705 (1,3,47,141) L.M
L (5L,15M,235M) P129
M (5M,15L,235L) 1290151.43779091.40130368419540180043461725371.P87
715 (1,11,13,143) L.M
L (5M,55M,65L) 2861.15731.568219795001.1835752527181.4734577062931.
.15650665725833711.P108
M (5L,55L,65M) 7151.9512818740950944022814380525757298363354145831.
.169164539024599794037276481218573886646346274125937851.P65
725 (1,5L,5M,29,145L,145M) L.M
L (25L) 1451.21751.1526625921911039333504551. C165
M (25M) 97151.508005163062054101.2986825327584332523851.
.1402006809136700630208151.P128
735 (1,3,7,21,49,147) L.M
L (5M,15L,35L,105M,245M) 1471.12388179201301.
.69883849889109985909137301.2330833648199530366716543767343661.P42
M (5L,15M,35M,105L,245L) 72031.56117251.P105
745 (1,149) L.M
L (5L) 8941.444296944929401474501177110211288771. C168
M (5M) 674865871526349844777781.862749058814541800048281.
.5366174006302748232769811521027916623304811644131.
.9339881975422965769035311954726327173904910651625492511.P55
755 (1,151) L.M
L (5L) 4631171.P204
M (5M) 1511.978138181410195378169072018321.P177
765 (1,3,9,17,51,153) L.M
L (5M,15L,45M,85L,255M)
42063108592714184976397190339929024980416586694201.P85
M (5L,15M,45L,85M,255L) 59671.152620561.7001133121.P112
775 (1,5L,5M,31,155L,155M) L.M
L (25L) 83663737356301.23070046134688729328401.P174
M (25M) 9986651.50717551.367041833651.
.407991163083560495035321532597201.C151
785 (1,157) L.M
L (5M) 25330381.2648952970439367096395238234716953022350096447801. C162
M (5L) 1571.62801. C211
795 (1,3,53,159) L.M
L (5L,15M,265M) 27031.465396726961.
.1759519043894301046372377642322402644556845061431561676869571.P69
M (5M,15L,265L) 6941839831.310928520390594886861.
.9428867545869562874663176246654957067219281.P73
805 (1,7,23,161) L.M
L (5L,35M,115M) 513476216471.3776990462491. C160
M (5M,35L,115L) 2000144310791971.
.52083866402604872103138538630779570592776194951.
.884759571094733769873572106626750614848619033081.P76
815 (1,163) L.M
L (5M) 21191.23230427545093989573574035606899884718671. C182
M (5L) 33596633405529951211752346481.2835390828069919584008238108700801.
.54938978785399383334196504918901015066871425911.
.4978019070778465969873397393941797403128296569832548381.P64
825 (1,3,5L,5M,11,15L,15M,33,55L,55M,165L,165M) L.M
L (25M,75L,275M) 1184981853909336451.1342155134288948494351.
.232159617295908150401568225810555451.P66
M (25L,75M,275L) 915689343435380401052957142231951033638922949189951.P89
835 (1,167) L.M
L (5M) 264278122166663495614091.56173271056427875611390781.P183
M (5L) 3329981.55690652993685370934111.P204
845 (1,13,169) L.M
L (5L,65M) 54658890184991.375253243497628098828340729608671.
.2158078190694169386056600385951598471.P136
M (5M,65L) 6761.633751.892321.11711701.P196
855 (1,3,9,19,57,171) L.M
L (5L,15M,45L,95L,285M)
29279767389963944149986328770810652642323537932397766795544349601.P87
M (5M,15L,45M,95M,285L) 227431.9581918519281271232331.
.1554246690784409607115661081503201.
.9438797532811279585143365523975961.P57
865 (1,173) L.M
L (5M) 445838345602031051099408504461587023312861.P199
M (5L) 418381471.446573551.
.37248661684213703064761312273115067533733792708040311.C171
875 (1,5L,5M,7,25L,25M,35L,35M,175L,175M) L.M
L (125M) 199501.21987719251.3292915346586251.
.714230949655553158292542550246822887001.P140
M (125L) 10885001.65201101781407160404501.21618698221031733473930251.
.290420343548877552397308040001.P126
885 (1,3,59,177) L.M
L (5M,15L,295M) 82837467331.440656089327907801.P135
M (5L,15M,295L) 18072629251.
.282500728032914696042973568098174674481979831.
.11142214628485169485922225114352330077923536391.P61
895 (1,179) L.M
L (5L) 1853672814935393064677577610841. C219
M (5M) 8951.901665213571.3808663720051.
.883309533541949415266717039218360375211.C181
5^{5h}-1=(5^h-1)L.M, L=T^2-T.5^k+5^h, M=T^2+T.5^k+5^h, T=5^h+1, h=2k-1.
Table 5+ Factorizations of 5^n+1, n<=450
n Prime Factors
1 2.3
2 2*.13
3 (1) 3*.7
4 2*.313
5 (1) 521
6 (2) 601
7 (1) 29.449
8 2*.17.11489
9 (1,3) 3*.5167
10 (2) 41.9161
11 (1) 23.67.5281
12 (4) 390001
13 (1) 5227.38923
14 (2) 234750601
15 (1,3,5) 61.7621
16 2*.2593.29423041
17 (1) 3061.41540861
18 (2,6) 37.6597973
19 (1) 761.19609.213029
20 (4) 241.632133361
21 (1,3,7) 7*.43.127.7603
22 (2) 89.1030330938209
23 (1) 47.42272797713043
24 (8) 152587500001
25 (1,5) 1901.50150933101
26 (2) 13*.53.83181652304609
27 (1,3,9) 3*.163.487.16018507
28 (4) 59509429687890001
29 (1) 5096867.6090817323763
30 (2,6,10) 2281.69566521
31 (1) 1303.21207101.28086211607
32 2*.641.75068993.241931001601
33 (1,3,11) 595123.190771747
34 (2) 1973.20129.45289.12447002677
35 (1,5,7) 15216601.4698932281
36 (4,12) 73.543097.1503418321
37 (1) 9103.29010221.45920153384867
38 (2) 4885168129.2864226125209369
39 (1,3,13) 3121.22735632934561
40 (8) 25601.909456847814334401
41 (1) 83.43543.221401.9472026608675509
42 (2,6,14) 2521.24587411156281
43 (1) 1549.9547.7866608083.1628744948329
44 (4) 9080418348371887359375390001
45 (1,3,5,9,15) 60081451169922001
46 (2) 5465713352000770660547109750601
47 (1) 2069.15888756269.3602372010909260861
48 (16) 97.240031591394168814433
49 (1,7) 49105547.1866013003.2481357870461
50 (2,10) 239201.424256201.89620825374601
51 (1,3,17) 103.8467.528667.60119016343
52 (4) 51169.537181587281.129044008326199409
53 (1) 107.28838378869.599659003321309822423087
54 (2,6,18) 14551915228363037109375001
55 (1,5,11) 10910444855403996246103496881
56 (8) 113.337.2520917617.37007700327977836913
57 (1,3,19) 229.75649382555448580095589
58 (2) 1334402673828313149547634216455312875601
59 (1) 827.5242462229.3237765225301.2059647179472887
60 (4,12,20) 23320317172851318360001
61 (1) 367.9029.15571335384347.14008364639128540436401
62 (2) 8124604717965111529.102651353523520067851969
63 (1,3,7,9,21) 883.406729.24132781.1692416503
64 2*.769.3666499598977.96132956782643741951225664001
65 (1,5,13) 18461.15188886343541.15199221608544481
66 (2,6,22) 1453.6509387183417404924784917
67 (1) 11293772630057337854244300009061892827351888021
68 (4) 137.623017.938894988049.1361753880209.4959636586609
69 (1,3,23) 66163549.253592389.403316413944121
70 (2,10,14) 281.13148832195720299503896018648521
71 (1) 4261.5747338499820296170481.288231038713838413442281
72 (8,24) 1297.2739177855667309845605995807633
73 (1) 63554310563.777612767772190289.3570677866897550288203
74 (2) 9769.40849.510241095096183757930733363918820917976121
75 (1,3,5,15,25) 118801.20775901.24665701.149439601
76 (4) 457.21363981507860375753.21654472202540732126905077281
77 (1,7,11) 20828886541.49970061516036179615325895945741
78 (2,6,26) 157.8684521.4056854881.667929705480493
79 (1) 18251687.7897663181.511465533067.37399095525167136010188229
80 (16) 131349761.167597261761.24625444126052524088217281
81 (1,3,9,27) 3*.1783.5023.2066067271380136212224701233463
82 (2) 193357.6355001.1148205782281.56373078952722628530598981268453
83 (1) 167.4029666108840585686296627.2560787702841639767474730913969
84 (4,12,28) 6553.90217.6019022585035590658668001
85 (1,5,17) 75752681.247515241.504156421.68795069664507129341
86 (2) 173.2171388367013.132331554743163541916284364878460504933118649
87 (1,3,29) 349.210390487070809.22500358133965991972941
88 (8) 13729.929281.71225159567951317923809.91029014606406186465761
89 (1) 39387996609449861.56522267529181963.12094715786677995586454978647
90 (2,6,10,18,30) 20478961.6794091374761.25535754811081
91 (1,7,13) 15887476811320661.15994146485373751289418997754783021
92 (4) 150220315444217.214752088491462210591995581828628861192144614553
93 (1,3,31) 258065887.75005167927.53345671490722200466369
94 (2) 5077.12409.329573417220613.935213864500231208652603316429973471246089
95 (1,5,19) 4561.179763436784239734042181.309828362361188845069741
96 (32) 193.5207826497153857.539344757336151926206665601
97 (1) 29683.261707.547663.90130760102421063383.P32
98 (2,14) 197.164204573839769.74535675530760254357.21441970593484574539001
99 (1,3,9,11,33) P42
100 (4,20) 4001.132001.776401.P42
101 (1) P70
102 (2,6,34) 6733.4613053.19724557.34288117.26837241260899651321
103 (1) P72
104 (8) 247161617.825256433.2220784177.31308249137777.P27
105 (1,3,5,7,15,21,35) 421.5236141.1354224218968567573270561
106 (2) 8871726015923707071209.P51
107 (1) 643.P72
108 (4,12,36) 73009.1853281.3314953.36280398313.13012873776055827785521
109 (1) 19403.4046322895447485867367.P50
110 (2,10,22) 245521.1458601.2802204291103029121.P26
111 (1,3,37) 223.5107.668221.13844587.107903101.221746234901611997486023
112 (16) 271489.1149569.10922689.465314420407473281.P31
113 (1) 227.1387189.12249784663.P60
114 (2,6,38) 22573.53590717.2108505761893.P26
115 (1,5,23) 73141.P57
116 (4) 233.929.33409.397823386118610689.1547355341777494553.P33
117 (1,3,9,13,39) 40483.43236180703.P36
118 (2) P82
119 (1,7,17) 2381.25229.4172141.P53
120 (8,24,40) 2172116161.P36
121 (1,11) 374499841.304639362281.11449313571047243.4600715686162128721.P23
122 (2) 733.61001.19811275733.26933356951273517.P50
123 (1,3,41) 30970420211207224741561.P34
124 (4) P84
125 (1,5,25) 3001.51204738027593108331001.P44
126 (2,6,14,18,42) 4661402165281.147053007410401.308942475257273345172721
127 (1) 509.2287.2735581.P76
128 2*.257.23653200983830003298459393.P62
129 (1,3,43) 327845761.558801427.1420986601.P33
130 (2,10,26) 87881.14402441.P56
131 (1) 263.P89
132 (4,12,44) 331660297.112835047682166217.P31
133 (1,7,19) 2129.354047.P67
134 (2) 20369.P88
135 (1,3,5,9,15,27,45) 164701.31472682400981.182517282870121.
.223823944168266601
136 (8) 17*.999329.P83
137 (1) 823.2741.22469.7642530702770043710321.61562630761411218787053569.P37
138 (2,6,46) 277.70942489.22600337281.66988220431117.P28
139 (1) 172694671812043.417786018853823.2459716746919477501.P50
140 (4,20,28) 514845603025661988644048801.P41
141 (1,3,47) 283.1129.24048335089.37516308093487.P35
142 (2) 853.72497533.8367932201.200771218157.554474665573.
.1095832589179957.P40
143 (1,11,13) 2010581.2253938672701.567618483045329.
.3028704600213534236926361.P27
144 (16,48) P68
145 (1,5,29) 98047293061.3532907090761.17149742984461.P42
146 (2) 293.27133517.84128413.772557938155429260697128053.P56
147 (1,3,7,21,49) 7*.9887502829.P48
148 (4) 3257.3542233.10044059578457.P78
149 (1) 85229.4394309.12703371381749.1084802496290323.
.864203844381482464122519761.P37
150 (2,6,10,30,50) 14401.299541552154912341601.P32
151 (1) 43367201.P98
152 (8) 14897.4189729.11524380579073027969.
.101284922414513827611672455293249.P39
153 (1,3,9,17,51) 307.6427.6297787.45618058027.P44
154 (2,14,22) 8009.40987409.74353801974761.P59
155 (1,5,31) 21701.108674992710961.145475949458129109023753501.P40
156 (4,12,52) 319143533738738955692755921.P41
157 (1) 1585387.223975620462535382927.P83
158 (2) 317.41081.72997.10390269663517.P85
159 (1,3,53) 5407.1725469.P63
160 (32) 46957667265666758402894952584920394200961.P49
161 (1,7,23) 116243.P88
162 (2,6,18,54) 503731168597.720314410420100602530036001.P37
163 (1) 1981740926993660561.286075553470422974507.
.721493104094461397911450801.P48
164 (4) 2953.811755457273.46964872205858855033.
.2211877372577215640856618933593.P47
165 (1,3,5,11,15,33,55) 661.9651181.P47
166 (2) 997.4649.99006230951147470700089.P85
167 (1) 4978061451403.50902967640396173052637279626869845515838501.P60
168 (8,24,56) 12433.44763922656823409574575008753.P35
169 (1,13) 493481.P104
170 (2,10,34) 1361.14281.14239201.87393601.1972618762904267665190337601.P40
171 (1,3,9,19,57) 60272250820183.6267476427578502461453809.P37
172 (4) 18233.30185745097.2646713294612838233.P85
173 (1) 347.42794294406607.P104
174 (2,6,58) 382801.506670253.146817720340602448117.P44
175 (1,5,7,25,35) 701.2801.6309154245455368301.P59
176 (16) 353.1827937.2704769.1800750547615213217.
.609201485490930587260897.830940907997357679202561.P31
177 (1,3,59) 709.1063.347629.49987218529.130325543183670643.
.504583856881942565107.1663887084465861537223
178 (2) 20365288294844141313970353677.P95
179 (1) 21320258969.12021304420747747.227138023883511049.
.20324346366468227562461.9711234996179070876201114229.P31
180 (4,12,20,36,60) 8641.440641.356646293281.50735307557193841.P30
181 (1) 1087.28961.101723.P114
182 (2,14,26) 3640732369.141437955091157453.P74
183 (1,3,61) 17203.11833147.2880471241.1117197595048793563.P46
184 (8) 14966561.7323187654220815881445121.
.36153673470666026958084532869022033.P57
185 (1,5,37) 2221.3701.P94
186 (2,6,62) 373.1117.1489.10269119521.P66
187 (1,11,17) 1123.12343.
.17871635646349095375983368709164224334356049680569.P56
188 (4) 90617.755009.951281.12795134934601897.
.4760594190627487654169124325931441.P63
189 (1,3,7,9,21,27,63) 2932903.238040587.3916103733109.
.1743424593819524631667.P27
190 (2,10,38) 98041.2574645949207561.P81
191 (1) 383.17932621608157901.45343989264399047245009865403089.P83
192 (64) P90
193 (1) 69481.1046447.
.13302022772145301912117245535348604521034254056544901.P72
194 (2) 25997.52769.66477837920609.374962321852666418369.P91
195 (1,3,5,13,15,39,65) 14011933046202781.1755692053873139750161.P30
196 (4,28) 19993.2333311009.38811185416697.P91
197 (1) 20420627.1526268143138331950101.P109
198 (2,6,18,22,66) 397.766142400277.750213207760936191769333.P46
199 (1) 2389.75223.44656987140518535039596003383.P102
200 (8,40) 1601.103390853395201.45804743639930233601.
.668219906430537590060380972001.P46
201 (1,3,67) 116555713473655927.30825527446446607747.P56
202 (2) 809.3637.5728721.3375268261753121.
.54234164649457019858090786783366331533.P74
203 (1,7,29) 29*.23039208450560482164167.104193411347291769738017451047.P65
204 (4,12,68) 2857.65127801352770865664923661368506241.P52
205 (1,5,41) 821.2175461.33996220923281.24834433083178321.
.3788285672971032867364321.P49
206 (2) 720016715917900826434290826659207222585733.P101
207 (1,3,9,23,69) 3727.17389.314227.2401937749.67153740229.
.215293115466454807184993896087.P30
208 (16) 149343725750590533761.5102538254078186071676415499055681.
.5717693557043829027825513019667841281.P44
209 (1,11,19) 10123543.213379486321.
.45859681134648298337859101583259138328629.P67
210 (2,6,10,14,30,42,70) P68
211 (1) 22144561409.8785612071234927581234843.1550760729196823058417670649.
.91807021517467057942827543491998459427.P47
212 (4) 24452081.P138
213 (1,3,71) 2893657379733917265396310772669592883.P62
214 (2) 25253.23252612956243152283169.18394448899336309965200241530917.
.997778184811820085932891049469009.P58
215 (1,5,43) 1721.P115
216 (8,24,72) 433.177553.39209617.170735041.246414260277520913233.P57
217 (1,7,31) 51647.44245867.1027650404358607.20864888505062314147.P80
218 (2) 938804357.36987176266711133.43330701999236285089.
.89818280744210450462726655090961.P74
219 (1,3,73) 1526556583.249603886403307106321078321358781541.P57
220 (4,20,44) 881.21121.148721.25301535619781301761.
.43117673217579194979701441.P55
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223 (1) 187373521.1588248792798900263.64020956436201443428737029803881709.
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224 (32) 3137.181398083777.35822800438975049964261933857034881.
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225 (1,3,5,9,15,25,45,75) 119701.826201.2596501.64317527962486535125801.P44
226 (2) 11913287466894338293503913814067039110653443245880449.P105
227 (1) 1769057265869086021.11015757643914646321123501403.
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229 (1) P160
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232 (8) 33632031931522326531782695489.
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233 (1) 467.29096873590481178947.P140
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239 (1) 17209.5729889967417247.
.1003240831021866550564937680732854800270693763847709.P96
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241 (1) 1447.271849.533122367.525411589067580318444083.
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243 (1,3,9,27,81) 3*.8263.39367.17995609.985562803.5986535931982369.
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244 (4) 57097.1475034311407732073353.P142
245 (1,5,7,35,49) 114661.187181.5758481.20334022013834451721.
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246 (2,6,82) 4560841.65465466516157.P92
247 (1,13,19) 4447.5853901.29599987.5513798691623.6655472266225553901469.
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248 (8) 1284020836753.557639293920224377596990976991388831169.P117
249 (1,3,83) 7726419616728409660092049.P90
250 (2,10,50) P140
251 (1) 503.27258601.
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252 (4,12,28,36,84) 1009.11824849.2759159593.49969930916222857.
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253 (1,11,23) 23*.390782201041.P141
254 (2) 18797.23369.60961.8134741350985769921.510854629111063017581573.
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255 (1,3,5,15,17,51,85) 206249584501.85077293022121.
.18654796603647183092401.P42
256 2*.1655809.101199664791578113.4563566430220614493697.
.12025702000065183805751513732616276516181800961.P88
257 (1) 176303.46830908691848972641835440256561849621017565302707681386771586166779822642173925770149.P88
258 (2,6,86) 56175373.
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259 (1,7,37) 4663.13879650012159635243.P129
260 (4,20,52) 2081.P131
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262 (2) 1049.17293.48821081.8573118546001560555564908129.P139
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264 (8,24,88) 518378519354634577.P95
265 (1,5,53) P146
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267 (1,3,89) 448027.59483329.32539908261456858140701.
.56086502499313161545149.P65
268 (4) P185
269 (1) 8609.93386204629.15538110699419449.P157
270 (2,6,10,18,30,54,90) 618841.2068201.
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271 (1) 1627.13009.412463.37013723.2476120019041.P156
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273 (1,3,7,13,21,39,91) 547.9829.842474804263.50907393322559047.P66
274 (2) 6891114051994032697301089.16945508997411292389468001.P141
275 (1,5,11,25,55) 44053990045343516701.
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276 (4,12,92) 1657.3368857.32786998209813096333308538793.P85
277 (1) 1109.9650681.1490305991985489901.
.126388159761055343234292253502483.P133
278 (2) 557.P191
279 (1,3,9,31,93) 59707.6293523585961325272635001.
.601177658416693050177473038760106861025677463.P52
280 (8,40,56) 3361.1046757601.554715662634844481.
.211311163972244819619417326617601756161.P66
281 (1) 563.1756844213936466378726696505807.P163
282 (2,6,94) 351416125984969.254754032198578321.5846086878571351849.
.4056894906182746738319224618717.P48
283 (1) 28867.10794921762136794464572609.30179284347246492551575903205690040477057659950513333027154449865801.P101
284 (4) 65873251351400529678881604643622504978360233.
.79054223989942445013826694675156397992474744610986129.P99
285 (1,3,5,15,19,57,95) 390722946406448237780581.
.9979141069997419042168820999353619521.P40
286 (2,22,26) 110809516598326058545635442124799433394333.
.25786248955108856095496727464834574220267319237679109854509573.P66
287 (1,7,41) 1723.49669943.59428670579923.P144
288 (32,96) 577.597889.
.38401599520882274416151769918729734539171500659227280833.P71
289 (1,17) 1644989.8528969.7225344822016874223743.
.12156847076444678217726556516258597180670422099432269314205601.P95
290 (2,10,58) 13921.11483163641.16972510486384731643441.
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291 (1,3,97) 20721014227435723.102243594151983391750660845889189.P86
292 (4) 1753.38907833.P191
293 (1) 587.645187.P196
294 (2,6,14,42,98)
26753443613214655421212169339114233130011764853739132929.P62
295 (1,5,59) 1181.3541.140145823858841.9625600889207570043521.P120
296 (8) 593.177601.814954734175776096337.P173
297 (1,3,9,11,27,33,99) 5448169.P120
298 (2) 244957.18988882573081.
.52509417634810887468425272956814828347615306977561.P139
299 (1,13,23) 1034424565011113115503.15218649781150668794223283.
.2460602344017504325543906769.P112
300 (4,12,20,60,100) 1201.7477331283039457201.
.1943721725056298631352604586154656001.P54
301 (1,7,43) 14449.42743.176989.26041733579107.
.71398356223351054354479829866663025664388644310993593530081301.P87
302 (2) 7853.8286881.4033512514609.677865814845240957392304024923821548572964677269102015272785066256481.P118
303 (1,3,101) 607.24847.1740662887.61597393790041.
.1148540966490621244258779533654923677123377383.P65
304 (16) 40129.52289.912480527030336132161.
.218353713527382179771166705049588259776583489.P127
305 (1,5,61) 15056021.22351621.2835547919074635255541.
.33568317875306837620981.107157282220986614613635281.
.668544860298171106062168575595041.P51
306 (2,6,18,34,102) 613.455983453.2194449013.95566927072257854677.P94
307 (1) 1229.11025070531745749.814616586610803721.2297296977063162527.
.754407444590658069665034348564831349816756299325427713589455248131953556687063.P81
308 (4,28,44) 617.P165
309 (1,3,103) 1487527.4527469.642310267.24193913287.330545029709161.
.422879580647947.1517713338849924001.P64
310 (2,10,62) P168
311 (1) 1867.27920959867.508715203947869243644884276021265065029502587.
.13132762900451821968706840158108829466847315743095478589617724372773046827.P86
312 (8,24,104) 1249.1873.293876827247645824001934037873.P99
313 (1) 4321661135227604368687.90107330782710173585723984396630473536745919968792358417711960610369521.P126
314 (2) 15980089.388038314748637665126113925790477.2728963224457842822106715175371794633135479952758694827622631951336401498830595178459933.P91
315 (1,3,5,7,9,15,21,35,45,63,105) 35281.69850912140360790741.P77
316 (4) 1195838801.10005578153.70432242073.82932824137.P178
317 (1) 4084229.172992716783529233443.3620382004977001942052983.
.998349008578576111331868104928413077313657947.P125
318 (2,6,106) 19081.20947933.436276206825076349879647249.
.110948582559121653141616707828218569.P73
319 (1,11,29) 28476798241.76276878979955184439531431817934729.P151
320 (64) 17921.
.33786487803728531919277441791678557990160649849731871941121.P117
321 (1,3,107) 2303573383935650005163767.273860673667943993469496783.
.15508073443324126840152709489.4753712821254698015771925989227.P39
322 (2,14,46) 1289.424397.4195885464702037.1198400376705575705576881.
.12658289026799429610110288303852317.
.37458200184731560512972757879121310733.P65
323 (1,17,19) 647.18089.727007771958290921190121741.
.1106833331463912890399339855877003093911395487.
.708062099953126128600812802478694643865554550280893749088603.P63
324 (4,12,36,108) 209290024478377.177309277461360218309390137951788241.
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325 (1,5,13,25,65) 1301.2024275501.31306627301.P145
326 (2) 653.2609.189895001.23288351985517693013.
.25666218950437934848265249.836678744221945580045751077.P141
327 (1,3,109) 10787032338307.16566453047149.24753046968859330729.
.29680517470861398776947048909.23801279212976547698450531783389.P46
328 (8) 17713.20907377.94877599143390227898211503024977.
.6610600308177707547653044400736535499160769.
.15914295375933233944181803813597505865874635752388929.P86
329 (1,7,47) 2549057618736721.13563720869035756711741.
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330 (2,6,10,22,30,66,110) 1321.4411608961.P100
331 (1) 48989.274069.404483.35098027085436321411407. C193
332 (4) 2058554713.65438094203676554432094356953.
.92204567651115096086964349490379361.P157
333 (1,3,9,37,111) 8260482604912643089.25085679215566320053389.
.20880879276654535886445179571008053406388481.P67
334 (2) 8100833605910528579098552256792313716093.P193
335 (1,5,67) 6701.628301435347801.3337802987674672671171503141.
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336 (16,48,112) 673.2689.8906835789071809.P112
337 (1) 99347042703101.8681942880812709284936701.P196
338 (2,26) 13*.677.349709778373997142089.452629512771138390982997.
.4020226117864755963006649.1314711044344945942445899409.
.68455761994776074550081198997.P90
339 (1,3,113) 18307.4392763.2987233423.117825760147.16509399574192003102207.
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340 (4,20,68) 8161.17681.48886055402391862040941201.
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341 (1,11,31) 683.21143.3055305555941.853869447408847.2846800854247901.
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342 (2,6,18,38,114) 50164561.197991079813.90492378184051683013.
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343 (1,7,49) 15078281.670548333797224163.497030883351192430344613753441.
.705782575459215386450100057697624063.P115
344 (8) 183399473.3070535057.
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.2568041714500286313054360802775479764283217061617.
.21457141563832546841295670414405769092880003276804641.P72
345 (1,3,5,15,23,69,115) 1381.43100384224227086881.
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346 (2) 3379037.1490847569.2133076820179418693.
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347 (1) P242
348 (4,12,116) 19316392153.26160681101041.701570688430849.
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349 (1) 8942070323.699603551730901.3562202055870367855123667.
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350 (2,10,14,50,70) 21001.4813889390953505801.P145
351 (1,3,9,13,27,39,117) 87049.3771847.P140
352 (32) 1409.369059329.P212
353 (1) 4943.1492860183629. C231
354 (2,6,118) 23662955437126651591573.
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355 (1,5,71) 65672997381060914413551821.30535022092590033631541127783262141.
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356 (4) 2137.187090930562706936930665593.840552573146809635459322735649.P187
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359 (1) 14870544741210523.P234
360 (8,24,40,72,120) 30241.43201.471354274081.
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361 (1,19) 140069.59588684185483. C221
362 (2) 154213.2533277. C241
363 (1,3,11,33,121) 727.P151
364 (4,28,52) 6165310743305738342794703714473897.P168
365 (1,5,73) 497997249288521.143360969004690255541.P167
366 (2,6,122) 1852487492507928532657573.
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367 (1) 73219364069.70057995652034894429.
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368 (16) 22817.3391255113651617.7673924820048666337.
.38355937362039743393.1181985669274649173537.
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369 (1,3,9,41,123) 10483773125218147.
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370 (2,10,74) 1481.5121318001. C189
371 (1,7,53) 743.31907.171403.42073627.2340865442872909.
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.241881732025657819145103362017436952827107.P82
372 (4,12,124) 854099353.P159
373 (1) 16827523.855947877694729.3402270307745780791746163. C214
374 (2,22,34) 36653.1833280694213.273799167334154011397.
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375 (1,3,5,15,25,75,125) 9001.994501.84719274001.P119
376 (8) 80637397290342655433338510282666959378353.P217
377 (1,13,29) 9049.26156261.140848709.590546419655063.658682853381229.
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378 (2,6,14,18,42,54,126) 757.20692918440938644983866317355828595289.
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379 (1) 4549.37850067509.1343210014472411202426336065918923.P217
380 (4,20,76) 13681.P198
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382 (2) 1053557.206218283317.146292198125317.234499916148809.
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383 (1) C267
384 (128) 11059201.11046880513.54263502654032658722910258215691970561.
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385 (1,5,7,11,35,55,77) 40420381.5394824821.
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386 (2) 773.157489.3357768242667569.29236154014192628894921. C223
387 (1,3,9,43,129) 711307.311491116057601.
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388 (4) 2558473.8761354357601.
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389 (1) 1918549. C265
390 (2,6,10,26,30,78,130) 106819198985704526442073820024512172507707681.P91
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393 (1,3,131) 787.5503.14149.365886952009.2346813979937685523.
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394 (2) 21277.52009. C265
395 (1,5,79) 7901.2452107355981.2450102857830301.
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396 (4,12,36,44,132) 4352560631862697.346866834441245977.
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397 (1) 37372787. C270
398 (2) 797. C274
399 (1,3,7,19,21,57,133) P151
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401 (1) 3209.68860956180521243.333064937028925224769589. C236
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403 (1,13,31) 142958609.50422342829.8134973129579141.
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404 (4) 12873449497.176729217433.579264071033.P247
405 (1,3,5,9,15,27,45,81,135) 359683606111861.
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408 (8,24,136) 5530033.469036801.
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409 (1) 567508524694081. C271
410 (2,10,82) 41*.583841.2896241. C210
411 (1,3,137) 280303.
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412 (4) 875089.143724625337.P269
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414 (2,6,18,46,138) 1271333135249191801.P167
415 (1,5,83) 961347785521.55785954324461. C204
416 (32) 9900401473.98759854245313.50303941887027464825562881.
.4670727010078891472720277353744610046303535783924992577.C165
417 (1,3,139) 1669.7507.68389.2972602849.62312778544931373437312353901828477385743715090139973652675999660403253132274229.P92
418 (2,22,38) 31769.1680361.7201636278388333.
.76891527486997630150967815266363922266871691437.C179
419 (1) 281595692549.79779766571538167749.18570424577878762265812169. C236
420 (4,12,20,28,60,84,140) 782349962686680131171831761.
.123682372689587234320272170926306609340495521.P64
421 (1) 75781.205114040909.2670138546849776123377091323. C250
422 (2) 49701926718842398034917.1838688342673461699900627759697114609. C235
423 (1,3,9,47,141) 222529765609.47221880173493743.8636976339699869318683821732318207901297057837683243210682129853674321.P95
424 (8) 1500134897. C282
425 (1,5,17,25,85) 56101.24320833768392901.P203
426 (2,6,142) 299097157.10980344624856402438121.
.33861120548112135250672625281.
.1042353298371672770854199410473194161120444561.P92
427 (1,7,61) 1709.78569.2478342640892955029371216779549673912736487569.C199
428 (4) 857.881695186297.1151785652724457273.
.1161803970449055432131784880415625128129.P225
429 (1,3,11,13,33,39,143) 8581.34744510854769.
.18538918397035986453797788078200765174683046595921.P101
430 (2,10,86) 2383921.19138570947468281.
.29523508733582324644807542345334789774261776361.C166
431 (1) 863.1319723. C292
432 (16,48,144) 16417.76946093484599331535592157286631660929. C160
433 (1) 59838112849.137082542813711740361. C271
434 (2,14,62) 32117.26490493.339914790655637.493140571225597.P211
435 (1,3,5,15,29,87,145)
8737168800277087090205609856511041915132043207241598729973141.P96
436 (4) 464777.1942414084717961809. C278
437 (1,19,23) 383527035556992289388236087.P251
438 (2,6,146) 877.7032466681.1278677279155561.4725897742147117.P158
439 (1) 471487.662755721911092119744737643749343823193619423487281. C250
440 (8,40,88) 359041.16079210384161.13901852309409971054059871521.
.30705281217618182630071422092483681.
.87530085823642527016184874776489974647524641.P99
441 (1,3,7,9,21,49,63,147) 63019783.177942365089147.334983841832046709.
.1412763237721728611106087634318515911781756690338345284469111587.P74
442 (2,26,34) 1925383738253.938705194413297601737101686241293330600757.
.27060574572993511759497340055450978609641029013.C168
443 (1) 887.8861.32783.58799821946580083201519815867. C269
444 (4,12,148) 662457647768722978873.288243041871591634870747489.
.2110210599897098921988264554383969.
.12183357210260619534067632764355337.P87
445 (1,5,89) 414780941.74122686370301.
.118105003026044634237696289344460081081.
.5895518746203541920435931300822793257683987241.P140
446 (2) 16682721313249361967072668559607434769. C274
447 (1,3,149) 1789.2493584477509.63998602029097150801.P172
448 (64) 2195201.3711466630036481.156991808999010049.
.1214606229579135791230337.C206
449 (1) 6287.24247.248636782340798457034945031270021. C273
450 (2,6,10,18,30,50,90,150) 1801.2516401.5115601.
.586035627698598209390491847184601.19112388231871991649234058440147001.
.670159729536080076087493765952253601.P49
Table 6- Factorizations of 6^n-1, n odd, n<400
n Prime Factors
1 5
3 (1) 43
5 (1) 5*.311
7 (1) 55987
9 (1,3) 19.2467
11 (1) 23.3154757
13 (1) 3433.760891
15 (1,3,5) 1171.1201
17 (1) 239.409.1123.30839
19 (1) 191.638073026189
21 (1,3,7) 1822428931
23 (1) 47.139.3221.7505944891
25 (1,5) 5*.18198701.40185601
27 (1,3,9) 163.623067280651
29 (1) 7369130657357778596659
31 (1) 5333.49744740983476472807
33 (1,3,11) 67.45686117391553
35 (1,5,7) 71.37863211.1469029031
37 (1) 149.7919.12211.2569799.334286825813
39 (1,3,13) 3143401.1262014275211
41 (1) 8648131.1854850885886497427178961
43 (1) 173.431.7383359.1048953903129961695599
45 (1,3,5,9,15) 2161.112771.19353635731
47 (1) 930911329.45110836129.17821718159716147
49 (1,7) 6527977.122694573317.600827908214213
51 (1,3,17) 307.927037099.23412002806867
53 (1) 13781.357293834576449.7091531088740602980647
55 (1,5,11) 3675127061.3031462959351050977391
57 (1,3,19) 47881.820459.219815829325921729
59 (1) 4866979762781.29050941569087.11522163007228653937
61 (1) 42461491.80057377.17252803354297421346943980322273
63 (1,3,7,9,21) 379.8387947.616332907.5239858051
65 (1,5,13) 11831.1420901.49398961.22533649654910414281
67 (1) 904949028329910415467529.3023706637809542222940030043
69 (1,3,23) 11731.1236385853432057889667843739281
71 (1) 3546245297457217493590449191748546458005595187661976371
73 (1) 44764549877.2436094907761.8439148071138817.138721648424756087
75 (1,3,5,15,25) 601.82051.271041511600591342728451
77 (1,7,11) 484847574510970082567.84002092056248016278479853
79 (1) 1147240288157.26283825237209622143.197531251446059329471533015409
81 (1,3,9,27) 27767002339.37725805717350619429950429139147
83 (1) 167.499.17597.41580677.80781507941.605274844997.P25
85 (1,5,17) 26807981.20891158391.P32
87 (1,3,29) 2694217.1833921547.4706691035521.1357610070580129
89 (1) 8011.2064441331.P56
91 (1,7,13) 48215910563832798697.P37
93 (1,3,31) 186187.290869963.659988451.842660004553.1358539033057
95 (1,5,19) 571.1901.825838991.1298704628041.25425408247171.2995523312517361
97 (1) 389.1747.1586365166597.18969653181299397175271.P35
99 (1,3,9,11,33) 16633.18380539.18414001.226407819331.38167293140100433
101 (1) 1275678077.P69
103 (1) 2473.5563.160681.P68
105 (1,3,5,7,15,21,35) 211.35281.58171.P26
107 (1) 643.5044140393054571.P65
109 (1) 30726149494277.P71
111 (1,3,37) 89728627.187333846633.1487716834806007369.3561693323285489089
113 (1) 107351.54466954894479739.201436862864351419099.P46
115 (1,5,23) 461.1151.44851.257917526307345124973861.P35
117 (1,3,9,13,39) 6553.5958157609.39031258670353.P29
119 (1,7,17) 16661.29032062767.103198889691409.12405291558509977.P30
121 (1,11) 4163261521.1304380464883.P64
123 (1,3,41) 25512169.141304123.P47
125 (1,5,25) 5*.9536585501.117811792772681609501.105875321588567599765751.P25
127 (1) P99
129 (1,3,43) 43*.P64
131 (1) 263.3931.6551.1284827442574221936870974393373403.P59
133 (1,7,19) 11971.188861.1101773.164331230229374083.P52
135 (1,3,5,9,15,27,45) 175509721.P48
137 (1) 6577.25247731.53280671.60042056488501962187.P68
139 (1) 557.21407.128159.P96
141 (1,3,47) 283.13537.753554761.122320721569.989671414201.P33
143 (1,11,13) 859.62545486153056268832471.P68
145 (1,5,29) 132241.150433631394488258261.P62
147 (1,3,7,21,49) 32093041.P58
149 (1) 38538553.1318713554713829548602512956686040272376450743377909.P57
151 (1) 2623968964411.4956504421137000338429923175878885954098593563.P59
153 (1,3,9,17,51) 9757142011.12644443230579801886843521019.P37
155 (1,5,31) 3559267608341.208210289142572055121.P61
157 (1) 6446107.6423436771.81127299702871294523556776543.
.8695994904356302134775281276601.P46
159 (1,3,53) 118721004139.67587459957091.P56
161 (1,7,23) 10949.593447.491787574454982121.
.3358586137753609961516447641418203949.P39
163 (1) 653.2378523250342970947582043555610171717174452063.P78
165 (1,3,5,11,15,33,55) 331.13724862774476458441.P41
167 (1) 19466857.10301691259.229027359614687.9703107759710968661.
.2200446540213260920441013.P55
169 (1,13) 677.3719.1420277.3066042413300025661761581713.
.351082413599031251316269147227.P52
171 (1,3,9,19,57) 19*.25896916098621777025320461067950269867.P46
173 (1) 924669087985921.495043698717322221180325946047148316337.P81
175 (1,5,7,25,35) 3822701.114265201.141218351.7292423951.34840572551.
.35107498301.2370825139201.P28
177 (1,3,59) 1421059369.P82
179 (1) 359.4297.399887.1126853766403.
.171074041901536300021132517497157303.P80
181 (1) 39821.12684206910817829.P120
183 (1,3,61) 22335533202362157841587721.P68
185 (1,5,37) 1063053988637874955869001.P88
187 (1,11,17) 382229.4208612395681.6467774498519851224197542939036067237.P70
189 (1,3,7,9,21,27,63) 10644859.292645031213683.P63
191 (1) 383.120477626957.141173343133408897.172804791061171733536391399.P91
193 (1) 748132849.3759493321.230824001813.344929902064301.
.577701497837906594854943.P82
195 (1,3,5,13,15,39,65) 523065274520717779891.795382366687653584971.P34
197 (1) 2235557.10123252906683101.P131
199 (1) 797.191837.3693839.484493690172684383.
.2389106853487241752315685035579349880354989277451.P74
201 (1,3,67) 3196645037857.P91
203 (1,7,29) 1458188789.432549126887388039664858367.P95
205 (1,5,41) 66571969781.28852807210022072371.P95
207 (1,3,9,23,69) 399097.P98
209 (1,11,19) 18873119.414230477.84125065520563.
.39547815403982363610457333838688241066157.P70
211 (1) 35768449921.127491843407.22502477360820492307768713607212049.
.953864267757776424221068538656285528154532046177627.P57
213 (1,3,71) 22301660719710979.P93
215 (1,5,43) 1291.19660072438421.P115
217 (1,7,31) 385227416351.26316013765873042806112463084693.
.1265855393578666785134496493194757776649681.P55
219 (1,3,73) 1143619.2820121693645487997956892799666256974847683.P64
221 (1,13,17) 4421.39721657.41183788762160210182927373892714194450477.P98
223 (1) 359734681.19261747635283.P151
225 (1,3,5,9,15,25,45,75) 320851.3388291201.
.2056583697041569929017137051051.P49
227 (1) 1393781.141273137445779487073.
.1994969355576066549710715311391607571195545033.P105
229 (1) 1505447.P172
231 (1,3,7,11,21,33,77) 174090854323.1526323866435523.
.83531679812360869820818648177.P39
233 (1) 568465670186789.3945524703927668484254051089.
.630076600824417505174717786052089.P106
235 (1,5,47) 941.88816955621.P130
237 (1,3,79) 15643.393024899619859590739537077043657.P85
239 (1) 479.555643125049.674693399227.2787187926109459.P144
241 (1) 248231.20481747682829.1840889044920084403.
.7710038279791808580832936799.
.246316726378395449466748758203811907753252397.P78
243 (1,3,9,27,81) 249844450267.47847655472636701140045116262913.
.103939380360329666746292370686492281.P48
245 (1,5,7,35,49) 22541.P127
247 (1,13,19) 1483.77071411.329143658741.82569737524705024142782304189.P117
249 (1,3,83) 17929.63871987.30565451980162779163327091617.P87
251 (1) 503.34204273.59351200969.80440705758435499.
.3489478020025154776405154855930832218902630153636858925509939.P97
253 (1,11,23) 23*.1013.75168534000121.
.259666046866989553234678839986188137176834471947.P106
255 (1,3,5,15,17,51,85) 1199699502336395787186091.P76
257 (1) 9767.17477.3309693452762216327.
.9306689489306197083232219997965248298881691751524941849307.P115
259 (1,7,37) 2458852243.128241016566344721609490367365530205308828951059763735701191925429688386832869.P82
261 (1,3,9,29,87) 523.467281506322297.1088767101178107721.P96
263 (1) 131982869.12634882984316388571047983239402938349932097252525834121084935889987017221049.P120
265 (1,5,53) 1061.12721.59499149215409565615862915027061.
.1443883079527663603943444340055791696913305571.P78
267 (1,3,89) 18530245891.P127
269 (1) 29083873645382611513.2334775781694290932919.
.14914054997566758664316062644331821838847.P128
271 (1) P211
273 (1,3,7,13,21,39,91) 547.2430143818773217.
.311093172628257376513996627655635721132089.P53
275 (1,5,11,25,55) 13751.10764601.1080416801397537451.P127
277 (1) 1109.5555507589053.152327217259127.
.16183852725411755980358386606565323256380349.
.14011053856556766554595009793438946968040153039.P96
279 (1,3,9,31,93) 326892685378628881.
.4195369622107561728725528588657828897923.P83
281 (1) 33721.186023.122413379955569789.228566796853368622765083206587.
.11762786832623811560644277958387970995125858157407.
.28717354535597728468537227064151476862005971007351781.P61
283 (1) 36791.217516631.6650510037106913164557499908650923. C173
285 (1,3,5,15,19,57,95) 47562842881.270596289241.
.209547179344816511252551051.P64
287 (1,7,41) 248848212837883.P173
289 (1,17) 671059.606329606788978761264759513146230361569.P168
291 (1,3,97) 111940600727841600317236399112257.P118
293 (1) 946391.193844113.2942031681694832257394740018524925949323820001499.
.77296633023286191721507964885438021314817447299007.P115
295 (1,5,59) 1181.19568032756311331.15208118255933834293359009545761871.P127
297 (1,3,9,11,27,33,99) 180794604080179.P126
299 (1,13,23) 599.5981.309379487.2341190333.394098064572643947287218201.C155
301 (1,7,43) 4941217.210619620359.387153001486618459.
.1026218994621353041220001358738943323.
.50018859578270750848409089664785836827007246435735770683387.P66
303 (1,3,101) 2529268867.4844162809.36536927761.257934717592273.
.31140192590150713382146219858775467.P77
305 (1,5,61) 86011.2112242585382465957468782381. C155
307 (1) 1229.4762799.774471014077469888593.205898436168261867044624683.P182
309 (1,3,103) 619.P156
311 (1) 1191554036683.3666342101717.1028123934962242970067317.
.7640150264100839651419559.C168
313 (1) 20032627.1280155603. C227
315 (1,3,5,7,9,15,21,35,45,63,105) 423123121.1076836800079531.
.72725680608108905121706081.P63
317 (1) 15217.494521.P237
319 (1,11,29) 10847.642814987.105726751219.891967447801.22138289428735393.
.1409088913314217103.50351395030858047251181629.
.4528381576097816452461578808677.P92
321 (1,3,107) 24212302455882717029271553.3989017680658351355297802631081.P109
323 (1,17,19) 647.P222
325 (1,5,13,25,65) 1301.15601.903471092281594039875101.
.9458999046244634687622911142066001.
.570312905179987052421467082275470442757451.P80
327 (1,3,109) 2617.5233.16823497.161662095193.P143
329 (1,7,47) 13581753427437725779783140643.
.5552584966550029192436491703687097023.C150
331 (1) 314314291.4180768321.23780962384145063253850061.
.129666906452652590684803897.217410311169868631779718575225367.
.65700141121171476089069828596037497497930556037.P109
333 (1,3,9,37,111) 157475333660422172779.P148
335 (1,5,67) 2011.412051.8595640749841.62977471383821. C170
337 (1) 103742130551.256196067835296580684999904063.P222
339 (1,3,113) 18307.13622377.17994204073.196433872316310611137.P133
341 (1,11,31) 17747199053. C224
343 (1,7,49) 1373. C226
345 (1,3,5,15,23,69,115) 691.241541401.139954341051841.P112
347 (1) 16657.92013588619490399. C249
349 (1) 8377.16171963.369649633.102551873890900123.
.126045115319866344351544439.C209
351 (1,3,9,13,27,39,117) 188270083.1132637392660177.
.255071870171283288213182239588434720112842353968893187.P92
353 (1) 135095261330112651830775049635590807381121031111382732318390846759744072165636542920143351738198057636666351316191686483.P155
355 (1,5,71) 2974779760081. C206
357 (1,3,7,17,21,51,119) 69259.18052799163122060087025155723065171174003.P105
359 (1) 719.27125323.4712635363.
.285280913757251941415180548664485621181937893.P215
361 (1,19) 47848036334820116132986462577147872267.P229
363 (1,3,11,33,121) 2179.309575803153.P157
365 (1,5,73) 6571.138502171.2244077756789983310918695541. C185
367 (1) 2203.634177.161021084117.7840142252089815392041.
.2816294841300993066546214031271001.3270112070990954768535379732765321.
.41860517287867240460042208225615145479852721.P133
369 (1,3,9,41,123) 739.2575675190386099.47146662106901857.
.2335432574534090617.899377009735615553325855097.P107
371 (1,7,53) 743.26801041.56691769.74107993. C217
373 (1) 1493. C287
375 (1,3,5,15,25,75,125) 2251.11251.56633527660731428440540758758251.
.3331020133962884772706727916696838942815963496129389001.P62
377 (1,13,29) 17703177067967. C249
379 (1) 46997.1600897.14007805315485347573527029147002036597.
.23229132519250730340307782442413365306631261048097.P197
381 (1,3,127) 33581615699197955777738387891299.
.89896478576590314583750832427049.
.6207497961491001860865708614869208845594249.
.63537996418411322893388678898019600654636747.P46
383 (1) 15229370711.26372116867.25278624741941. C264
385 (1,5,7,11,35,55,77) C187
387 (1,3,9,43,129) 280763808312313.396617565007083620931188002164448757655876754586218585374821747799540417379.P108
389 (1) 18292834838737894009.P283
391 (1,17,23) C274
393 (1,3,131) 787.20611007006851.57231871913078689.
.54447870968020052083592006408483550889.
.1647221037293847764066430890065139050987.P93
395 (1,5,79) 2371.104281.190391.21360811.22525271.4851210671.
.1415540984959721223423221.1786772676608961922807433452451202488761.
.881461349288847520341747277290496162004544991215461.P91
397 (1) 47019887.11890246390895945222779.P279
399 (1,3,7,19,21,57,133) 109928491.5640242043129165715899642841.
.2503258139391324274352072172458469939793.P93
Table 6+ Factorizations of 6^n+1, n<=400
L,M for n = 12k-6<=798
n Prime Factors
1 7
2 37
3 (1) 31
4 1297
5 (1) 11.101
6 (2) L.M
L 13
M 97
7 (1) 7*.29.197
8 17.98801
9 (1,3) 46441
10 (2) 241.6781
11 (1) 51828151
12 (4) 1678321
13 (1) 53.937.37571
14 (2) 421.5030761
15 (1,3,5) 1950271
16 353.1697.4709377
17 (1) 190537.12690943
18 (2,6L,6M) L.M
L 73.541
M 55117
19 (1) 1787.48713705333
20 (4) 41.68754507401
21 (1,3,7) 2527867231
22 (2) 58477.70489.863017
23 (1) 113958101.990000731
24 (8) 5953.473896897
25 (1,5) 3655688315536801
26 (2) 313.2341.6291946695217
27 (1,3,9) 114967.883383463
28 (4) 281.337.617.81035189089
29 (1) 59.32713.2727192763388813
30 (2,10) L.M
L (6L) 61.74161
M (6M) 181.3541
31 (1) 189491931189200021056951
32 2753.145601.19854979505843329
33 (1,3,11) 463.72073.127236649
34 (2) 934117.8289713345361373993
35 (1,5,7) 631.701.2311.9241.585131
36 (4,12) 577.3313.2478750186961
37 (1) 3923.1096762734443.2054788991719
38 (2) 1030762781149.9736145643041809
39 (1,3,13) 79.9049.868999.8857759
40 (8) 17761.3696985841.121206120881
41 (1) 83.28537.4837453663777044375040181
42 (2,14) L.M
L (6M) 804146449
M (6L) 6055984789
43 (1) 412482688627178079807598675848631
44 (4) 89.150080764792922988676714149209
45 (1,3,5,9,15) 4760317816590150361
46 (2) 6073.2259889.9564781.128407494947883673
47 (1) 534577564460822791430647883899825591
48 (16) 193.8641.688490113.6931400449
49 (1,7) 7*.762332681442053.90179616936384011
50 (2,10) 343801.22243201.1748016735462726601
51 (1,3,17) 103.919.980146969.99617785207
52 (4) 192193.14090441.8284434950526240125727017
53 (1) 107.97351567.33685364386033.71080464397105403
54 (2,6L,6M,18L,18M) L.M
L 591841.171467713
M 109.932461936453
55 (1,5,11) 11*.1031141.16336066781.84155540944421
56 (8) 113.4817.4048129.10189440239012883075423169
57 (1,3,19) 457.137713.190324492938225748951
58 (2) 349.105134528469779071670501631159328247729809
59 (1) 1163658999540220416412446482708919139658591671
60 (4,12,20) 13441.592575109627400042641
61 (1) 9151.4577830180684945360162613198286645069141001
62 (2) 47552767764994953232854569779888803761183529901
63 (1,3,7,9,21) 127.154260982009.528921402377887
64 4926056449.447183309836853377.28753787197056661026689
65 (1,5,13) 131.199930782298483523040584108028862541
66 (2,22) L.M
L (6M) 3037.96493.4629769
M (6L) 622513.16266405013
67 (1) 269.418349.90571543952974835963.191757760647639121941197
68 (4) 137.5849.1536052010629489.51420576374811381403609445473
69 (1,3,23) 24648570768391.816214079084081564521
70 (2,10,14) 13509594555661.1708114263204222806519161
71 (1) 37489.11735704315681.5757417485448059422914748320317168839
72 (8,24) 22452257707354557235348829785471057921
73 (1) 293.439.120855443.1389436303.4221883459378030470824476438562257
74 (2) 37*.4441.3300043400835529.190892407618022993841069346975403017
75 (1,3,5,15,25) 151.168151.573178201.918628247364601
76 (4) 4561.355518408146401.5028187486478069273.13038313680704041577
77 (1,7,11) 57019087134151254061666621717728669167279862151
78 (2,26) L.M
L (6M) 8893.197743936282933
M (6L) 13*.157.6429178169720749
79 (1) 317.5531.2832941.99687312908749681.8592319153827988586815914947213
80 (16) 9601.2810800069601.2347110840158563816028186318246561
81 (1,3,9,27) 1783.149862151.3920344350409644507093715799617
82 (2) 4046701.174521133001.246179376206361788466441901958293949537091001
83 (1) 710813.6547890917.21608536062644851877771.54824363564629401758409941
84 (4,12,28) 1176362433121.19100900655540830489319601
85 (1,5,17) 1383638161.72085651321561.740797672014674927371043791
86 (2) 1033.6501601.2914764989376043020733.P35
87 (1,3,29) 68209.92569.1439329.380675809.519258631.24378360481
88 (8) 9307950433.P53
89 (1) 179.P67
90 (2,6L,6M,10,30L,30M) L.M
L (18L) 5597780112726834061
M (18M) 9001.211501.2106930961
91 (1,7,13) 2003.2549.36947.52769627.P38
92 (4) 14537.433176829049.P53
93 (1,3,31) 31*.P46
94 (2) 1693.1029538544148223697293.30585762365533687252981.P25
95 (1,5,19) 6271.2666738161.37260330001.61671024221.3229504809106404383981
96 (32) P50
97 (1) 7449708398813963.6571212276076854019883.P37
98 (2,14) 288628033.P57
99 (1,3,9,11,33) 199.110881.P40
100 (4,20) 4801.5801.224401.1006795824867486182291801.P26
101 (1) 607.82013.3866281.P64
102 (2,34) L.M
L (6M) 2953728137900959095135649
M (6L) 1785001.12346985995648844989
103 (1) 7211.135025379.P68
104 (8) 36265841.141365953.P59
105 (1,3,5,7,15,21,35) 71191.P33
106 (2) 26713.175436926004647658810244613736479118917.P39
107 (1) P83
108 (4,12,36) 433.115963921.8781208996949976153601.241282001155985351966017
109 (1) 9661979.P77
110 (2,10,22) 423852369601.P51
111 (1,3,37) 223.7993.142969.P45
112 (16) 490972383553.P64
113 (1) 227.8363.586471.5043448999988542328333.P54
114 (2,38) L.M
L (6L) 43321.659334264781883756771821
M (6M) 229.25309.2197693.300537265358917
115 (1,5,23) 23126990778420152651.P50
116 (4) 233.250793.4916777.6198809.9008169903032260803977.P44
117 (1,3,9,13,39) 1873.P53
118 (2) 554971222573.P79
119 (1,7,17) 22885730141.2681104713967.P52
120 (8,24,40) 55201.122401.21027841.P33
121 (1,11) 727.15186641018595718629290023681.P55
122 (2) 60757.348433.558416270857.P72
123 (1,3,41) 1231.268313928259442786323996685119.P30
124 (4) 106179166897.1062529732255153.505430595651453051641.P47
125 (1,5,25) 251.751.5501.2694730860384999001.P51
126 (2,6L,6M,14,42L,42M) L.M
L (18M) 1009.17389.10339309.48129311534221
M (18L) P29
127 (1) 509.2287.6557252639250807127523.P71
128 257.763649.50307329.3191106049.2339340566463317436161.
.2983028405608735541756929.P29
129 (1,3,43) 2322118361887.P54
130 (2,10,26) 425101.571140885901.1095110988527465328644161.P34
131 (1) 118766959.5620905557.18059147791.1519139468453.
.137286124588876043259567675817.P32
132 (4,12,44) 602977.87917281.1581003091009.332526664667473.P22
133 (1,7,19) 1050169.27838508435875439051.6110613202111672866319.P37
134 (2) 4021.P100
135 (1,3,5,9,15,27,45) 271.2195738619437791.P39
136 (8) 17*.2376897969771200667937073.P74
137 (1) 51480217.4582965162279152779295741463389.P68
138 (2,46) L.M
L (6L) 277.12344559539431993.14030036355387001
M (6M) 23027140435639321.279219519230141641
139 (1) 478404033683.P96
140 (4,20,28) 123099618068232205681.P55
141 (1,3,47) 1129.P69
142 (2) 4485781.33571579633135513.969155837815909463425781176679854621.P50
143 (1,11,13) 2861.3712567.P84
144 (16,48) 115777.31057921.P63
145 (1,5,29) 168491.35969851301.71188611917485018014870131.P46
146 (2) 877.16658893.20007314401.P92
147 (1,3,7,21,49) 32670457.1152319183.P49
148 (4) 12950593.10742681826196124641.P86
149 (1) 17808481.3908095969.P99
150 (2,10,50) L.M
L (6L,30L) P32
M (6M,30M) 38149201.340800981614130538049401
151 (1) 1877258342367076264555657.57719839964417489988525624247.P64
152 (8) 417827633.505981859041.26836193435793601023998323852801.P61
153 (1,3,9,17,51) 147799.29274753335383.1888411753890127.P41
154 (2,14,22) 40590776689.P83
155 (1,5,31) 73925704213704945236169449354196288841.P56
156 (4,12,52) 816213379522588431707233.P51
157 (1) 1571.53381.259993.32577356503.P98
158 (2) 10429.P118
159 (1,3,53) 79850963147627239.886629624220623485114684453959.P35
160 (32) 82241.15954097282309262360999041.
.4903626466768570999224738379365121.P36
161 (1,7,23) 231841.3091531661.P88
162 (2,6L,6M,18L,18M,54L,54M) L.M
L P43
M 39661919912737.P29
163 (1) 11411.1712959177.52108050586547.417317792492527332337.
.390331841336302929436994813.P52
164 (4) 90823862327833086800386352513067248343828857.P81
165 (1,3,5,11,15,33,55) 661982172984001.P48
166 (2) 997.778873.3020869.13852369.161184670755001.
.437801891817492814657.62492225855662442512009.P48
167 (1) 2339.24362285875922356868655021961427.P95
168 (8,24,56) 673.3276974780364284482799810397121.P42
169 (1,13) 4057.116720070342348721.
.3378307227685242623713508116989468524398534111.P56
170 (2,10,34) 1021.372810476994982432801.2244807299700346905001.
.41819674674441587529015061.P30
171 (1,3,9,19,57) 62174327387790051073.P65
172 (4) 1721.1904729.5993513377.3449220534377.
.2400135849956129030979293221108376113.P63
173 (1) 347.P132
174 (2,58) L.M
L (6L) 104485957.3347320129.P27
M (6M) P44
175 (1,5,7,25,35) 3851.12601.1305192701.66631795301.P66
176 (16) 2653655703600055300471675940271611363631320368111914433.P71
177 (1,3,59) P91
178 (2)
92874768913720582900858911299754687243149941868501755733246139460861.P69
179 (1) 16111.3490859.317649821.2164201732799819.1890213088140761141.
.684015593168267521517.P65
180 (4,12,20,36,60) P75
181 (1) 1087.13757.13952929.632269201.33644936669.1032407342933.P95
182 (2,14,26) 1093.8955493.P103
183 (1,3,61) 367.1676281.1882477437757002169.P67
184 (8) 118593079873.364095314695155207401455201.
.160021185991868323844533898916209.2912254503405497874522782767870577.P34
185 (1,5,37) 5311351.3371674951.30858852252821.P83
186 (2,62) L.M
L (6M) 373.316201.532333.1680597049.1802142841.95388829922809
M (6L) 1489.P44
187 (1,11,17) 480615433.P116
188 (4) 4513.4889.347984031638813867788384938483862609.P101
189 (1,3,7,9,21,27,63) 216217.4622286817.2038230013432107097.P51
190 (2,10,38) 300961.21905019726901.347101070179037778781.P73
191 (1) 1258380199.1524539579459364377717928165817.
.20894274974038675363980511918504639.P75
192 (64) 769.272040961.103352381953.P78
193 (1) 773.1931.6563.964591900729.P128
194 (2) 145501.572240484565153.4043711238187229705754319631461.P99
195 (1,3,5,13,15,39,65) 1951.50311.78296791.P59
196 (4,28) 352409.171103297.110495360641.P106
197 (1) 4729.P149
198 (2,6L,6M,22,66L,66M) L.M
L (18M) 397.7129.1184960471459158549.12335988891985043955517
M (18L) 23761.13705107769.697344975757.254253859796489462713
199 (1) 236029523.3799311562897.31878912911333.77719140435208369.P103
200 (8,40) 401.886109293550401.812610713899205201.
.59773386522355896001.21463170766480994553601.P47
201 (1,3,67) 682489921447.2665157957929.1919920225888720033879.P58
202 (2) 53902351586977.19472139427564696216240566673.P114
203 (1,7,29) 29*.23549.140071.41316543716813.406457127805781473.P89
204 (4,12,68) 8715697.35540881.P86
205 (1,5,41) 821.2186469381475738293871.2191683692912452263530405964341.P70
206 (2) 8408219407597.
.2678624143952808457516330191792080322718547840887752493464690277.P83
207 (1,3,9,23,69) 4811469913.61040960263.25280883279243199352415750302719.P51
208 (16) 209945929109939792807681119841.P121
209 (1,11,19) 419.87713957.
.690793919157674734946282168446665910678652191468497041123.P73
210 (2,10,14,70) L.M
L (6M,30M,42L) 66361.21387387918961.41649085891390429201
M (6L,30L,42M) 9120301.P30
211 (1) 91997.52572017528450872868981647.P133
212 (4) 69693040414889.20089340310546423313.1110998112983390874377.
.83183051545234447336922778521.825099745124166389803400429081.P49
213 (1,3,71) 5113.74551.26734056474599359.P84
214 (2) 51141721.7254122353.P148
215 (1,5,43) 8171.1211741.21619111.9458892894402537221.P95
216 (8,24,72) 3457.19009.P105
217 (1,7,31) 89816745465847.1100141411455580533471034569.P100
218 (2) 335790424559680201.2880933848374725856201.
.3783033369252816683960000152382576688052300376449.P81
219 (1,3,73) 10513.65600137.7426195831.467260890471943.
.6388551471149527279.P57
220 (4,20,44) 8247361.778055521.254055515561.20695248084558521.
.518060072335148988041.6560970004839878965676927281.P33
221 (1,13,17) 443.66728502368731644257834188952657813.P113
222 (2,74) L.M
L (6M) 82660813.12023017393.P38
M (6L) 270841.2057604700829917.63717427974558037.8296875768265773901
223 (1) 10259.968713.2245233071284547.232518156972996725239.
.666546492524951029181.
.835790655259197870586319955878764574136853697743.P59
224 (32) 449.14050095361.
.4347931587984824386556915294792767725957873418590100902582977.P76
225 (1,3,5,9,15,25,45,75) 1801.4468904551.5267460432151.
.180277202943196638580206001.P42
226 (2) 2678668139593.74520969665581.
.82787563486530615710539383062016180279313.P108
227 (1) 71556809087935085523319.398350176141493935951217441.
.1018570181134240741346108055571875575391606285444055532689903.P67
228 (4,12,76) 8502577.70467297434301315496188595297.P77
229 (1) 24692063988803.P164
230 (2,10,46) 489901.95281002601500920612829641487527580629461615901941.P82
231 (1,3,7,11,21,33,77) 944005034375463727755464073082424887.P58
232 (8) 324022971925566874177785587856089835544193115261789544399681.P115
233 (1) 467.1399.
.163877375237672870789806157730284778902135451688145768178589145021.P110
234 (2,6L,6M,26,78L,78M) L.M
L (18M) 1044927469.P47
M (18L) 21529.58066129333227697089409.P30
235 (1,5,47) 15030104175623018357289123321690093206664773346039681810841.P86
236 (4) 4992035366913467897.21948439513969181164578188512458069689.P125
237 (1,3,79) 47093998376912230366243110271664383.P87
238 (2,14,34) 2857.23683448262457324289601073.1223399441578981329719781061.
.7340907147976143090067393104626029.P60
239 (1) 146715409.4577909312531.11996736557726158297.
.55580337982189268741.3253071351150192878011946957.P98
240 (16,48,80) P100
241 (1) 1447.112580893750715877136155593604993493690347963315703776847.
.333831660223844323127131130894040876670322240703311304485275421.P65
242 (2,22) 1453.1699886791329510277176681109.
.5453446088829154504711498574457194514513814553759428356613.P84
243 (1,3,9,27,81) 487.939439.1254367.3816559.12685746961.P95
244 (4) 5857.412849.45348699038754859014549156612995761658952618079003220954072833694399350313.P104
245 (1,5,7,35,49) 491.531714998599056253801.57718117561355946617161.
.2076531867755196744245501.P61
246 (2,82) L.M
L (6M) 7873.59589415533456305173269384769.P30
M (6L) 37448441257.15918716269297453972620877.P27
247 (1,13,19) 238428819287279709454394780799468728063645576507.P121
248 (8) 2655332007287526596353.P166
249 (1,3,83) 18879747223.P118
250 (2,10,50) 1834744914758653996868853565501.
.7612068647760892587567279171698469451260170146501.P77
251 (1) 27969811991472751.
.431914676388241037434814954856635940501826690937344259.P125
252 (4,12,28,36,84) 2017.1425398717511217.P94
253 (1,11,23) 2916281795549.
.442490447397887376506449530663800706637907696507.P112
254 (2) 140348646913.25974264373441.49515878278227889669.
.91963118572171789377372037.235333294242628727570734732881529.
.1516570873669019166779118275948915051773.P55
255 (1,3,5,15,17,51,85) 47431.241317924973591.
.850271719214350502835132764398471.P48
256 18433.69615986569139423375849495295909549956813828853888948633601.P137
257 (1) 13569401715894806672855945455795340408308144107419.100013092725890544669630696532241946180071054595333636462851779928224547.P80
258 (2,86) L.M
L (6L) P66
M (6M) 752393127973.P54
259 (1,7,37) 334868353.42555528171653758816503341.P134
260 (4,20,52) 521.380641.98735521.2862931023015114481.
.32779195022307860881.25984196582137484361518374801.P67
261 (1,3,9,29,87) 8283963567043783.3099209924759291137.
.44894245166647019137.15353979770405175216493168455121.P46
262 (2) 25153.P198
263 (1) 5261.303834678444151.
.4063115777250325384767947818375933601230465114857832639.P131
264 (8,24,88) 3169.2508001.3537601.8245249.
.653601194883855117881156720639553118131649.P60
265 (1,5,53) 9011.30871938731.73883730374153134711.P128
266 (2,14,38) 1597.28729.181514505515281.19900271591604097.
.74795600265930240481.1292011440308023716953924874633901.P77
267 (1,3,89) 102895570700431.737380287479449.
.105974548536692346164432707569940342022635766599.P62
268 (4) 8569643669801.8608623365921809689881.
.1581108618083594602253847328498841.
.60463026759617698152647921561062661727047290177.P91
269 (1) 258241.178613311.163286342907309883903.
.26917859611055656728302165725740157055483.
.35746607157236594412624392508297681751878912847182075711967.P76
270 (2,6L,6M,10,18L,18M,30L,30M,90L,90M) L.M
L (54L) 39326041.51353541541.75408883542901.699120429548646987756001
M (54M) 4861.159594687181.34775499883178521.3940374423374379301990321
271 (1) 4443299354431499.13183575905594260196736199315938752662569776604725870555613249392774714020137072241.P113
272 (16) 257857.80189953.350828321.P178
273 (1,3,7,13,21,39,91) 3216487.P106
274 (2) 77269.1422061.19955176141.
.102147016323508821701835272647335651140011622973540889.P138
275 (1,5,11,25,55) 11551.1458601.541019051.P137
276 (4,12,92) 100600260657132106393367429005921.P105
277 (1) 8311.9419.113017.8065133.143476139909.P184
278 (2) 1561232989.P206
279 (1,3,9,31,93) P141
280 (8,40,56) 3361.275521.11672641.5576968321.P124
281 (1) 563.8431.1351757950997.14063062521302839553357.
.19974696199623424031237.115600460578650720383010805853.P126
282 (2,94) L.M
L (6L) 3337903223042569.P57
M (6M) 9491602000279600777.P53
283 (1) 2229970063115387665250948239.153320572414770948386910841628616650567801854356507716423740493699401.P124
284 (4) 569.392489.469077689.896041468925733187137365896107353. C168
285 (1,3,5,15,19,57,95) 40844746349999464436020322521.P84
286 (2,22,26) 252253.29518633.
.14425628966027164308715224542454444662285944591729.P125
287 (1,7,41) 1121023.2853115756372329930021879179.
.247859037729470996906245243451923112548845447499779115951590660463.P88
288 (32,96) 1153.1984301569.1567103187499033148929.P116
289 (1,17) 8093.23278892925034258318294404644503.
.7679962361209350795245766079339091.834133483834326443733029832034691140142113884984749002560011496915683.P74
290 (2,10,58) 1741.375841.P166
291 (1,3,97) 135607.3343385035897.P132
292 (4) C225
293 (1) 587.17828792392643.P212
294 (2,14,98) L.M
L (6L,42M) 8434052750068597.P50
M (6M,42L) P66
295 (1,5,59) 20441552166028072811.P162
296 (8) 593.137045594113.6758410568257.55197682698737.
.8375829463350094657.45637046233441330193.
.2829247728806215136257.147071192694046077687504556871041.P92
297 (1,3,9,11,27,33,99) 2377.4159.50147190436375827433.P114
298 (2) 6825688699471381. C215
299 (1,13,23) 3241759.5666051.P193
300 (4,12,20,60,100) 2056871500653135843616345033288599993601.P86
301 (1,7,43) 298183187219.393091150299531749364205297712116979.
.175978301474188430735250552822188278709.P111
302 (2) 19515241.8951289532327540357.27564163622315314490824935535295293.C173
303 (1,3,101) 10303.21561481.73214437174870569896546747183839338067993.P104
304 (16) 440123297. C216
305 (1,5,61) 10542843898331.P174
306 (2,6L,6M,34,102L,102M) L.M
L (18M) 613.12241.846370054558596518376711409.P41
M (18L) 6121.57372656104261.P58
307 (1) 4732562084333249714196514227673.55385698371129588030629087875349.P176
308 (4,28,44) 65725969.59649652128793520533433.P157
309 (1,3,103) 427039.26432479.P146
310 (2,10,62) 27901.50221.372201769081.56112296349610045406881.P144
311 (1) 25253560139.4310758347899.18707517257089.
.65268623352510374655683719.15375997422186291719933915126668351.
.2495174740032337104455007012996408231601.
.3864978146331181248248106309395051058288828336437.P57
312 (8,24,104) 1249.94578317595841.P133
313 (1) 2269959032465874003365857.P219
314 (2) 558436298701.43877671534791092362933. C209
315 (1,3,5,7,9,15,21,35,45,63,105) 2725667472495241.
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316 (4) 1578867457.16162944961.88362484215497. C210
317 (1) 974459.4340223635815993. C225
318 (2,106) L.M
L (6L) 40133011425325338673.P62
M (6M) 6997.10786528430680870971861642463992861493.P40
319 (1,11,29) 1277.169709.1034019361.1252217116623387773.P183
320 (64) 641.6827521.621432697463041.1743036582663429761.
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321 (1,3,107) 2651847769.P156
322 (2,14,46) 1933.2593505209.4762756207579441.P178
323 (1,17,19) 13567. C221
324 (4,12,36,108) 2593.3889.40567195306213128342900074449.P133
325 (1,5,13,25,65) 43798301.88461995051.
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326 (2) 9128653.862123028232465233166133318203195759014737.
.3478484006896508613553622086740249725635333.P161
327 (1,3,109) 32560222715988756820062781110511873.P134
328 (8) 554977.1487809.P238
329 (1,7,47) 659.6581.131589345007.29091932006593.6417221204788802521.
.99379633714344941623.560877906720787934003619587.
.688032426812647379990413979.P92
330 (2,10,22,110) L.M
L (6M,30M,66L) 661.144541.14966414761.P45
M (6L,30L,66M) 1321.110221.188074921.P46
331 (1) 648675797064247.1236023944589761. C227
332 (4) 1262929.16069876234711676274286505322384377.
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333 (1,3,9,37,111) 3655654025276752913719.8340044242652322623767.
.307179506952290966206956065569.
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334 (2) 26921446615521768997. C239
335 (1,5,67) 31846061939218752031563804583960071245498521. C162
336 (16,48,112) 3307958515009.18322466545692289.2626011290685546903553.P100
337 (1) 51899.112493774365342418002822667.
.60858373865624835157949011267694339.
.11429767744966866607725417511319063408867.
.84382257093351217403808536729720911956398743537658819.P103
338 (2,26) 42589.413713.249753555949. C222
339 (1,3,113) 2713.3226831830647224961981839.
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340 (4,20,68) 105401. C195
341 (1,11,31) 683.738801699065626101203.
.201829461618484065097678058023863456803.
.1931579004923335893545766492796645505817541279.
.54244210028135332014784214833039498558612327178902639.P74
342 (2,6L,6M,38,114L,114M) L.M
L (18L) 60204997.4765941001.235011794248567117.473164737913969822009.P29
M (18M) 37187713.P77
343 (1,7,49) 7*.2452897437521376917.12929162654221584653. C191
344 (8) 186136337.8889718818436619623637354417.
.214670565313869275249305269579078241.C190
345 (1,3,5,15,23,69,115) 55727811361.10829601768590858922799569083910271.P93
346 (2) 699705783037077375644948197. C241
347 (1) 8329.1632339647473996207.
.4254678785395250635090914262464410641424477007559249.C196
348 (4,12,116) 4177.657514530802998237121.
.37702065257063784412356623467930092827469446641278116128045705297.P86
349 (1) 3856451.102442056124834405281837500531.
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350 (2,10,14,50,70) 4201.6301.10501.844201.17190601.P163
351 (1,3,9,13,27,39,117) 23167.25382817428740298677823401.
.130987955745496562079528487.48195628755548807440285827712404103.P78
352 (32) 978494460213024200513.
.34008501773774613881206536370027348041226433.P185
353 (1) 5991823.78205041689362902245131470268247495747.
.4245833498805354083788298428051503901631774178454283.C178
354 (2,118) L.M
L (6M) 709.2833.254923189.P76
M (6L) P91
355 (1,5,71) 26385731. C211
356 (4) 1067653695449616193001.6282957834660568354129.P232
357 (1,3,7,17,21,51,119) 17137.49195951643511367169525208925567479001.P108
358 (2) 42961.788317.9500447808790033.
.33400288069890510050856036346738819956549841.
.290041398476413114819265440597823622823175677.C163
359 (1) 9110965748024759967611.47703250896149280693917. C234
360 (8,24,40,72,120) 13599361.6776234506081.
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361 (1,19) 5426629939912152649129.57905799063241395665537419802123. C213
362 (2) 49957.189695801866717.526959712531424757289. C241
363 (1,3,11,33,121) 103373476033477388263515282957106895317857131511194597652434632687520479231.P98
364 (4,28,52) 77055473691242478433.13308759072006165899041.
.671172865763366711117443724389009.
.808915328590499386254591774467556408539129.
.35319536904816424059659524632822071355049464122680657.P55
365 (1,5,73) 494295245128245131.16540741646767991411202121.
.254856004505238557834753259615355816338030694854500477132141.
.6415267023859934992688035953439081187660996277772392359853751.P62
366 (2,122) L.M
L (6M) 8053.241561.10161211191529.457346879849878822260409.P47
M (6L) 733.3069462805228338593646133.173941000965538537755852657517.P38
367 (1) 24223.P281
368 (16) 136897.1510273.2787233.65983873.4521249267735713.
.46264645253729717287768155233.1747165409191861211943873827004641.C171
369 (1,3,9,41,123) 2872723303.
.13962920965423422985070859383439633233088296131740062300197159.P117
370 (2,10,74) 6703378804899541.3783707229719954256901.
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371 (1,7,53) 2783700126792688988335822421768098189386895987206391.P192
372 (4,12,124) 1578769.20308493329.
.19259080382453841122679088710848926436527873.
.1645166645707768849055046041846220911468426737.P82
373 (1) 2239.305861.53749783974339246040628451522941961707.P243
374 (2,22,34) 6733.6773155698277.2501850879498651781. C214
375 (1,3,5,15,25,75,125) 3001.344316256809732690001.P132
376 (8) 198529.590321.2172688893409.6860018751366721.
.609625726569565390289681.C224
377 (1,13,29) 5259151.103678433717.P244
378 (2,6L,6M,14,18L,18M,42L,42M,126L,126M) L.M
L (54M) 10794083454463066294342208029552733580361.P45
M (54L) 757.9829.2592266236335984818021237855668549.P44
379 (1) 6215678932110055670241299. C270
380 (4,20,76) 761.689321.3939048167443707601.
.1991255326339643820867934461881.165124761236284971873587401742681.
.430900697980532343944742725010481.
.204151655878303598851190023785774256244024641.P58
381 (1,3,127) 136399.7833361.11461131511.740027726500071028321.
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382 (2) P296
383 (1) 91921.1914729212942473.7001252622923959.23223797215609849.
.4880870513072449263361047718936256658889.
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384 (128) 10753.194651137.2239060935664468407122127993082759905953606443009.
.359746302534492382597189148070134087984989179216224257.P85
385 (1,5,7,11,35,55,77) 356816447037821.8130967004568101.P157
386 (2) 1203703485433.573447428855263537365759829837.P257
387 (1,3,9,43,129) 1805255624146951.25208846746385420431. C162
388 (4) 3881.153649.464324257.1384174985368468177.
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389 (1) 762313187. C293
390 (2,10,26,130) L.M
L (6M,30M,78L) 342421.55088625341568479584667598703368001.P35
M (6L,30L,78M) 1222106886101401.P60
391 (1,17,23) 5093167.170730151. C260
392 (8,56) C262
393 (1,3,131) 5503.9433.340167293377.P184
394 (2) 3337969.132698503366306271934385117. C273
395 (1,5,79) 132141700575804202914947063008901.P211
396 (4,12,36,44,132) 23382324279333844748353.
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397 (1) 2383.296077043. C297
398 (2) 28657.773713.81428796036994210780049931080405416482699461473.P251
399 (1,3,7,19,21,57,133) 9951571519.1268637449760199.
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400 (16,80) 1520801.5268698971721637892050105264560801.P210
-------------------------------------------------------------------------------
402 (2,134) L.M
L (6L) 1609.18493.6400916741826776608939188781.P68
M (6M) 98266387530667777.P86
414 (2,6L,6M,46,138L,138M) L.M
L (18L) 1657.102673.284833.31739306955000318682004605762105132924971289.P46
M (18M) 829.11959280174921358157113444778096591384713470257.P54
426 (2,142) L.M
L (6L) 853.99535753.15006883477.17403644677.
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M (6M) 17041.5123509669.61803564541.253055139049.P73
438 (2,146) L.M
L (6L) 1753.26245837.51911357917.3329634082406617.
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M (6M) 8761.283480200282934561.P91
450 (2,6L,6M,10,30L,30M,50,150L,150M) L.M
L (18L,90L) 26922319201.P83
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462 (2,14,22,154) L.M
L (6L,42M,66M) 7393.55441.449989.2123353.3834601.
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M (6M,42L,66L) 938733964477.46094532937993.81154591004568313.P52
474 (2,158) L.M
L (6M) 3793.P118
M (6L) 5689.18709729.317233981.1945096921.P94
486 (2,6L,6M,18L,18M,54L,54M,162L,162M) L.M
L 763296049.P118
M 170827321094639893.3409463117689442128783261.
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498 (2,166) L.M
L (6M) P128
M (6L) 1993.245351666247788560312408234856037538218169.P84
510 (2,10,34,170) L.M
L (6M,30M,102L) 484601490571886903493518015104501.P68
M (6L,30L,102M) P100
522 (2,6L,6M,58,174L,174M) L.M
L (18L) 2089.290924056117.947349493773774517.P99
M (18M) 359137.2797958656485541.P110
534 (2,178) L.M
L (6M) 1069.694201.28031381649109.196947355253345341.P97
M (6L) 2137.723739848857641030189.P114
546 (2,14,26,182) L.M
L (6L,42M,78M) 15289.P108
M (6M,42L,78L) 16381.1627627815399713377343163471649631733474853.P67
558 (2,6L,6M,62,186L,186M) L.M
L (18M) 11161.157462752204253.21124214217163783261.
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M (18L) 1117.P138
570 (2,10,38,190) L.M
L (6L,30L,114L) 2281.2358661.3817262181721.6197208621830041.
.888066870806284147801.P53
M (6M,30M,114M) 18805516694127001.P97
582 (2,194) L.M
L (6L) 1696995935981617.P135
M (6M) 97*.
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594 (2,6L,6M,18L,18M,22,66L,66M,198L,198M) L.M
L (54M) 28964629.15536649073902661.29426749337349541.
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M (54L) 3155329.17698960601683054308649.3512830966112683782744191389.P84
606 (2,202) L.M
L (6L) 1213.25453.215737.930985424669173.P129
M (6M) 3637.181339441.73805592037.257309257577257.343320968801689.P104
618 (2,206) L.M
L (6M) 33703023049.31712196448668781.P132
M (6L) 1237.33479895313601650365695117603613865333.P119
630 (2,6L,6M,10,14,30L,30M,42L,42M,70,210L,210M) L.M
L (18M,90M,126L) 514379712421.9226830539692081.
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M (18L,90L,126M) 2521.6797701.34640925953158940597772893101.P74
642 (2,214) L.M
L (6M) 5972962561.1426969200507388358761.1740269104463086681404229.
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M (6L) 10273.533550328536694908746148449547022477.P126
654 (2,218) L.M
L (6M) 132109.878550901.70971053221.7163969211901657.
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M (6L) 6894923806164352506202420464931123386756217534377965706106654189483085207293.P93
666 (2,6L,6M,74,222L,222M) L.M
L (18M) 17317.242345413.6802442095321.2714523890620249.
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M (18L) 343237139281.123715172009307654951839645203821713509.
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678 (2,226) L.M
L (6M) 39386377.72565033821295009.105290759786101044241.
.953764805172418806721069.8968496972740368420580830979099439448387289.P63
M (6L) 14944477.P168
690 (2,10,46,230) L.M
L (6L,30L,138L) 2508943501.16919595211074421.236385533406503858612881.P88
M (6M,30M,138M) 1381.4269721.5078401.15550223641.2396217516717195541.
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702 (2,6L,6M,18L,18M,26,78L,78M,234L,234M) L.M
L (54M) 47737.8831161.188486038261.P146
M (54L) 1514917.27140169445190569.16812746447104300364261461.
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714 (2,14,34,238) L.M
L (6L,42M,102M) 1429.12853.99961.762096489421.
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M (6M,42L,102L) 190792782886329146262600258637.
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726 (2,22,242) L.M
L (6L,66M) 4357.11617.100189.949609.3024276179746273.
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M (6M,66L) 2450040986053.1266392442690013.10476416255479706797.
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738 (2,6L,6M,82,246L,246M) L.M
L (18M) 174169.30089737.6505451552303016203738681444159513490728930149.
.3817733856969957712995018866618650405701538477261.P80
M (18L) 2953.10333.1036153.1678974479302069.
.4526204177767840748623909655533.
.1472102256284019236716925991047155829911467672973.P80
750 (2,10,50,250) L.M
L (6L,30L,150L) 327001.514068001.8485607361001.P129
M (6M,30M,150M) 106501.10864275587422501.
.40201669583886249313475106001.17652944112619681484515989877740001.P72
762 (2,254) L.M
L (6M) 6053329.24312373.247672325565461557.
.801635022497602549961802363275046606409.P126
M (6L) 3049.9203437.277440178523437143401157337. C160
774 (2,6L,6M,86,258L,258M) L.M
L (18L) 7741.1976797.632803528420302650173016503452913.
.764306314103209605006540297087286189813.P115
M (18M) 1549.5907169.61621539416556138109.475101073392341497734075633901.
.5327631746573407308414105279051343357.P100
786 (2,262) L.M
L (6M) 17293.5646129480180477793.
.10118929876038053687106294473402896087044223570381.
.4319857456953911989541977914492633405793099703033623785697.P73
M (6L) 625657.1303189.4304137.5055407781577.
.1445119992880549305748401049273.
.56960371058218895540378943239158793077204018529205703221409.P83
798 (2,14,38,266) L.M
L (6M,42L,114M) 60613424867803248411521814481.
.286227504202337752215096844369178117421662207554962805489.P84
M (6L,42M,114L) 10453801.26846778030654037.
.1158150966336915157483991531934587159293.P106
6^{6h}+1=(6^{2h}+1)L.M, L=T^2-T.6^k+6^h, M=T^2+T.6^k+6^h, T=6^h+1, h=2k-1.
Table 7- Factorizations of 7^n-1, n odd, n<400
n Prime Factors
1 2.3
3 (1) 3*.19
5 (1) 2801
7 (1) 29.4733
9 (1,3) 3*.37.1063
11 (1) 1123.293459
13 (1) 16148168401
15 (1,3,5) 31.159871
17 (1) 14009.2767631689
19 (1) 419.4534166740403
21 (1,3,7) 11898664849
23 (1) 47.3083.31479823396757
25 (1,5) 2551.31280679788951
27 (1,3,9) 3*.109.811.2377.2583253
29 (1) 59.127540261.71316922984999
31 (1) 311.21143.3999088279399464409
33 (1,3,11) 3631.1532917.12323587
35 (1,5,7) 2127431041.77192844961
37 (1) 223.2887.4805345109492315767981401
39 (1,3,13) 486643.7524739.44975113
41 (1) 83.20515909.4362139336229068656094783
43 (1) 166003607842448777.2192537062271178641
45 (1,3,5,9,15) 1527007411.125096112091
47 (1) 13722816749522711.63681511996418550459487
49 (1,7) 3529.1074473.13473433.6106505825833677713
51 (1,3,17) 103.365773.2316281689.10879733611
53 (1) 8269.319591.38904276017035188056372051839841219
55 (1,5,11) 5457586804596062091175455674392801
57 (1,3,19) 19*.19609.879399649.6957533874046531
59 (1) 459257.134927809.550413361.354639323684545612988577649
61 (1) 367.4759.177237331.1914662449813727660680530326064591907
63 (1,3,7,9,21) 2643999917660728787808396988849
65 (1,5,13) 131.157951.787021.4446437759531.434502978835771
67 (1) 228337.147300841.206244761.10052011757370829033540932021825161
69 (1,3,23) 139.402011881627.235169662395069356312233
71 (1) 990643452963163.169002145064468556765676975247413756542145739
73 (1) 439.3675989.359390389.1958423494433591.7222605228105536202757606969
75 (1,3,5,15,25) 29251.217648180992721729506406538251
77 (1,7,11) 724487149.6809710909.88262612316754526107621113329689
79 (1) 913242407367610843676812931.1056836588644853738704557482552056406147
81 (1,3,9,27) 3*.1621.3727.3368791.70722308812401674174993533367023
83 (1) 167.66733.76066181.7685542369.62911130477521.303567967057423.
.18624275418445601
85 (1,5,17) 1531.4931.P48
87 (1,3,29) 2576743207.196915704073465747.358475907408445923469
89 (1) 1805633.18489605314740987765913.P46
91 (1,7,13) 7304123737.231410451435538144122809.P28
93 (1,3,31) 5463751.2211164386353499.P29
95 (1,5,19) 36671.1966385431.P47
97 (1) 389.971.P76
99 (1,3,9,11,33) 199.173647.P44
101 (1) 607.809.6263.P76
103 (1) 17923.P83
105 (1,3,5,7,15,21,35) P41
107 (1) 227109283745807808529.1620221568881364582821.P49
109 (1) 14551288401737861.63505707690048880101785428103.P47
111 (1,3,37) 6217.177379.56713875643149053038693.P29
113 (1) 227.P93
115 (1,5,23) 1151.188831.1446701.723461377501.27229507836853201541.P29
117 (1,3,9,13,39) 1873.322921.2280097.7687225261.P36
119 (1,7,17) 12377.34273.305213588009240737.440779823883628367834893.P32
121 (1,11) 1453.65099.11795261559086963.58792315124013823398811997.P44
123 (1,3,41) 267403.P63
125 (1,5,25) 251.2182816753758823696751.P61
127 (1) 260461507.554351226505275380676162672703.P69
129 (1,3,43) 10837.63350976270733.175446584281395198837259.P30
131 (1) P110
133 (1,7,19) 401563177.2662276961.373740808373213.897558513407803666357.P38
135 (1,3,5,9,15,27,45) 271.185221.175561876921802311.P36
137 (1) 2741.213721.251533.57162922399254002352124124899.
.65480203458464902965944539043.P44
139 (1) 19739.673039.P107
141 (1,3,47) 283.5960917.P69
143 (1,11,13) 528808508322667.376215890379315997311416372784691746214777.P46
145 (1,5,29) 4899841.277463632645667965008782910911.P59
147 (1,3,7,21,49) 4060603391041.424770871339903301567509.P35
149 (1) P126
151 (1) 115356256117.36076003832567.206462520503013793561.
.2856349001315592319937.P61
153 (1,3,9,17,51) 307.613.4591.44371.44072862804091655188147.P45
155 (1,5,31) 21391.21701.1622982371.9254997611.P74
157 (1) 4397.5653.1039945344901.P113
159 (1,3,53) 32119.1695259.84247682063005850464952755729.P49
161 (1,7,23) 4406588677.4615185796935334098258901.P78
163 (1) 653.9781.1260643.962207945014470392304193.
.1648536343690282975764489383562678396141955057.P55
165 (1,3,5,11,15,33,55) 7591.36647640811.1946951063386221338821.P32
167 (1) 2158061509.623932374204290945359.
.494816894793945434195756741367539.P78
169 (1,13) 1452979915402500135854417362573926368874134931212567.P81
171 (1,3,9,19,57) 18684829.9674698906207.175336938770236118176950803989.P42
173 (1) 9491935586594867440367391646466925926211879363793.P97
175 (1,5,7,25,35) 701.1237578612719152201.1094471317606762277701.P60
177 (1,3,59) 709.89209.22724865586634953261986967832791.P59
179 (1) 41887.149874987000926513705179.P123
181 (1) 1811.13873726021.618805947190964867.364308807786322943430987769.P95
183 (1,3,61) 5153013553.104199666470736545959920137256413473.P57
185 (1,5,37) 1481.6661.219041.P110
187 (1,11,17) 10099.107969286569.
.157663427378398137465490451049503570558624435143.P73
189 (1,3,7,9,21,27,63) 757.5906255349477660375285361.P64
191 (1) 383.35546396841548971517329.P136
193 (1) 14669.85728285355409267895679.756937155910390044916932629.
.5994946327304712468705571873826831.
.4539546970485536436424707475812653713.P38
195 (1,3,5,13,15,39,65) 567538141.14046059431.P63
197 (1) 3547.6159369299.P153
199 (1) 3583.214661295139431885643832154153997.
.86539116653269014086961051020627012232284504261471.P82
201 (1,3,67) 85627.132955527487.775594571863.98527557194917.
.428995274049217.P55
203 (1,7,29) 29*.60089.145916619612283783386370190568409.
.1158560595990812530792619356788467777477674946730941.P53
205 (1,5,41)
834035491628067397615971778938263976927180494349982302975033997201.P70
207 (1,3,9,23,69) 77569456660417.227556220136287506028942276770826968937.P60
209 (1,11,19) 8048541876545647951.P134
211 (1) 141793.25901828181222890897428585774179766860170863299438695413795254930505191880636307.P93
213 (1,3,71) 968299.582053568181.
.1274759667849259732505774376326193816317726317.P56
215 (1,5,43) 31391.822161.11300176322829911971.147795410845880963171.
.11916717598664539151308306888803765941891.P53
217 (1,7,31) 604997.1956808820481173.602858801824822604293.
.626475940065539137153553.14784849807251837047947491359227676537.P50
219 (1,3,73) 877.16999040225222266951.P100
221 (1,13,17) 22543.760999500977.9761302041992117524910703947100342853.P109
223 (1) 17288166877.132218621369.P167
225 (1,3,5,9,15,25,45,75) 8101.1708445701.121257418374086998051.
.20297781182169478546946347835701.P37
227 (1) 62463078483642684523805927784689103088686041429.
.985628969754881487322427476013002845424287651017904086946721.P85
229 (1) 50839.8771561006313491618219260558398401.P155
231 (1,3,7,11,21,33,77) 1793870233.125844538662442909.
.3752691545947560669458268649.P48
233 (1) 467.79227874003.13514998546886646078035233993.
.56785654839475818636487235265635121007558707816641.P105
235 (1,5,47) 2812894619735804087343816418261851587705080375647708714001.P98
237 (1,3,79) 2371.529637338334729405483135077873.P99
239 (1) 479.871986721.643384173113837.4040609273925388685799856703093687.P142
241 (1) 1447.28439.33486078253526557.580351872045743557.
.547283138069536869412948975377385222182769003.
.2937026550451562627666151150279078330125909163812627.P65
243 (1,3,9,27,81) 3*.1459.169129.1382671.73870787476849933393474604683663.P91
245 (1,5,7,35,49) 4896864001.9152363081.11492120512321.
.353207957997402826578121.P86
247 (1,13,19) 6917.22931541257.14975869588530371.P153
249 (1,3,83) 11606389.41491794184631137.
.76354359945860977734571491962874304923412180177.P68
251 (1) 503.27611.8895962998159.P192
253 (1,11,23) 1106436299.
.35764102873412466090911077602159546824955533626915413469.P122
255 (1,3,5,15,17,51,85) 580381.326568900271.604822302841.P80
257 (1) 1543.1998784090958019204289.2526704026262106199301917676294257618227834546616502466183053066833047277.P120
259 (1,7,37) 3109.65269.357708888729481429441295130414301389734167320382217282028474835603757.P106
261 (1,3,9,29,87) 523.5743.83226515419.710074092185677.
.474062506708242760701771553376690953.P75
263 (1) 111473077.246420328513.
.125964970427584638596267035086794589086977.C161
265 (1,5,53) 1061.3041671.19069931.187978422699271372501.
.212135996587857465774994583472077008056991.
.105322961980986497356836647823085697438251004501.P51
267 (1,3,89) 2871385577390592352932558612960572694702993634318932174130446555537271.P80
269 (1) 2153. C224
271 (1) 6780421.164514887. C214
273 (1,3,7,13,21,39,91) 1093.
.894265285117657047082911243254861366638596090445735393.P65
275 (1,5,11,25,55) 2429297864813474051.
.13108478445679585187945846562792720732451.
.152254207931524870640907264181257222395351.P70
277 (1) 137947.8954857.607705768105925529871. C201
279 (1,3,9,31,93)
8248454734032306396350042707176588234070405742014804291507291.P92
281 (1) 563.8431.341614931501.4420135738596254569.
.372634096091628229321039358180848549.C165
283 (1) 644316289.182739497717749501.P213
285 (1,3,5,15,19,57,95) 523261.93586760776923620671.
.80183934664292567561851.P74
287 (1,7,41) 12412177.2405532607493.21747676457911610417.
.738710854664932373205737588298090279327121.P123
289 (1,17) 1828793.801172436655296029591646500403317187.
.26773640876541335875821092444484138995809.P148
291 (1,3,97) 4657.134002009.951340693.23363930803.
.588884936839088389773662393029.11089767531884977816638380462821.P71
293 (1) 587.15823.P240
295 (1,5,59) 123311. C191
297 (1,3,9,11,27,33,99) 5347.27170749.P141
299 (1,13,23) 1045903.5240570609.64432450872271.
.124017815182557414772494313985201.
.121219249940833404770079915022116301.P127
301 (1,7,43) 4817.219516040470409575257.
.58628254861045912568724329431228508415599499441292512521.
.3748787688169844402513004599633138785431253179050314600655297.P73
303 (1,3,101) 1213.3637.9354849642511833165720058628257.
.276052467777407518967272068222889.P99
305 (1,5,61) 16199725471.1362349539551924951.
.5554678022917560417664065958900541081.P138
307 (1) 8597.54647.173149.507779.P240
309 (1,3,103) 619.220400431.29650439178674631118602918288131887.P127
311 (1) 3733.106363.310379.171251016147061382719721. C225
313 (1) 9450044264774621. C248
315 (1,3,5,7,9,15,21,35,45,63,105)
24391637204467995942644375209216533440485081.P79
317 (1) 240287.1507019.32815841.
.22918346757630316344596090121007369869273875683.C202
319 (1,11,29) 35729. C233
321 (1,3,107) 643.859121000285791.23884590227767303.
.477280063808143381.1842220342523756359.P110
323 (1,17,19) 647. C241
325 (1,5,13,25,65) 416101077937444349085210448786432651.
.76703889230394194088755921186703377051.P130
327 (1,3,109) 28962941977.135330649536067.P158
329 (1,7,47) 2633.19384636573.P220
331 (1) 7283.60110252104542020699.1761395429514151665769314691427.
.2105702271734308254421459196775092778340834008221.P177
333 (1,3,9,37,111) 37*.33301.1294285248964974863021909311067422276786354955064661561483669329671165989.P105
335 (1,5,67) 56951. C219
337 (1) 1902213942891704396239.
.82636601001479675794891608182882964209535285466591.C213
339 (1,3,113) 1854331.952667477245436772047525567653711.P150
341 (1,11,31) 1594517.2665939.51216931087169.2538309587015599.
.13422653085156210083.P193
343 (1,7,49) 1373.8233.49393.734021.83517610741606021.
.1575721793366942921257214180187566081951195327261.P166
345 (1,3,5,15,23,69,115) 691.1381.430907693063791.376720035234076771.
.13349802972012134814680881.35136774371091884747048323143601.P54
347 (1) 895387781898751979426080914689.
.89823582672830825295829211905814036272016809423171.P213
349 (1) 81667.127037.7291309.29320685133749.91161291484807478873801.
.18284716149059665426389383.
.2258039418211166054470067466217161065944246913.P171
351 (1,3,9,13,27,39,117) 20359.594937279.2433313988259555128131.P149
353 (1) 166829729227263074982846979557342097. C263
355 (1,5,71) 2131.25561.56289276349396871456041.
.8626512997499727156919264091.76517845980555473610468712199440815091.
.3173000019403116087424802551781937763200511.
.641713853752178839895479942132287119308113963511.P50
357 (1,3,7,17,21,51,119) 1429.1175001241.23992463461.136437693760145149.P123
359 (1) 719.2051327.3093863.22452201769. C277
361 (1,19) C290
363 (1,3,11,33,121) 727.3191497.800245174328620352257663.
.241421225374647262615077397.P127
365 (1,5,73) 32605498797939226954141. C221
367 (1) 5713457.1232836358179.1903011950286996065819486607665149965823.C252
369 (1,3,9,41,123) 4287781.855981109.78025052362534309.
.967153401006619950054687111653107.P138
371 (1,7,53) 37500869458383846642957881261029.
.4546356086776970486532855270462193.P199
373 (1) 2239.342763782842586373606490121792284462755239269. C267
375 (1,3,5,15,25,75,125) 8668167751.7518480999776007258001.
.9749495229710098497186543870986809880214868507743932200504888128751.P71
377 (1,13,29) 26006969.920146163.1023200621.4768847677673.
.257366523022644644999963.P223
379 (1) C320
381 (1,3,127) 130303.2208277.9809667961.11699360074183.3451948895547127.P163
383 (1) 254655724117.132718300095362903152250689243124998807. C274
385 (1,5,7,11,35,55,77) 4621.2613660216179879661629787646541.
.432414771234341663469178268617841682553148346701.P122
387 (1,3,9,43,129) 289414765514841661.
.1515492051809463320804633626637111430388057.C154
389 (1) 1035744587833.354364364887111871. C299
391 (1,17,23) 2357731.721203469358049113389755819257183928662405067449.C244
393 (1,3,131) 787. C217
395 (1,5,79) 141853148269311930125011018018040572551975041. C220
397 (1) 2383.11117.232643.7843916473.P313
399 (1,3,7,19,21,57,133) 39109981.
.6931988925147970715443756192320558859369717.P133
Table 7+ Factorizations of 7^n+1, n<=400
L,M for n = 14k-7<=791
n Prime Factors
1 2.2.2
2 2*.5.5
3 (1) 43
4 2*.1201
5 (1) 11.191
6 (2) 13.181
7 (1) L.M
L 113
M 911
8 2*.17.169553
9 (1,3) 117307
10 (2) 5*.281.4021
11 (1) 23.10746341
12 (4) 73.193.409
13 (1) 53.228511817
14 (2) 13564461457
15 (1,3,5) 6568801
16 2*.353.47072139617
17 (1) 29078814248401
18 (2,6) 13841169553
19 (1) 351121.4058036683
20 (4) 41.810221830361
21 (1,3) L.M
L (7L) 309079
M (7M) 51031
22 (2) 661.1409.83960385389
23 (1) 3421093417510114543
24 (8) 33232924804801
25 (1,5) 79787519018560501
26 (2) 157.1195857367853217109
27 (1,3,9) 1628413557556843
28 (4) 337.2129.517553.515717329
29 (1) 402488219476647465854701
30 (2,6,10) 61.555915824341
31 (1) 373.9754399.5420506947192709
32 2*.7699649.134818753.531968664833
33 (1,3,11) 67.1357105535093947
34 (2) 137.59361349.133088039373662309
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L (7M,21M,91L) 674857.1621621.P50
M (7L,21L,91M) 547.539795803.174958633832822113.P32
274 (2) 4933.13433296255033.171346228229597943670543645694319949.
.2542857714192606828585355854082026552645113473.P133
275 (1,5,11,25,55) 3301.390042354509501.P151
276 (4,12,92) 530122269701621893033.5068394466355183450313378335551130897.P92
277 (1) 1663.81439.3045893.588286507.76443543191.305666773213.
.35666484627504843161821.C165
278 (2) 2434989769.270980007941.10311220574264857306049.P191
279 (1,3,9,31,93) 1117.161263.2458549.2015984789029.
.37181027273307023448030259.21997634133124705942517215606813138917763.P60
280 (8,40,56) 9691924412174719842472801.P138
281 (1) 6631039.22239047886922111388109709879782334859. C193
282 (2,6,94) 1129.86857.23146232881.
.8507408135928822982973809812954510818773.P98
283 (1) 1069846697769288119.P221
284 (4) 23857.148249.1267394873.190442563479129737.
.5980904229992785230777515196566061969934200643121.P152
285 (1,3,5,15,19,57,95) 643475985978004141.188783917797883464042250083871.P75
286 (2,22,26) 148171453.863977699157.680772171302969384246346369013813.
.18489093999230985031269595355473053970276854216314509.P98
287 (1,41) L.M
L (7M) 175804721.8005403352699006217853.9434065448210481479155118150417.P40
M (7L) 1723.13903914179.1463273844607.266604208732109666783.P56
288 (32,96) 577.86533516346363137.P143
289 (1,17) 185539.265229252768157343110127.92511297531161087879268599.
.10566952063659962543089422225791274843961177.P133
290 (2,10,58) 1741.47137463621.156998159690501.
.417686802890095486149791834048621.P129
291 (1,3,97) 4197967.4883462672030653.6350450713263866826214495081.P113
292 (4) 27160673.6181086196826924696146082929.
.9873849114499026811699931887107121.P175
293 (1) 395065379.9090234837292954970767.227144291051573623617426972653.C187
294 (2,6,14,42,98) 15289.7846427233.
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295 (1,5,59) 84961.14329331.94424191.751440502001723166551.P156
296 (8) 593.1777.15731809.274166594399233.396632319992796527936468929. C190
297 (1,3,9,11,27,33,99) 4159.14357519353.707165317783.
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298 (2) 36290833944740436954817.P228
299 (1,13,23) 599.1410683.746472099748883.25291032111194818151.
.7100637712713772555039933861459.
.26646467325353629274152005432430189091.P112
300 (4,12,20,60,100) 601.100801.3189188880923487431401.
.61852110266729382934188518364722401.P72
301 (1,43) L.M
L (7M) 3011.5504069054303.P90
M (7L) 171571.P102
302 (2) 2417.1668365766278161297.30219676840007995649.
.28511759576074786856678063851815881.
.480925736337089725396043071450637639329.P140
303 (1,3,101) 25453.P165
304 (16) C244
305 (1,5,61) 1008331.1276099871.20388487501.38371409301751. C164
306 (2,6,18,34,102) 11582101.17558098849.P145
307 (1) 1229.1749287.208101793.40571013452585053. C225
308 (4,28,44) 41551118009633.14111228924014993.
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309 (1,3,103) 1925071.4406341.1294315497847.
.187279038302512787946006053034457.
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310 (2,10,62) 12401.10851241.66185621.730302341.187764647774645561.
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311 (1) 13063. C258
312 (8,24,104) 10876685470992760700818169875954484159860005620568806718357344747678228737.P90
313 (1) C264
314 (2) 13352751702673573080181436651369067473632828336537. C215
315 (1,3,5,9,15,45) L.M
L (7M,21M,35L,63M,105L) 2521.16381.934291.P48
M (7L,21L,35M,63L,105M) 631.118974628711.P47
316 (4) 490328593521961.124414658504278647927541481.
.6051139266127197692503265897.14357343749884563609231238469273.
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317 (1) 1853161213201373653.104663898277020477230861.
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318 (2,6,106) 14629.1116507783855757.
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319 (1,11,29) 22243428090577. C224
320 (64) 51016321.280372481. C201
321 (1,3,107) 44841133.27021933957682455661.
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322 (2,14,46) 811441.39916941655753.115831833517457.P190
323 (1,17,19) 3593053.597825197. C229
324 (4,12,36,108) 1297.7821361.317328896377.
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325 (1,5,13,25,65) P203
326 (2) 593321.34257791501. C258
327 (1,3,109) P183
328 (8) 219761.2522977.10579647217.4679647228481.1448007102933484129.
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329 (1,47) L.M
L (7L) 92779.P113
M (7M) 659.1714104805001.P102
330 (2,6,10,22,30,66,110) 87130088761.2131954692121.
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331 (1) 756667.337097021.1625589427949. C253
332 (4) 2657.7678457341921.3061940059655156719656241.
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333 (1,3,9,37,111) 1999.P180
334 (2) 94101829.3410050832187001.1818175798347430018651001.
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335 (1,5,67) 32831.1554401.P213
336 (16,48,112) 27447194849244194531582120774054932805666322241.
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337 (1) 101020140256422276570987002251440602782290400709. C237
338 (2,26) 677.2029.5964342811175142412201. C236
339 (1,3,113) 45427.P185
340 (4,20,68) 15641.15079254951041.3585220859700498881. C181
341 (1,11,31) 683.139319098254023721793.12228833210846956506947. C209
342 (2,6,18,38,114) 33490693.137150063288706714023838837484988677.P140
343 (1,7L,7M,49L,49M) L.M
L 2722731943.568927133840129.141067436349500417.
.20313193382308673633557.P61
M 32442313.10724186844800812803083930897.P89
344 (8) 2753.38417867349927946206092222481953.
.1049139601018587804651174395448130408419345356019601.P198
345 (1,3,5,15,23,69,115) 8008493768299201.P133
346 (2) 3461.1573955757890471126964486261145675841. C251
347 (1) 108959.11804941.192781522488867055091939761.
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348 (4,12,116) 5569.3585097.13545141650308737229292561976099248633988167409680361321446680102434281248348196388481.P94
349 (1) 25389751.1693220267.14366716769276268217.
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350 (2,10,14,50,70) 23801.28001.387021601.5270389601.7216438449620401.
.2272918368416695077401.
.5168898551438758822224323913308984024753373866126288201.P84
351 (1,3,9,13,27,39,117) 116533.250746679.29114146387.P159
352 (32) 42104833.209824040449.964510269858148990692302437887078593.
.406809506051618384400177067131926148165377.
.70791251810995075042206759186175502213980649089.
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353 (1) 237428507.134133064963.38237940047343833683963090037369556149. C241
354 (2,6,118) 174877.6449881.74445493.25955435558687116453.
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355 (1,5,71) 3994007399141.9811249645852259921. C206
356 (4) 1263042449967635074439149289297. C268
357 (1,3,17,51) L.M
L (7M,21M,119L) 772585843.2202998449.P64
M (7L,21L,119M) 6756409737221257.1485662731036994178049477733239.P35
358 (2) 5704373.143693722097.P283
359 (1) 50261.111432883.2830826774651. C278
360 (8,24,40,72,120) 754316136806426696131406878764131048161.
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361 (1,19) 1901027.1651646666443.
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362 (2) 45285425774443532037543457.209345172871306850059883087217977.P247
363 (1,3,11,33,121) 11617.9042331.2690813731.11844287071.
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364 (4,28,52) 14561.30577.265713823649. C224
365 (1,5,73) P244
366 (2,6,122) 733.1396060350556672249196617.16109294386384045811825101.C151
367 (1) 549039341. C301
368 (16) 40620890273.151531589633.P276
369 (1,3,9,41,123) 739.3691.119557.167851939527353391162496590905135083.
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370 (2,10,74) P244
371 (1,53) L.M
L (7L) 1820869.228185777.
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M (7M) 743.999266838007025198420629785638217716921.
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372 (4,12,124) 1010353.11883169.
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373 (1) 1493.404851217. C303
374 (2,22,34) 7666222829.23242873318045439805121.
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375 (1,3,5,15,25,75,125) 10501.23251.492870751.P152
376 (8) C311
377 (1,13,29) 64212392257547.38418787051138665624727.
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378 (2,6,14,18,42,54,126) 7561.28729.2721626296394041.3115861585149097.
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379 (1) C320
380 (4,20,76) 761.1081419961.34646209438350825630601292760303965684281.
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381 (1,3,127) 4863847.53339239.37082744372083.
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382 (2) 3318570757.5885504436233.427818973920857.4929826463208112537.
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383 (1) 5784067.318721929785784434255525336887.
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384 (128) 4480513.13790117724241231070977. C188
385 (1,5,11,55) L.M
L (7L,35M,77M) 331871.P96
M (7M,35L,77L) 1466073841.1258096891591.P81
386 (2) 773.64849.378881050637.286400155926593.18154096793869693.
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387 (1,3,9,43,129) 1549.21673.384499207.6708720853.P188
388 (4) 3881.16724353. C314
389 (1) 35875651037.P318
390 (2,6,10,26,30,78,130)
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391 (1,17,23) 2347.93999720298493.
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392 (8,56) 3137.50177.3237785153.657688790977.524772324254629187521.P234
393 (1,3,131) 27310632673.112665111978611182141. C190
394 (2) 1477031145181238990102844609682429.
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395 (1,5,79) 5531.1607350764885165856119882549207509671951. C221
396 (4,12,36,44,132) 19801.26277996848401.845560308953668177. C168
397 (1) 1735830097.2561457623453.70258473243281. C300
398 (2) 797. C332
399 (1,3,19,57) L.M
L (7L,21L,133L) 9868867.1670786475971563131721697851.P57
M (7M,21M,133M) 1597.429406297507783.64008944055992470821992391547.P45
400 (16,80) 3987291273906709909469450259816001. C237
-------------------------------------------------------------------------------
413 (1,59) L.M
L (7L) 827.31036077322741.
.40991599138422796033459901850750268659422849367762081133062231001.P67
M (7M) 4957.83426014043.64442922154738163.262909913482545708331.
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427 (1,61) L.M
L (7M) 3344317139297.145599641870136959.3646347128361088619014438417.P95
M (7L) 1709.835213.8052785365241.309439649561434666017980378843611.P99
441 (1,3,7L,7M,9,21L,21M,63L,63M) L.M
L (49L,147L) 7057.2658349.394387183.18506674369.
.210814490395058681119744912719151.P46
M (49M,147M) 28473607.14154038259733.115759514862686269.
.1001914514798811391.11150854626101679939871.P29
455 (1,5,13,65) L.M
L (7L,35M,91M) 39368202746181575651477996103158141.P87
M (7M,35L,91L) 21841.20416811364869616971.P99
469 (1,67) L.M
L (7M) 3745249137936077575894219292545707110891285448085229305573219.P107
M (7L) 1877.58113289356699002427121.
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483 (1,3,23,69) L.M
L (7M,21M,161L) 1933.51199.2152701447163.33127892504734987.
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M (7L,21L,161M) 967.612139711.316122430589196488923.
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497 (1,71) L.M
L (7M) 727354553235428733469289.16140614228102499143832286457.P125
M (7L) 295219.9182573.242556962948881834246849409.P140
511 (1,73) L.M
L (7M) 6133.9199.61678723.
.234193550062767228282404947816391968770155615913647.
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M (7L) P184
525 (1,3,5,15,25,75) L.M
L (7L,21L,35M,105M,175L) 17851.2982139333951.12866510764382766303751.
.3258624224115672560243320051.P36
M (7M,21M,35L,105L,175M) 1051.519071701.82189065001.111649516421101.
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539 (1,7L,7M,11,77L,77M) L.M
L (49M) 521096004795829.793835915139705265367.
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M (49L) 440903.P172
553 (1,79) L.M
L (7M) 3319.19336199.379794871.72021557595389137. C162
M (7L) 560276508936447227.66240373517962417335857.P158
567 (1,3,9,27,81) L.M
L (7L,21L,63L,189L) 1150005277.7657984783.18893984137732812609271.P96
M (7M,21M,63M,189M) 74553553407147697.550365355317860186830834043508553.P88
581 (1,83) L.M
L (7L) 1163.P206
M (7M) 10459.156909509.199728047.1859414971.P178
595 (1,5,17,85) L.M
L (7L,35M,119M) 210631.3179225740586661416281.P135
M (7M,35L,119L) 9291484250876801.775341901787730204901.
.12448594440581981295316991.31555413494012729293961731.P76
609 (1,3,29,87) L.M
L (7L,21L,203L) 2437.109621.78904583697997.507481638092458480407185167.
.3916362015928563387814073029810016946121.P53
M (7M,21M,203M) 14015527.57891035272497673.1155250205872508744839.P98
623 (1,89) L.M
L (7M) 158805448424200237976976445040408274994448726011.P176
M (7L) 670349.100883801622232441.
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637 (1,7L,7M,13,91L,91M) L.M
L (49M) 2549.10682491.291613023727066334841429714476827.
.1024498945294348646953845513217361917.
.4389274716369749169224537326423676751096821695267041061129.P77
M (49L) 10193.14019097.10025383072905019.P186
651 (1,3,31,93) L.M
L (7L,21L,217L) 1303.410544245623.
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M (7M,21M,217M) 3907.54532969.607236403956967.3584760524971219147.
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665 (1,5,19,95) L.M
L (7M,35L,133M) 1657181.16227331.30148441.157451918735203121.P145
M (7L,35M,133L) 8488061.1872706830680561.20146907558946001.
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679 (1,97) L.M
L (7M) 347703995374319731325999927.21936099437966303302667748208881299.P183
M (7L) 23087.68183252476219193469550636171647279710664416713.P193
693 (1,3,9,11,33,99) L.M
L (7M,21M,63M,77L,231L) 16139971.524800143421322938023599776221499.P113
M (7L,21L,63L,77M,231M)
23509522525741531987539708712100457056678614181767.P103
707 (1,101) L.M
L (7M) 6065738579359300974329.1692052029189932668113307128446000057149.
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M (7L) 217588502852114502391794367173731322419549459. C210
721 (1,103) L.M
L (7L) 5855609828993.36123992865445932316333328433947477237909.
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M (7M) P259
735 (1,3,5,7L,7M,15,21L,21M,35L,35M,105L,105M) L.M
L (49M,147M,245L) 1471.246010381.136439846341.2927852753885431.
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M (49L,147L,245M) 82276227479817903808810970597529292280083393051.P96
749 (1,107) L.M
L (7M) 2062747.2236348877729181063126517. C238
M (7L) 1013948874068526395276184975562643.
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763 (1,109) L.M
L (7L) 5798801.1083437111.4591723800217.104697552198163. C232
M (7M) 117503.1410779124777733708469558213.
.8753305781897572893478955697579874169.
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777 (1,3,37,111) L.M
L (7L,21L,259L) 578080231.85099439377.735472800074251.
.1213954203258259.11446438181576517896996799469.P105
M (7M,21M,259M) 1142191.18174031.1444104229.22657345528392499.
.3798420401097204566617669.562690994138969285631547265153983.P87
791 (1,113) L.M
L (7L) 113*.1490518704809.83524128159364670429.
.1197527398881028830274422369304586151197207748716796367.P197
M (7M) 149160744894153581. C267
7^{7h}+1=(7^h+1)L.M, L=T^3-B, M=T^3+B, T=7^h+1, B=7^k(T^2-7^h), h=2k-1.
Table 10- Factorizations of 10^n-1, n odd, n<400
n Prime Factors
1 3.3
3 (1) 3*.37
5 (1) 41.271
7 (1) 239.4649
9 (1,3) 3*.333667
11 (1) 21649.513239
13 (1) 53.79.265371653
15 (1,3,5) 31.2906161
17 (1) 2071723.5363222357
19 (1) 1111111111111111111
21 (1,3,7) 43.1933.10838689
23 (1) 11111111111111111111111
25 (1,5) 21401.25601.182521213001
27 (1,3,9) 3*.757.440334654777631
29 (1) 3191.16763.43037.62003.77843839397
31 (1) 2791.6943319.57336415063790604359
33 (1,3,11) 67.1344628210313298373
35 (1,5,7) 71.123551.102598800232111471
37 (1) 2028119.247629013.2212394296770203368013
39 (1,3,13) 900900900900990990990991
41 (1) 83.1231.538987.201763709900322803748657942361
43 (1) 173.1527791.1963506722254397.2140992015395526641
45 (1,3,5,9,15) 238681.4185502830133110721
47 (1) 35121409.316362908763458525001406154038726382279
49 (1,7) 505885997.1976730144598190963568023014679333
51 (1,3,17) 613.210631.52986961.13168164561429877
53 (1) 107.1659431.1325815267337711173.47198858799491425660200071
55 (1,5,11) 1321.62921.83251631.1300635692678058358830121
57 (1,3,19) 21319.10749631.3931123022305129377976519
59 (1) 2559647034361.4340876285657460212144534289928559826755746751
61 (1) 733.4637.329401.974293.1360682471.106007173861643.7061709990156159479
63 (1,3,7,9,21) 10837.23311.45613.45121231.1921436048294281
65 (1,5,13) 162503518711.5538396997364024056286510640780600481
67 (1) 493121.79863595778924342083.28213380943176667001263153660999177245677
69 (1,3,23) 277.203864078068831.1595352086329224644348978893
71 (1) 241573142393627673576957439049.P41
73 (1) 12171337159.1855193842151350117.P44
75 (1,3,5,15,25) 151.4201.P35
77 (1,7,11) 5237.42043.29920507.P45
79 (1) 317.6163.10271.307627.49172195536083790769.P43
81 (1,3,9,27) 3*.163.9397.2462401.676421558270641.P27
83 (1) 3367147378267.9512538508624154373682136329.P42
85 (1,5,17) 262533041.8119594779271.P43
87 (1,3,29) 4003.72559.P48
89 (1) 497867.103733951.104984505733.5078554966026315671444089.P39
91 (1,7,13) 547.14197.17837.4262077.43442141653.316877365766624209.P27
93 (1,3,31) P60
95 (1,5,19) 191.59281.63841.1289981231950849543985493631.P33
97 (1) 12004721.846035731396919233767211537899097169.P54
99 (1,3,9,11,33) 199.397.34849.P51
101 (1) 4531530181816613234555190841.129063282232848961951985354966759.P41
103 (1) 1031.7034077.P93
105 (1,3,5,7,15,21,35) 30703738801.625437743071.P26
107 (1) 643.999809.9885089.215257037.2386760191.511399538427507881.
.646826950155548399.P38
109 (1) 1192679.712767480971213008079.5295275348767234696493.P60
111 (1,3,37) 37*.30557051518647307.8845981170865629119271997.P29
113 (1) 227.908191467191.P98
115 (1,5,23) 31511.19707665921.20414137203567631.
.5799951513941382144830754391.P30
117 (1,3,9,13,39) 240396841140769.537947698126879.3352825314499987.P28
119 (1,7,17) 923441.3924966376871.768736559421401249042753476963.P48
121 (1,11) 15973.38237.274187.P96
123 (1,3,41) 1811791.626920594693.9425856976319889649.P43
125 (1,5,25) 751.1797655751.176144543406001.P74
127 (1) 18797.90679.P117
129 (1,3,43) 210769832431.407429732767505248479163.P50
131 (1) 80173.109517.141811693.446790173.7370364319027.15594845538029429933.
.7317723970031057677693.131758351065116151205213.P27
133 (1,7,19) 1597.2021015460335957.P90
135 (1,3,5,9,15,27,45) 1577071.16357951.310362841.258360989311.P39
137 (1) 2467.2535528323.1029879756928762117455431.
.140175894162990609843314797.P74
139 (1) 119124859925363.P124
141 (1,3,47) 283.721030498171501831.P72
143 (1,11,13) 2823679.180523201.47428676444591705727929369346443.P74
145 (1,5,29) 9605671.15589280974996818911.
.80684370001269698853996151670133742711.P48
147 (1,3,7,21,49) 63799.4715467.267652966241599.2603941883787374089.P40
149 (1) 12517.535596779200919.P130
151 (1) 907.429360649.29877981480806017715604631.
.28656552837574546515657117360191971140211910788651135283.P58
153 (1,3,9,17,51) 307.18973.11910133.25332185271529.41331541464123787.P53
155 (1,5,31) 311.9294566806081.P105
157 (1) 301670477.5180282664612031.11427999892821876397004936937893.P101
159 (1,3,53) 351391.3852774594841.185328247384490197483.P66
161 (1,7,23) 6763.472341157.11273170771131750391.
.1626777403161656797092007877.P74
163 (1) 5764066668537270911379761.
.403925722833778378107304989280994102850314855068615959021587563.P75
165 (1,3,5,11,15,33,55) 471241.138267770127916457629034873443951.P43
167 (1) 18843947.106811083848465643.
.37576897811119167463436962410483708090653.P102
169 (1,13) 11831.2709246550432452192307438140153898730002165574677.P104
171 (1,3,9,19,57) 229162071140015324614111.
.1104249349362995181144668003642191.P52
173 (1) 347.21528169344472027.
.46194618816084982100679234312974236345786346173.P107
175 (1,5,7,25,35) 18525843918490695886751.991474271662986957800680951.P71
177 (1,3,59) 3187.232199557797964905143390121842739619033812919.P69
179 (1) 359.36558961.4201521652717.352543640588653.P141
181 (1) 12671.28865519.995130761.16814655289.414479952329.P138
183 (1,3,61) 2520277.
.26384856922809741239246281240888980994567902544116187.P62
185 (1,5,37) 6511230041186560022095681.1936570114827069923550119591.
.63441573295906607253783211246544893041361.P52
187 (1,11,17) 143899867.19886424182370875870239184131623563.P118
189 (1,3,7,9,21,27,63) 878075126908698927928483.
.33030636037992147205820927521.P56
191 (1) 4473297929.112103021940812743353521.P158
193 (1) 773.39373.561470969.639701219449517.4274417556076113498947.
.26409540111952717487908689681403.
.447798287131284928051408304965265782892174953181087929.P55
195 (1,3,5,13,15,39,65) 1951.35081393881.360924572424391.P68
197 (1) 52009.79040479805615687465683.
.3599474961483053310878605135585111374469138078226023233589649293.P105
199 (1) 797.29453.2253079.P185
201 (1,3,67) 1609.2046166739518832881.
.184976479633092931103313037835504355363361.P70
203 (1,7,29) 18620680471.68616805173400502243.223072327648229020879.P118
205 (1,5,41) 41*.275521.21158848681.P143
207 (1,3,9,23,69) 109908191603107.
.823799348530495507269035013254489287846904557.P74
209 (1,11,19) 257489.1246477.9269802917.
.42545662673095831743789692955596677.P124
211 (1) 692624557324389620662782322677336711138108482588281739734375570506492391931849524636731866879.P118
213 (1,3,71) 853.1594093.1182534679.17469229933.P112
215 (1,5,43) 431.
.41398275939670867448911914339156680381343777006826487831.P110
217 (1,7,31) 3662093.
.51508652116008872412773338336289708669037765081397085489.P118
219 (1,3,73) 439.2212293763.
.39316310783659104892252157287077969239619734325044334592964583271.P68
221 (1,13,17) 443.1661422610776235605151630089.P163
223 (1) 2677.130975483.182458277086165261611622073457934047326239127722446775785510707991660410777011553955711177150186323623147.P107
225 (1,3,5,9,15,25,45,75) 2002877551.2636899200194401.
.97671987485517534751.125899659866627764313267482289910001.P41
227 (1) 113136621886721.617431748093238554410874808506989442264783116181403206744221352101186333.P141
229 (1) 9161.43544351.9006996017757809392117.P195
231 (1,3,7,11,21,33,77) 2311.22187551.535212994471849.
.234904066377148960506871003.156813120797253579231191970121.P40
233 (1) 467.47533.115081654907.89412401116867.42983757528467293.
.10857980200444401822643.
.20131492120828919814484857298874674155298711142397769181347.P103
235 (1,5,47) 518203357921.190893195970004711.1589908647339072250321.
.605431706028029946531059199512572282414786250085768871.P80
237 (1,3,79) 90758677.1603873536486496162414778277997333003.P112
239 (1) 479.142847911. C228
241 (1) 125997820213. C229
243 (1,3,9,27,81) 3*.411361786890737698932559.P138
245 (1,5,7,35,49) 336737801.23609565631.8274923251622825388807721.
.74689140199104459031993110210054016743223513365511.P75
247 (1,13,19) 1483.1024516164479902988921.1299823520026173021751.
.153360717056181938148119886537684707068363643930609.P121
249 (1,3,83) 4483.1413141919363039.
.79631228080621938573499710253940180960724841.
.3524445389714777887659796421466286321350017806951.P53
251 (1) 52371653.P243
253 (1,11,23) 1013.3037.72932311.2615313691182114927177553117.P179
255 (1,3,5,15,17,51,85) 77967508765681.17452955481423492661946457391.
.34194473116159546979818689031.P58
257 (1) 1017721.4271961427. C241
259 (1,7,37) 2591.64638631.3663802449983927390483.
.68941184253610253169908132923.P155
261 (1,3,9,29,87) 523.670249.44974999.9113995243.7299238406959.
.9136734149894295938064503769037.
.131108694538423601496731528051392288744803439.P54
263 (1) 40199712048008930571428131875902950777477607917. C216
265 (1,5,53) 116721153193946736160194298023751.P176
267 (1,3,89) 9613.540913940517169.P158
269 (1) 5418307589425009.44052813154697065841. C233
271 (1) 1627.56369.4790817014835738008638872886922952208975172696533. C214
273 (1,3,7,13,21,39,91) 1093.32786209.139708570703521.
.5331924088485663758835996822909123141656859869805374791.P65
275 (1,5,11,25,55) 7151.15401.59951.2495283264895779020253203931608951.P154
277 (1) 1016157022810759.102092644289739525085919338335107091799. C224
279 (1,3,9,31,93) 18989357081041.
.1986554577939642346080445591065987383029299397551517.P116
281 (1) 563.2597610354323.380431988961690791.
.133355295524380732608674846305692470329.C210
283 (1) 16809360945688609. C266
285 (1,3,5,15,19,57,95) 18449288550044654139241919401.
.844267447094321323435601792968017601.
.219414044208440803345204019137889332111.P42
287 (1,7,41) 1723.13365428707.1941851180301719. C212
289 (1,17) 42773.93195753455238027770502373.P242
291 (1,3,97) 1747.18043.1625625533641.1953725183587.1012047221926483.P145
293 (1) 587.9476124263231731100867.
.72753092406224481018194292737207864791672573037959.C218
295 (1,5,59) 366111286951.215168431547401.6898649252938113791.P188
297 (1,3,9,11,27,33,99) 55243.198397.1981560241.31600574312077.
.165426670443186506567467.
.7907009307594694001053552000588658391100974093457603716419437.P64
299 (1,13,23) 599.646777215499244129.P244
301 (1,7,43) 821856609631.13403893556831. C227
303 (1,3,101) 2096761.272295362253883.P180
305 (1,5,61) 1831.2441.38981441.23886931441.2589575105599981821056130911.
.119724826129796860249638217747306760831.
.15036424216810835394267218232384724378143658798913881034271601.P89
307 (1) 526199.100066684713521521.11357792009472146190882003383320587841.P247
309 (1,3,103) 167798066344417387.3462948230491376473027. C166
311 (1) 4344673058714954477761314793437392900672885445361103905548950933.P247
313 (1) 1879.2099818661161079.P294
315 (1,3,5,7,9,15,21,35,45,63,105) 631.142809770881.P131
317 (1) P317
319 (1,11,29) 723493.798763879.25815444138362212501215782602427193330961.P225
321 (1,3,107) 167805961.P204
323 (1,17,19) 851908127328669427. C271
325 (1,5,13,25,65) 77351.200201.4347195468174001.280672874149406424401.
.3733209604853765522511798189559871765401.P155
327 (1,3,109) 1147117.13675561831.46553630477420371690681.P178
329 (1,7,47) 1964089881669809395643.
.37633698993045258670863410188544865190871951.P212
331 (1) 1987.507849415889107.P313
333 (1,3,9,37,111) 96455449.2503678796850536532770633167883644999. C172
335 (1,5,67) 161471.50473006151.8480807579201.164168826950706906612751.P212
337 (1) 427991.282549563.288525099368866187.
.16917315519781128734365649437223631827.C268
339 (1,3,113) 406123. C219
341 (1,11,31) 683.1309536986943791.1214990613179601809.
.246254302494824359942225692028596828479.C226
343 (1,7,49) 1977439591.62612348451548943616787.
.7754637448036836493958053.C238
345 (1,3,5,15,23,69,115) 5521.74521.487831.19277911. C155
347 (1) 27067.P342
349 (1) 127037.28974679.6558190177933.P323
351 (1,3,9,13,27,39,117) 35803.355087294364791.
.1786946360382838276990549597027.P167
353 (1) 1781225293.1044667255801249. C328
355 (1,5,71) 12071.48630031.14541138145721801.637608923699011111.
.2816176140325775182481.12291800548749837777601.
.30124399372383431732349878765015295744155071.P148
357 (1,3,7,17,21,51,119) 4999.143556841.3329808692827.
.43451713720907517733.1118941080585995263069320373.
.15958610536514031269673402704345512354924969.P78
359 (1) 719.73237.799853.33569502677.18200054748466867994849.
.8745075387933004096394385246656921347.C275
361 (1,19) 81671197.88231338953639484307.103143975536225777711.
.2747268108721464854672161.11614395396735967816534625117.
.220706363362058009698248377980921202870796191.C198
363 (1,3,11,33,121) 622001227.1830142890743707. C196
365 (1,5,73) C288
367 (1) 3671.129919.1628747.20211847881829188997.
.2455930880606076809434613843.P305
369 (1,3,9,41,123) 1900016393894413508477719.
.3151445759294008336434146467746716852125711.
.4624740815741021164555032450406356165555243059597323.P122
371 (1,7,53) 2969.51199.
.26628696860763170757415075888614691991511099147227.C255
373 (1) 1493.125329.P364
375 (1,3,5,15,25,75,125) 21751.47001751.4471031976001. C176
377 (1,13,29) 11311.30161.75401.428991023449. C311
379 (1) 3581077009.123816570976184709280372723.P343
381 (1,3,127) 9783462102370544239.45830377642600710169.
.591082109095345424416413908752729.C181
383 (1) 852559.1628675880394909638591813700831880313095925587.
.23181229247696012268805890210990826546682789683.C285
385 (1,5,7,11,35,55,77) P241
387 (1,3,9,43,129) 23667927744614744947915146673639. C221
389 (1) 1991681.9673567199.30613946219676519851696681.
.534106762532886493971950663223965323.
.295666607855148525951669299929669849601357.C270
391 (1,17,23) 7039.15641.140346818465014013770407271092917. C312
393 (1,3,131) 787.11983466231266295686798098306470812807267.
.1100517845115354201024243897527295703743726722437.P169
395 (1,5,79) 870801991.25439781075319591.4706625334158237778391951.
.388603184868446209952357338208961774763421470820867551.P209
397 (1) 15941835894241.414655644406744473813179034437272581119641.
.306705064286388936780828266137942480452220517447677.C291
399 (1,3,7,19,21,57,133) 6316969.34282879.1473464802559.
.7459654752238258604700923083.P162
Table 10+ Factorizations of 10^n+1, n<=400
L,M for n=20k-10<=790
n Prime Factors
1 11
2 101
3 (1) 7.13
4 73.137
5 (1) 9091
6 (2) 9901
7 (1) 909091
8 17.5882353
9 (1,3) 19.52579
10 (2) L.M
L 3541
M 27961
11 (1) 11*.23.4093.8779
12 (4) 99990001
13 (1) 859.1058313049
14 (2) 29.281.121499449
15 (1,3,5) 211.241.2161
16 353.449.641.1409.69857
17 (1) 103.4013.21993833369
18 (2,6) 999999000001
19 (1) 909090909090909091
20 (4) 1676321.5964848081
21 (1,3,7) 7*.127.2689.459691
22 (2) 89.1052788969.1056689261
23 (1) 47.139.2531.549797184491917
24 (8) 9999999900000001
25 (1,5) 251.5051.78875943472201
26 (2) 521.1900381976777332243781
27 (1,3,9) 70541929.14175966169
28 (4) 7841.127522001020150503761
29 (1) 59.154083204930662557781201849
30 (2,6) L.M
L (10L) 61.4188901
M (10M) 39526741
31 (1) 909090909090909090909090909091
32 19841.976193.6187457.834427406578561
33 (1,3,11) 599144041.183411838171
34 (2) 28559389.1491383821.2324557465671829
35 (1,5,7) 4147571.265212793249617641
36 (4,12) 3169.98641.3199044596370769
37 (1) 7253.422650073734453.296557347313446299
38 (2) 722817036322379041.1369778187490592461
39 (1,3,13) 13*.157.6397.216451.388847808493
40 (8) 5070721.19721061166646717498359681
41 (1) 2670502781396266997.3404193829806058997303
42 (2,6,14) 226549.4458192223320340849
43 (1) 57009401.2182600451.7306116556571817748755241
44 (4) 617.16205834846012967584927082656402106953
45 (1,3,5,9,15) 29611.3762091.8985695684401
46 (2) 1289.18371524594609.4181003300071669867932658901
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128 257.15361.453377.P116
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150 (2,6,10L,10M,30L,30M) L.M
L (50L) 261301.P35
M (50M) 601.3903901.168290119201.25074091038628125301
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160 (32) P128
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170 (2,34) L.M
L (10M) 7568346838961.237612993541791006121.P31
M (10L) 26861.P61
171 (1,3,9,19,57) 19*.2053.4410785971.2911579215499.
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172 (4) 277641151780258438310079109077611969.
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183 (1,3,61) 367.51745081.40498340376691.
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184 (8)
120553054891405588545727822543281066162803459003848166118314367809.P111
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202 (2) 101*.3679329001.19384130081.12793360409007449.
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203 (1,7,29) 19489.243720583.2563963356465898129.
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230 (2,46) L.M
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250 (2,10L,10M,50L,50M) L.M
L 4001.76001.P92
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256 10753.8253953.9524994049.73171503617.P225
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275 (1,5,11,25,55) 1501539197401. C188
276 (4,12,92) 1657.1469409649.38115215074391056784287931569.P136
277 (1) 9419.9973.2583222779. C259
278 (2) 1669.154220035640400941.
.22566203851955475809719636369904190294286729.C213
279 (1,3,9,31,93) 1117.183372282864547916749018225828651.P145
280 (8,40,56) 1378721.5758943337281.6717658458758041138199521.
.1081862991605594332069477594870669601.
.70488250368897247920709885766793062547616862669921.P63
281 (1) 6560496291091.58513940129535379432477007. C242
282 (2,6,94) 1129.3792128943527581.2246285860430986548506215527001.
.441659454625809720192647055276257528637832621638030289.P82
283 (1) 1699.241117.61945573305222690279363663578823967.
.49019999488937337866558715558211303750925973449.
.151168348012920493188164812150408056175148228488823.P142
284 (4) 4672937.11473030297.273919647900781361.
.22848119041855139346027890461325138752752437281.C200
285 (1,3,5,15,19,57,95) 571.11382273828031938028891.
.43135513763991692454656851.P94
286 (2,22,26) 17576772101461.754309323029578981494450523147961.
.4832227158939716614468345433242909.C161
287 (1,7,41) 19214818177409.P227
288 (32,96) 577.317752351489.P178
289 (1,17) 511438099.587063793048979091.42323992639419349049079264521. C217
290 (2,58) L.M
L (10M) 1767955366388381478541.P91
M (10L) 14087942679857610940613213182901.P82
291 (1,3,97) 120993298365129876163173210302328063293143.P151
292 (4) 73*.1753.468953.162393769017609303761. C258
293 (1) P292
294 (2,6,14,42,98) 23742102289472351423104605582718329399560972065457968561934785062599221.P98
295 (1,5,59) 2353867026803341982771.25602601418102182972721.
.193428272579096534429098931.803454205095303821868753731.P136
296 (8) 593.P286
297 (1,3,9,11,27,33,99) 7129.8927244623941181398233253.
.1866763546567680996103417376059.
.112970308382439859401726947341740704554951737408511354573.P65
298 (2) 10729.607921.136916416686052955621. C267
299 (1,13,23) 32494323733. C254
300 (4,12,20,60,100) 32401.4711806100010561082466291127577601.
.4482637729513780747000872935673625025127940754401.P74
301 (1,7,43) 3613.212057054080446499.120525789336558438197.
.6798855735656881396055959081077830421892567.P169
302 (2) 15101.20481641. C289
303 (1,3,101) 133321.329059.389659.
.3041043667691453912297172888609639950518597.P142
304 (16) 3031489. C282
305 (1,5,61) 2447385101917578576518614756091. C210
306 (2,6,18,34,102) 54469.158963941.2709009355501.3626707988341.
.157538980319816607121.846160494149365798478410729.
.112544281755782732673671367061.P78
307 (1) 3311436805543.1490473286202873492575327109823.
.5523722596446330977448218249241349336929189661174997.C212
308 (4,28,44) 53241089690155545084545617441.
.780010410791719540565140196582552053062384449.C167
309 (1,3,103) 619.P202
310 (2,62) L.M
L (10L) P121
M (10M) P120
311 (1) 82727.2122689869717.7966595011106561.3416317897947415066069561.
.835375365056917236891484436143.C223
312 (8,24,104) 148068337.10662171313.325807801400017. C160
313 (1) 5009.1074844665139845442819616837.
.3942061217624131929520541160207424212724650028976527.C230
314 (2) 28415783195151364586816438858689. C281
315 (1,3,5,7,9,15,21,35,45,63,105) 2521.131041.525326613841.
.1275784731048123659634702312820051.P91
316 (4) 259121.73921249.P299
317 (1) 3536453.12361733.68009240067498931554643059611689714176253. C262
318 (2,6,106) 3181.125929.1650244260647104976802437090486126821.P164
319 (1,11,29) 1277.357281.49561573447.
.776277205967881079419436133930781972785940099183.P213
320 (64) C256
321 (1,3,107) 7569823.2366998879807.899788378170104270110161037.P166
322 (2,14,46) 216613430183025989.
.1009805096139614383066323378818605356821967673241.P199
323 (1,17,19) 647.108529.738379.1644353478367.1078893279821424911891. C242
324 (4,12,36,108) 68562937.43599922525432064821850834951727679807657.P168
325 (1,5,13,25,65) 107251.4271801.82009322851.318942474614140390001. C197
326 (2) 498698470009.76232914055207003005318654163381.P281
327 (1,3,109) P217
328 (8) 6051298241.48656086054529.669995415570582921859463287135169.
.18798124481332409484502894235050519095834690259132073729.C209
329 (1,7,47) 659.P274
330 (2,6,22,66) L.M
L (10M,30M,110L) 507868012934701.6143203800519931376420641.P41
M (10L,30L,110M) 17247781.1082745841.18516980928601.9000931379651641.P35
331 (1) 38329801.5943603127859.1932782378208168486700373.
.66287629848519079879793946893.573408944084407647616987278212508727.
.37597427372633848169498753071057309208493613.P178
332 (4) 1993.1627839311921131673455277189737. C295
333 (1,3,9,37,111) 902659997773.7116181512528105949933.
.62562101977662753776437.P160
334 (2) 476103356904941.411603787218349354280868589.
.1387401303965667453093373669.
.198607499132490748242152175454768755769289.C223
335 (1,5,67) 2011.248807851.7261216121.P243
336 (16,48,112) 1454209.9396577.77700458351603754241.
.465149401935712615628055361.20275219423179517169965224971521.P101
337 (1) 121321.2251702571.55027074590990508852961.
.71489171229856447321502908314697600957469967193571.
.1687858617956114857563779160203327248258725852773131.C198
338 (2,26) 89909. C308
339 (1,3,113) 104120568827856356216891091637981484179. C187
340 (4,20,68) 1361.787131281. C244
341 (1,11,31) 2729.43649.204601.626254207448316529499143.
.2521683376335623264853169025426175893.P227
342 (2,6,18,38,114) 126541.2050658332436114459080741.
.367758735915513355987163036605562773789741.P146
343 (1,7,49) 1373.14407.46649.209917.275087.4020987966062173.
.506500014792811998378163728668881.P223
344 (8) 41281.34883769795276074742193.301141397581994586210257.
.524418195375754143552289.C262
345 (1,3,5,15,23,69,115) 11313931.127688571001.194656286401.
.7386441591567953769105190285927615814299177561.P101
346 (2) 19368443729478869.9970640571320679438520961989. C300
347 (1) 368720813.805697219.89700105169. C318
348 (4,12,116) 13921.11090099157944399977.
.246900403017958787131873605843061988161.P163
349 (1) 3491.3361543170437980531667161105832265329.
.35927713091621749764338565947172319082597.P268
350 (2,10L,10M,14,70L,70M) L.M
L (50M) 701.422100001.1125310645201.P97
M (50L) 213567756617511209506778605497489645838025587933288349770601.P61
351 (1,3,9,13,27,39,117) 592489.30742515591607. C197
352 (32) 23447080358593.26670033927811409112897180097.
.222688353792418778799593928777532880641.
.3162086824598326714007856976523611232833.C201
353 (1) 1006029527.56540001776360839594874218856939642617050503. C300
354 (2,6,118) 709.P230
355 (1,5,71) 2131.8521.1026684688942915478900251.P249
356 (4) 158777.118638175449391414217.
.205634535002357125750465106981645977.C292
357 (1,3,7,17,21,51,119) 17851.P188
358 (2) 530819489.7788750761855821. C332
359 (1) 25849.19210610797963667218565939. C329
360 (8,24,40,72,120) 2582785559040998185916696136639544586696154922477921.P141
361 (1,19) 43321.5140192330491733331414521378576126342075768810496980939.C283
362 (2) 928417781.469968172441.2136569912461.15470952779187481.
.3467369151629862044701.314547891171506427278717744569.
.22780106292572351730658730234738216404394547689.P214
363 (1,3,11,33,121) 727.1453.3481311540961. C202
364 (4,28,52) 574393.10727809.286569193. C267
365 (1,5,73) C289
366 (2,6,122) 76129.190321.390889.4801921.2834820061.3812801341.
.2418666002101476599410229029.C172
367 (1) 6337012003051224701798337646203298967.P330
368 (16) 153089.107896522139513920752730643638401909724513.P306
369 (1,3,9,41,123) P241
370 (2,74) L.M
L (10L) 1481.6336499381.
.271880675850180367872653023164942909880799363524216099671322919521.P67
M (10M) 15541.68821.74615611921.4098464044501.107771345624719321.
.16206170837408945509907221.P69
371 (1,7,53) 743.1057997274797.2584863032795023.
.157098960626439851618648929549692694031560694047.C235
372 (4,12,124) 700849.11110153.5419392721.1220725699657.42367299139993.
.16584440161215846282167330487128069170776821649169.
.23140616853203983900922551785166946660605063239337678349130406077337.P76
373 (1) 90060564940204590241091.31789742592325236493677867077.
.216526856157522033346992833381986034131.C283
374 (2,22,34) 7481.155623169021. C305
375 (1,3,5,15,25,75,125) 25005172023963824973001.
.59244397795882902986928930001.C149
376 (8) 84977.3056129.801310897.71306567377.17432639655812883290745409.
.24675897452175673572108819041.
.497739854873037449538282211022770570513.P245
377 (1,13,29) 484688693362852875650185421098728254915802251. C292
378 (2,6,14,18,42,54,126) 165358820733883770736233015527320175869593121.C172
379 (1) 10613.30817249.4918445244727502358176820280164673127.
.33584520860278767011970207517032237108309731086439023.C278
380 (4,20,76) 12231385993824607429587973444912801.P254
381 (1,3,127) 2287.451897625287.1053449334720579590200819.
.4444349792156709907895752551798631908946180608768737946280238078881.P147
382 (2) 77929.106961.13968004259021399202183274452648726337203224861. C324
383 (1) 11491.262739.4685623. C366
384 (128) 434689.859393.33649448872371457.145778507161340929. C211
385 (1,5,7,11,35,55,77) 3851.170873011.
.1051543809110704722613632495009411089889481.
.3815465557445576556927066195758955772398238343771.P138
386 (2) 1439921227944130405196041866693950149. C348
387 (1,3,9,43,129) 1708219.10455967.41130156794062447. C223
388 (4) C384
389 (1) 110477.147351852638675482771921.
.20869977631748901447120178621975588066249.P320
390 (2,6,26,78) L.M
L (10L,30L,130L) 201721695849323521.2685647186330706081032050321.P51
M (10M,30M,130M) 19501.9160020509281917601.P74
391 (1,17,23) 2955961.2140571729.37633218241.9101279023169.
.473608692432035450677211738101499095303.P275
392 (8,56) 54881.403539336813078648113.
.5649333362757164788488040397332687608183771313.C265
393 (1,3,131) 78447517. C253
394 (2) 27581.39183683903547299202471125940449908897423309.
.95857172574244109092139928579854506165297073472804809.P291
395 (1,5,79) 6295632499623851.4539787279569136988691351491.
.24966203549341539495819194854679625225811.
.36135553580039597739744803188558136917651907171.P182
396 (4,12,36,44,132) 761113.99677548081.440718109921.
.4987445373502665124237014313.
.7408727338313716781446937691661250885891761.246288943607463575049631057704872789315648893038409344335438892115177.P73
397 (1) 15149521.16790376230301757.P373
398 (2) 581140178513809.25318162873760593102299508147845874260505144789.C335
399 (1,3,7,19,21,57,133) 425991366045253.
.17499101101496101893247811440257935152097401.
.9284668536078237580134472469990637899155265743957.P110
400 (16,80) 4801.43201.980801. C306
-------------------------------------------------------------------------------
410 (2,82) L.M
L (10L) 59090021.1266925593264677597290950641.P126
M (10M) 821.639601.11036695406441.1073380218518144441.
.1350059351915828990550200161.
.139074671904011778473984366758527524121792121.P49
430 (2,86) L.M
L (10L) 7741.2198478623863901.
.7549370642855106064318428883982856249713821.P107
M (10M) 1044817620601.P156
450 (2,6,10L,10M,18,30L,30M,90L,90M) L.M
L (50L,150L) 1801.33301.139501.560701.5030101.
.152372720018473862927761564984708391701.P57
M (50M,150M) P120
470 (2,94) L.M
L (10M) 941.29096340761.474181059033108701.P153
M (10L) 18465110677523332168571918701.
.36278027867431861993452659830529311893020335861.P110
490 (2,14,98) L.M
L (10L,70M) 268330861.32422034720694602873554553373241.P129
M (10M,70L) 366395073564101.354434210886621881.
.28706164502711390875680641913825481.P102
510 (2,6,34,102) L.M
L (10M,30M,170L) 8161.2586721.5071197096181.
.677827125083342723075551469213357648491441.P64
M (10L,30L,170M) 1021.855781.
.114797635898427958794033542315180663747542680841.P72
530 (2,106) L.M
L (10L) 10601.5087682140647502286078523305727177388588041. C162
M (10M) 4241.1103461. C198
550 (2,10L,10M,22,110L,110M) L.M
L (50M) 2471701.486904001.133157371602664723858501.
.212890462662706052906860201.49094895915282817628267672401.
.3668996113223183559833250396711179251902642533701.P59
M (50L) C201
570 (2,6,38,114) L.M
L (10M,30M,190L) 211592942161.481612717573381.
.117008737749609201563737321.P93
M (10L,30L,190M) 20521.7594681.70532941.3685902392604541.
.9025836525591423620461.14634428294824755331225520581.P59
590 (2,118) L.M
L (10M) 193274561.347811486461.12013233555242641.
.8505896978256278656680007081.P168
M (10L) 1181.35764621.3064985101. C213
610 (2,122) L.M
L (10M) 21961.51241.9818561.28474644365651641.17716886277230798340041.
.39069669288697789469488625615834711944836425801981.P136
M (10L) 6101.217345835281.555818110301.8950221294967070861.
.17751033585336286181.C176
630 (2,6,14,18,42,126) L.M
L (10M,30M,70L,90M,210L) 158201922061.56541586842121464411050521.
.229209947541611916250468549073491977346097487987121.P57
M (10L,30L,70M,90L,210M) 1351855459456741.33822732328831925621101.
.19825744781339712457003608841.938366482703941691072746568832156530761.P40
650 (2,10L,10M,26,130L,130M) L.M
L (50L) 1301.P237
M (50M) 431684501.23098714167966114959599501.P206
670 (2,134) L.M
L (10L) C265
M (10M) 99908656408081.28120888763986481.P234
690 (2,6,46,138) L.M
L (10M,30M,230L) 1381.63691382029918881694921.
.316699822269639096888937801.114061789660900413328637822705950861.
.73137716939443396538710479664316724061.P52
M (10L,30L,230M) 9661.6193371433274461.59483540558994759763795801.
.53836677179343252802536411876638569921.P93
710 (2,142) L.M
L (10L) 3988107351414007354990781.9986944549901581065584141. C231
M (10M) 2006461. C274
730 (2,146) L.M
L (10M) 1574095173557315161.665787365080314723361. C249
M (10L) 405007685327621.8383648187691944581.14947162642878875393981.
.4941698957237831273165154533595725287181.P194
750 (2,6,10L,10M,30L,30M,50L,50M,150L,150M) L.M
L (250L) 473217092140501. C186
M (250M) 3001.89285503565971501.3405964732740856789870552501.P153
770 (2,14,22,154) L.M
L (10L,70M,110M) 177663162067596466801.557377949694929416901.
.198618138138638637771823241.P173
M (10M,70L,110L) 20021.1607415137021384783510881. C212
790 (2,158) L.M
L (10L) 14671834360812557354682189761.P285
M (10M) 102701.99834305852659737721.9881484126026806397682037921.P259
10^{10h}+1=(10^{2h}+1)L.M, L=A-B, M=A+B, h=2k-1,
A=10^{4h}+5.10^{3h}+7.10^{2h}+5.10^h+1, B=10^k(10^{3h}+2.10^{2h}+2.10^h+1).
Table 11- Factorizations of 11^n-1, n odd, n<300
n Prime Factors
1 2.5
3 (1) 7.19
5 (1) 5*.3221
7 (1) 43.45319
9 (1,3) 1772893
11 (1) 15797.1806113
13 (1) 1093.3158528101
15 (1,3,5) 195019441
17 (1) 50544702849929377
19 (1) 6115909044841454629
21 (1,3,7) 7*.1723.8527.27763
23 (1) 829.28878847.3740221981231
25 (1,5) 5*.3001.24151.1856458657451
27 (1,3,9) 5559917315850179173
29 (1) 523.303309617049998388989376043
31 (1) 50159.2428541.157571957584602258799
33 (1,3,11) 661.1453.637265428480297
35 (1,5,7) 211.42437717969530394595211
37 (1) 2591.36855109.136151713.2615418118891695851
39 (1,3,13) 79.157.547.84631.480091.32508061
41 (1) 83.1231.27061.509221.14092193.29866451.840139875599
43 (1) 1416258521793067.42534656091583268045915654719
45 (1,3,5,9,15) 9842332430037465033595921
47 (1) 2069.22666879066355177.18806327041824690595747113889
49 (1,7) 510810301.1065264019.100641220283951395639601683
51 (1,3,17) 10711.457315063.15085812853.25994736109
53 (1) 107.351497.6005113.6918082374901313855125397665325977135579
55 (1,5,11) 25301.39161.643170158708221.645654335737185721
57 (1,3,19) 19*.1047623475541.1412900479108654932024439
59 (1) 1181.70845409351.33083146850190391025301565142735000331370209599
61 (1) 440177.520518327319589.1461808298382111034194027645506019619578037
63 (1,3,7,9,21) 127.8317.867259.106431697.316825425410373433
65 (1,5,13) 131.673267426712748387612994804392183645147042355211
67 (1) 15277.2160349.76394148218203559.P42
69 (1,3,23) 139.8209475377.P34
71 (1) 1847.64327.159248456569.1273880539247.P42
73 (1) P76
75 (1,3,5,15,25) 151.59302051.1826934301.27665283091695977275201
77 (1,7,11) 593554036769.P51
79 (1) 317.185277551100523662054683911.P53
81 (1,3,9,27) 139026457.14010692617072784593.P29
83 (1) 167.12119.178057577.52447614013.P61
85 (1,5,17) 584916791.553393500180551.P44
87 (1,3,29) 398113.54415717.P45
89 (1) 73111721.2103114787086589.4180235017418376525776333.P44
91 (1,7,13) P75
93 (1,3,31) 2791.3163.P56
95 (1,5,19) 67989221.180124441029509240214675551.P41
97 (1) 389.4247091263.P88
99 (1,3,9,11,33) 397.2377.1240500097.P48
101 (1) 341459085477993311443.86408339296208914807632672776254957729.P46
103 (1) 24103.37723802531.995301206162659155091.P71
105 (1,3,5,7,15,21,35) 421.540751.599551.2598121.126713791.P22
107 (1) 1276033068038437.304971297664201988898688683700564748747693245597.P48
109 (1) 35970728459102446279558069.P87
111 (1,3,37) 651950416864148392635280596760630561.P40
113 (1) 227.45902861.20884152591287817709.
.22455907106840364577416382241618449.P53
115 (1,5,23) 95911.333041.9964291.17184010031686356151.P55
117 (1,3,9,13,39) 9127.1810693.P65
119 (1,7,17) 239.20580793913.5787647502138040836760695667.P60
121 (1,11) 30977.1595696213.12407691244609.P88
123 (1,3,41) 174907.28385941.142971820992006871646588679396397417.P36
125 (1,5,25) 5*.1632185486501.27678437808551251.P75
127 (1) 2985212831443.6073732108394141.108345618426999904901.P83
129 (1,3,43) 1549.1389891409.2338110553.44012945778511.
.3440126314390780951.P34
131 (1) 263.7791763956749016154215607697892626144401.P94
133 (1,7,19) 292601.1889399.4085166784889.P89
135 (1,3,5,9,15,27,45) 271.P73
137 (1) 8221.339761.3677081.136238281.394711476243912154244261783.P91
139 (1) P144
141 (1,3,47) 283.64192789.44682948968412414039336007.P60
143 (1,11,13) 3433.3111663528084541.191144869353686249.
.39087214421959708068637.P67
145 (1,5,29) 38861.144801130358116982559692328954495371.P77
147 (1,3,7,21,49) 7*.6469.712319250521341.1965320765521339221407672989.P41
149 (1) 95648167.12386903337067381971073.P125
151 (1) 16944919.13665285883.18462023135737378116249335576687.P108
153 (1,3,9,17,51) 307.1531.35236819.25167354031.2926326645433.
.290204982599509251565261308001.P35
155 (1,5,31) 112582632731.21008012759943211.12981042678412809421.P79
157 (1) 88388104773677.40715753678177846062481.
.20186536221332782615476135581.5898938014844761247631748773851299.P64
159 (1,3,53) 1399201.2622229.23393486084531921650287976389757830429777373.P53
161 (1,7,23) 967.48359249.P127
163 (1) 391313358915050362321.1568405349185888385874441.P124
165 (1,3,5,11,15,33,55) 1321.121679581.1454598708730201.P57
167 (1) 2339.1353068069.312708742481.2371759568436871497727.
.3523115712994289296116782558201078504837006181920850717652507.P67
169 (1,13) 2029.362685493.
.5276574100195101793609935574565521674231026096229661942697690104397.P84
171 (1,3,9,19,57) 32491.406981.368030647.27361000362650239.P78
173 (1) 347.593979931.19313697101202731.P152
175 (1,5,7,25,35) 1849051.P119
177 (1,3,59) 31153.128857.77162089.
.7005596150545816426029108678026870967790150254367.P55
179 (1) 359.260690365910973937.133424628147697995732126527.
.30262061969946294833518392497.680728835990076713808763658029.
.459009579117136530987907464707351.P49
181 (1) 42811641487.8439877927139263645774810523.P149
183 (1,3,61) 1640962831.470011312403953.252792952756496725399.
.120213931658422906698644629.P55
185 (1,5,37) 3701.2341771441.8942042341.586894211641.
.9469266456252868041356465741.111979611651060119297676530503786924451.P50
187 (1,11,17) 625293470077.1187896992833.
.759915556656723468789897776052021738313604080983777078304038497.P80
189 (1,3,7,9,21,27,63) 757.2150969311.452555562844477.
.5578141711502710729.36959230870280730074750882077.P39
191 (1) 195967.232767887540024567510779793146810415249588466971308867.P140
193 (1) 1931.P197
195 (1,3,5,13,15,39,65) 50311.3762447001.P86
197 (1) 3012710549939.1060717191208815311.5407146368827614877351.
.616346818465450400938401858863608277357.P114
199 (1) 797.140893.18242336369.4645373755026923.74228785249216074982007362154907801499582555623361265045414501593697.P105
201 (1,3,67) 1609.66046284412625914877623090150129.
.14160915264340305525070590511634038738687.P63
203 (1,7,29) 5279.60901.490738600321966404709119573187611258997827809661439583138969212062707.P98
205 (1,5,41) P167
207 (1,3,9,23,69) 2631980958036751.P123
209 (1,11,19) 6689.3107455009693.3215499310277.1056394526657537.
.342732573655364605155483163584083618987113.P103
211 (1) 88672307809797915061.P199
213 (1,3,71) 4813252624072182882141229.44043095909867219792359537381.P93
215 (1,5,43) 431.133680121.6371112819065042612731.P143
217 (1,7,31) 29605139295060799.345143305383570896315487449563042088092193070582663064824478011700982631848113970347.P88
219 (1,3,73) 439.4072194187.
.514949924967851751873479083936952760941875001182553509.P84
221 (1,13,17) 27847.312937.3473237.1126168894058957269.
.13720057759140780365187158337101.
.63175972422516768191112129923662644433466537589571.P85
223 (1) 453137.47060137.7672126756781.326495629795175719.
.1368635346986648651098441242784461410529545236877.P140
225 (1,3,5,9,15,25,45,75) 5851.2438939252251.P109
227 (1) 14106056111465766059.1792798399719936463007. C195
229 (1) 84743741.15587642569099. C217
231 (1,3,7,11,21,33,77) 312313.6103043101.355797740761.662072596417.
.10965056258773.P74
233 (1) 1399.2797.57401881.308184993449104253.
.175138501604778346236805296173.C181
235 (1,5,47) 2351.14749541.
.1795306125519308524148513029485573280444347858061.P133
237 (1,3,79) 34273461979846373350261832761.P134
239 (1) 479. C246
241 (1) 2916583.96275249243.17283881969371. C220
243 (1,3,9,27,81) 340201.27927019.772481047563804024037.
.103669238531679886100470429.87544425099333860745692064391.
.94217522053663555122045893874149431.P45
245 (1,5,7,35,49) 491.10781.
.35298179827301484394489355118456864978337754561.P122
247 (1,13,19) 6917.24476655191.735397416472535503838087.
.149892886761153843524520239.P161
249 (1,3,83) 24350945041.7888937372474051689.1827801163850144120227.
.599211790772708425085047.1390253425907256501848065153.P70
251 (1) 503. C258
253 (1,11,23) 266458589.P221
255 (1,3,5,15,17,51,85) 1021.1249304905334053222308181756477664071.P95
257 (1) 1194023.293147639462911.292888771585604069921. C226
259 (1,7,37) 15541.205129. C216
261 (1,3,9,29,87) 252951559910787169.19864252986467602941327475561536514877625112981282421400939628042342057.P88
263 (1) 1579.273046601. C262
265 (1,5,53) 6361.11131.27949021. C202
267 (1,3,89) 1087344877207993177554437630922355039.P148
269 (1) 11299.3333683107.5828875024969181.255350778829531783. C233
271 (1) 1627.4337. C275
273 (1,3,7,13,21,39,91) 9283.2794301073442243.P131
275 (1,5,11,25,55) 9051647644285437885101.223893595825973074419211201. C160
277 (1) 15811956653.30664514555051823767929.862162491495911858677651.
.156184546393536577782392890775878891.
.160675559417607736722985168684203817.
.142462975852899743955336966823561898597398549051.P114
279 (1,3,9,31,93) 5023.3149911.684249865168469384243216119737381211.P142
281 (1) 563.34283.133593583.158691941.33336224302061537657.
.1302985948504262874372500460540357486269.C210
283 (1) 157349.2911476233737954178339. C268
285 (1,3,5,15,19,57,95) 571.19919700302204669731.
.173516799777015420048132343577477787151.P90
287 (1,7,41) 2297.1350623.2880001951.
.2966421405449263029972348335713817510596628749.C186
289 (1,17) 228311.54761697917.8310166294858615047708541.
.525222955395094276264268486999488266551.C204
291 (1,3,97) 532266937.2344437427.28829500653651421.
.234778562725637665057.P145
293 (1) 56843. C300
295 (1,5,59) 106185841.P234
297 (1,3,9,11,27,33,99) 90289.699733.1247401.20085349681.
.3249930677185678753950409.
.24893014912495257280062069983035338781764623985517535857.P81
299 (1,13,23) 1779649.1824499.2642814404626969.
.720460482163043076385421612673778487.C212
Table 11+ Factorizations of 11^n+1, n<=300
L,M for n=22k-11<=583
n Prime Factors
1 2.2.3
2 2*.61
3 (1) 3*.37
4 2*.7321
5 (1) 13421
6 (2) 13.1117
7 (1) 1623931
8 2*.17.6304673
9 (1,3) 3*.590077
10 (2) 212601841
11 (1) L.M
L 58367
M 23.89.199
12 (4) 10657.20113
13 (1) 53.911.59583967
14 (2) 29.1933.55527473
15 (1,3,5) 31.7537711
16 2*.51329.447600088289
17 (1) 71707.264793.2218331
18 (2,6) 3138426605161
19 (1) 191.229.83791.1390636259
20 (4) 41.1120648576818041
21 (1,3,7) 3421169496361
22 (2) 251857.2649263870814793
23 (1) 47.1013.241363.6493405343627
24 (8) 97.241.1777.1106131489
25 (1,5) 46601.14436295738510501
26 (2) 9768997162071483134919121
27 (1,3,9) 3*.379.4889988840047743
28 (4) 113.449.2521.77001139434480073
29 (1) 59.10979607179423.204064664440913
30 (2,6,10) 46329453543600481
31 (1) 311.1303.10789.3658524738455131951223
32 2*.193.257.21283620033217629539178799361
33 (1,3) L.M
L (11M) 9439.991651
M (11L) 67.1169382127
34 (2) 137.2481791513.9598959833.641625222857
35 (1,5,7) 71.71.7561.17011.1649341.10047871
36 (4,12) 73.40177.3358335487319458201
37 (1) 2691614274040036601.10527743181888260981
38 (2) 1990415149.15403468930064931175264655869
39 (1,3,13) 313.63649.538953023961943033
40 (8) 5281.399806412551699044818733915681
41 (1) 711628063.1216150172449.479378523680060338823
42 (2,6,14) 19069.520799717831587692709
43 (1) 5333.9413099125139413690486707432096974989067
44 (4) 353.72689.13585441.1298256794387169996154165633
45 (1,3,5,9,15) 181.631.86306335830799838011
46 (2) 201757.2004414397.24737721275161.656943272596448809
47 (1) 844309.549524471.26097456317.60699948346804199382437
48 (16) 577.3659233404740477018363752843393
49 (1,7) 11467.800171.176784259.33761096386802842263303497
50 (2,10) 101.2248313994601.1993099906542710819727884501
51 (1,3,17) 103.1348033.16576413357576409067287639
52 (4) 97010607829826070873559937268360584022789501553441
53 (1) 1697.5353637.17148893.8357265774463208206521728596439861293
54 (2,6,18) 109.541.388174681.1350472353550875103121929
55 (1,5) L.M
L (11L) 21537414911.85480219991
M (11M) 4951.411841.131525983711
56 (8) 337.394129.236352238647181441.3090443962383595123379137
57 (1,3,19) 6043.75013.74337838382167137728921322559
58 (2) 349.16585333.32637413.109181877624126996017801852385627698243261
59 (1) 22067.32833036072593109.59845177539010249.53199025841281128499153
60 (4,12,20) 52020741601.40589999671017742452961
61 (1) 53320740257.137218978667473446671.38147158686655703132426388314683
62 (2) 4311672901046383796549.70039146133823870629334170297294343364149
63 (1,3,7,9,21) 3304981.468843103.71596275661.278853374647
64 2*.316955440822738177.7032401262704707649518767703756385761576062060673
65 (1,5,13) 1301.25741.3160327139569513638485230516120919120957201
66 (2,6,22) 9863099401.46266666682081629547022793157801
67 (1) 269.181303.2354458793.2778466094669.76388592846687031.P23
68 (4) 409.11969.739755736441.14387579997041.P35
69 (1,3,23) 691.394648951.18013255921.932225927887.1577386579003
70 (2,10,14) 2970941.P44
71 (1) 149852362577.5604196051154865381517.P40
72 (8,24) 110161.331921.P40
73 (1) 668243.147031637.51866303408957.9863258277206753.P32
74 (2) 149.243595717.254246981.3275634569.5555901630889277.P31
75 (1,3,5,15,25) 751.299401.P34
76 (4) 457.35613601.52215193.P58
77 (1,7) L.M
L (11L) 23577401.2040583524866430994330651
M (11M) 43037232701.160418704149053207551
78 (2,6,26) 13*.7177.26833.225889.21493057.11771471409361.683665316878909
79 (1) 7901.681676939.3238766178025207268898109882481893.P35
80 (16) 641.2081.4001.232961.295090738600481.1037593750081121.P23
81 (1,3,9,27) 3*.163.5705803.P47
82 (2) 2789.57073.P76
83 (1) 325440677.47433880332031195178437273.P52
84 (4,12,28) 201407641.70107576001.P31
85 (1,5,17) 34511.P63
86 (2) 173.11862832433.P76
87 (1,3,29) 13399.7596493.1727522113.P39
88 (8) 3169.269281.2224106369.1409524185566665684709841121.P38
89 (1) 179.188606309.5089163291.75893828851.23510589261592841.
.371848407757843241773.353082502532286628861787
90 (2,6,10,18,30) 9001.16921.22501.P38
91 (1,7,13) 12343942084000822751.P56
92 (4) 34961.324599369.P79
93 (1,3,31) 237843323473654847623.P43
94 (2) 1693.6678701.181894150853.1823151514157.P63
95 (1,5,19) 125391374277955216479795494641.P46
96 (32) 2689.850177.7746049.13928006777524033.P35
97 (1) 3881.200924352971689432250644561.P71
98 (2,14) 197.33976720793233.P72
99 (1,3,9) L.M
L (11L,33M) 95885659.166222146279939538766671
M (11M,33L) P32
100 (4,20) 401.2254601.5931105001.69084589801.P54
101 (1) 20201.228104057.1732951869588220873.P74
102 (2,6,34) 382645993638157.563620766036953.P38
103 (1) 1237.51396929137.3842537250772226605747.128288938117946418355541.P48
104 (8) 86759222313428390812218077095850708048977.P60
105 (1,3,5,7,15,21,35) 275310421.137031343051.P31
106 (2) 410982353.23746234974173.22250800656016001.72744498860303958101.P51
107 (1) 841021.P105
108 (4,12,36) 433.8209.P69
109 (1) 11119.14389.P105
110 (2,10,22) 1327481.36318547582241.110374378040081.
.136371262802069831801.P30
111 (1,3,37) 37*.223.P72
112 (16) 10529.15233.132833.7782479531201887486913.P65
113 (1) 909877.P111
114 (2,6,38) 37820720459377.308673703543834165513.P41
115 (1,5,23) 2531.558956737278445325461.P68
116 (4) 233.287681.60604269272032563100609.1502477990708696255525449.P62
117 (1,3,9,13,39) P75
118 (2) 1291321673.1013563312793953470363741024001073.
.64838817747578095323592827914385846481.P41
119 (1,7,17) 110917283.124214819.69796946717.256644509902201.
.63063653308203311.2091456376138057349.315440418833726113081631
120 (8,24,40) 3121.114001.1698371041.12658046117876244394801.P27
121 (1,11L,11M) L.M
L 727.1663628038071022183838437.P31
M 122453.2095721.103569468207767.P32
122 (2) 61*.733.15373.19042493.615339081285269009.
.166945076296840267580084657135863728824204737.P47
123 (1,3,41) P84
124 (4) 1489.6449.11161.5721113.92247817.P100
125 (1,5,25) 251.559001.30877424283969568616368678353563069501.P59
126 (2,6,14,18,42) 2017.21673.1540217047797575204407748160801193.P35
127 (1) 509.2140352083.
.4402640625848258016840688846660358437130425243742595514279.P62
128 2*.15361.111489577217.574341646346402207998363393.
.4018529583345312964042058778793458689.P55
129 (1,3,43) 1291.P85
130 (2,10,26) 521.P98
131 (1) 9858799.119235724375228558113076040277225949839796708740043.P79
132 (4,12,44) 57563039928769.504278350263601.P55
133 (1,7,19) 23204027016899114504903.P91
134 (2) 47271776033.555596265747977.5653530366032833.P97
135 (1,3,5,9,15,27,45) 283771.861465705211.P58
136 (8) 17*.29584734433.P122
137 (1) 823.2467.12932527.666751384702583.33702237384570719055067.P91
138 (2,6,46) 277.6128029.P83
139 (1) 48560832383207.23835478071413231.
.226911237770389320465096194749609274682969829.P70
140 (4,20,28) 281.7406965671094607547812305361.P70
141 (1,3,47) 2539.P93
142 (2) 192553.6896695512898403271082223952161993974407591311981.P92
143 (1,13) L.M
L (11M) 859.2003.23167.36037.172626755159.619151422486169.P21
M (11L) 2008696691.303798181831.P43
144 (16,48) 3457.114500564929.P86
145 (1,5,29) 54521.P112
146 (2) 293.877.10851207624233.
.1642924373932604240398418631306800170146224088997.P84
147 (1,3,7,21,49) 54447297367.593567588238393763.P59
148 (4) 1481.
.10170146161160624507589185121238262249266667161256127057415217.P86
149 (1) 1193.1530827.
.775322709138856254112793450158954494201167319485721463.P91
150 (2,6,10,30,50) 7884604271247668072701.P62
151 (1) 907.3323.255421785001.372781462691737543021989945244913.P106
152 (8) 13681.1077214649569.P134
153 (1,3,9,17,51) 2143.70740970147.
.1840706193591427502373477305882643135847.P47
154 (2,14,22) 617.99793.28785963361.65808672978228777210147008368433.P75
155 (1,5,31) 25111.668671.1945899780650862081973056361.
.25153949825237973485338723920570841.P54
156 (4,12,52) 1873.24337.332327331649.341226120551908708215217157918113.P49
157 (1) 424843.P157
158 (2) 21621681589.195687304237.2325820989287069.
.2016628650692376508178693692448257.
.177115854116776674014598663778398923878397.P51
159 (1,3,53) P109
160 (32) 225601.10628056841921.69220917578031208961.P96
161 (1,7,23) 1466711.6875023.18248063.2506937119.
.75580484933767277650090124382122269.P73
162 (2,6,18,54) 793130293.P104
163 (1) 653.13693.5894172551186797.405880245798991364856121577.P120
164 (4) 13121.42641.2074273.7130393.40257849161.97352750991169.
.2861311221613049.281713699327243441.552748497406807193.P70
165 (1,3,5,15) L.M
L (11M,33L,55M) 331.3301.P37
M (11L,33M,55L) 3631.P38
166 (2) 4331273.24967511537.34960378781681173508155621.
.2308531347471863958469313620650223778129.P89
167 (1) 1339169327.
.3300432761858103866348058105008794336060997740879896086290505245157.P98
168 (8,24,56) 52081.126001.247437888847604652162337.
.118738136976330434629762417.P41
169 (1,13) 3719.P159
170 (2,10,34) 3260777957463840456531891601.P106
171 (1,3,9,19,57) 395126219277461154409190377869979.P80
172 (4) 10321.895777.2291140793.4612466317049.18917231969257.
.8993481304534541048526696863581326290994262879631297.P78
173 (1) 25218258782887.4657650196273780561.P148
174 (2,6,58) 12735009193.25405175682157.36144770810077.
.9529369734426439596848326843374200197.P43
175 (1,5,7,25,35) 723451.28289718815384888394734507227024951.P85
176 (16) 35201.7434241.3035183032047230625631489.P131
177 (1,3,59) 709.8852479.418286047.29920690297.
.4383533260821719783424892027.P65
178 (2) 46993.P179
179 (1) P186
180 (4,12,20,36,60) 554041634889835667266333598012061961.P65
181 (1) 1087.10499.28961.4928993.494599122567229.5899787768233636472146368563428870969150867311352013680252498451159641.P85
182 (2,14,26) 2549.76872047790169633.603597442693160189.
.21389858671812927839610150156529.P81
183 (1,3,61) 367.530733538977688353451.P102
184 (8) 5153.13249.3393866564381362044449.18762254284652611492897.
.2178663038468353297718910823091125671985841.P90
185 (1,5,37) 13678726350491.510478568651306035780751621.P111
186 (2,6,62) 373.20089.323744320653227644676293.
.387491950733013190146272614153.P65
187 (1,17) L.M
L (11M) 1123.P80
M (11L) 1871.P81
188 (4) 149441953.1714152864944115675437076084258702132587418118797713.P133
189 (1,3,7,9,21,27,63) 6427.41959.637438224833677.
.652499617543540520675222321113591.P57
190 (2,10,38)
516262800270346286750957015107437143584755022581205411759884765761.P85
191 (1) 383.9295607545074385946753599.
.10943652034918306516518686327929621233253.P131
192 (64) 4999681.188203763329.59825484896641.2522204187418753.P87
193 (1) 773.P198
194 (2) P200
195 (1,3,5,13,15,39,65) 1171.2159041.5347681.41711671.P77
196 (4,28) 4396564922913073.1000215069936448424297877519565769.
.27584316197960616324036313486526262294434452581372529.P74
197 (1) 65318540977834167019309197528496746435730351.9892817292333841349326992570525012475558072147134506608232615478288870172703.P85
198 (2,6,18,22,66) 851401.4697405477458849.P104
199 (1) 8685953.146650663.3823602319.79365167307383.P168
200 (8,40) 90001.291281336764801.16625767615199325017280401.
.896720806439075722628289609391420338234464212801.P75
201 (1,3,67) 3217.P134
202 (2) 3637.37442421086030953.P189
203 (1,7,29) 30061259593891.26317706159551360565552444185165409.
.2393098526213023802467303772332124696379948606359.P79
204 (4,12,68) 21373370567867161.9389207830134041872135543904593.P86
205 (1,5,41) 35671.80519081.8240924561.19465938411835695151.
.11970655810401989943242413896209071.
.1118220897006993145148786216979797392760797171.P46
206 (2) 1820248831453728903079155734889112351429153639197869.P162
207 (1,3,9,23,69) 1575425458075847579018029.9430195587624521199783253.P89
208 (16) 5745664293565249.937106993318605353391918345676692606835799914934541577963079807089450560607964644697022433.P95
209 (1,19) L.M
L (11L) 397519.1304601827.5713257611105981119921.P58
M (11M) 419.48023563923633871.P75
210 (2,6,10,14,30,42,70) 4774799693782383634276354861375486612699501.P58
211 (1) 79842611423.24068102703304254483013.1274197670665384896310643.P162
212 (4) 20346651139084609.409470782853013748735863451789865410118763659687052370396286605246191314150038291977.P117
213 (1,3,71) 1279.4261.38767.241314517.8698096969.14980015231.
.146725989283141.61613677654149261712293660932063639173483.P52
214 (2) 715189.2220041882273434361683633.
.167682147711592821398735713993001367086093.P150
215 (1,5,43) 813189004171.3197135804492492971.
.193765176290056379756793725307814540891.
.56621045460781648098610503847956528696245241991.P60
216 (8,24,72) 1297.6481.3182647681.13685944897.23652283000971422593.
.1752300177786274178539088217518113.P71
217 (1,7,31) 241739.6151633335373.11105291873337733.
.92128660012292036719950667586473.P122
218 (2) 15442249.90833189.343390549.13701517129.
.181306868248707833295353728052481385990771769.
.301212390212002814883255640626944149605602579417904714609746158777.P82
219 (1,3,73) 3943.148483.13294559689.21149169451.
.1227023342787622738230402973.
.10554863204373603664496700868383796000277143.P51
220 (4,20,44) 881.23525041.2423799841.
.527289775722528574174349479910552468987211095330394241.P94
221 (1,13,17) 443.15214967.P191
222 (2,6,74) 9499172909234906032067412079201033.P116
223 (1) 443686153.1140498656251.4147547632284793527095981801.P183
224 (32) 2758337.
.100699774185076143584959698279743470289641915893670089461255381057.P129
225 (1,3,5,9,15,25,45,75) 906054085876149781651.P105
226 (2) 3617.228821837. C222
227 (1) 21549352320724159933.67332325557222369139.P197
228 (4,12,76) 430009.16460435892921560549676267982779313.
.1530577370570695515843056744341672838593.P71
229 (1) P238
230 (2,10,46) 461.134445581.343290128859872186919542448578621.
.103071901047413396946309859357386553260732128481656308481681.P81
231 (1,3,7,21) L.M
L (11M,33L,77M) 463.1563791740201655119.P43
M (11L,33M,77L) 4621.6007.130958161489.41987897476328997733.P24
232 (8) 929.718243697.P222
233 (1) 467.47574407.1681082419.15300218543.2800063085689. C200
234 (2,6,18,26,78) 754417.P145
235 (1,5,47) 171956300431.16732908994672493211848745375333042751.
.3306580253683352188869825697683770888504126003881.P95
236 (4) 1245137.1820977.196612846857339161.
.1305467643879383363694621983023020889.
.34640632020616953364419872758035731606321.
.43398158261134913555879300403231730887907132613176534633433.P77
237 (1,3,79) 1298119153.442887255388335544085068774311818032069.
.349848591222229454676083898046375211577130459.P71
238 (2,14,34) 18089.29125297186513714033.P177
239 (1) 63097.102293.57577969.13096317022627.1760573169194453.P202
240 (16,48,80) 3361.497281.
.402968902472395360889178149434861784137338065281.P77
241 (1) 272176243. C242
242 (2,22) 45497.5962871316336384943261135215553.
.1199119001850948230986854240045406260074881.P152
243 (1,3,9,27,81) 3*.487.1315603.202152123653206527082017066120067.
.5827671612449851662879469068732877.P94
244 (4) 977. C247
245 (1,5,7,35,49) 7351.345598612291320615082871.
.12216580378839012896357471.358991345455489961835259460247719272631.P84
246 (2,6,82) 1994569.P161
247 (1,13,19) 79358043623.858550186211303.61332418022317781.
.1453182918130724209027.P162
248 (8) 55057.2867377.162328311310326403201.P219
249 (1,3,83) 499.29881.71713.268921.3073657.
.552709621267858702596843809412349.P115
250 (2,10,50) 484244800986063880839657966318880669001.P170
251 (1) 16567.11459146595973931097986105427.
.4138657102675008244890188328022069.
.36101600753960537233530380672704042599879511.C151
252 (4,12,28,36,84) 3262393.139032641114575020289.
.90120052032290940281097673.P98
253 (1,23) L.M
L (11M) 23*.34358491915519861.15081546136004856381787.P75
M (11L) 93792287513.1413086923931.P92
254 (2) 33529.6801057801220881625524316916777. C228
255 (1,3,5,15,17,51,85) 157081.268909741.P120
256 2*.15190529.4696846849.19618834249745000485889.
.4393553986026616439660661873903822389581313.
.290103547098489711747952055517085778590240759297.P138
257 (1) 1543.40657480248251.1498146589050611.53886103039702043189929.
.8037296702304505946266363297859.
.134234734318727705202901021852004753140712867.P137
258 (2,6,86) 4129.224461.
.9599423534626776866966882139683535711285841280449.P118
259 (1,7,37) 13469.43485382614231906309361.14243550056009699286060193.
.3069438462071886674551139969465895798273671.P131
260 (4,20,52) 54601.62401.207481.10155601.144170212041093047547902840521.
.158598051875658496019605045735778598245626251920942535281.P93
261 (1,3,9,29,87) 8353.5067496657.44269432999543.
.28605102021671393910936635011.P120
262 (2) 1049.1726563757.224334267645161505049.406834251786873467627657.
.109304370041520985264395813352114933882177009.C171
263 (1) 5727841026618058971769. C252
264 (8,24,88) 69697.38861080877225459657929735198017437129109028801.
.135668205089825693347619869055111658146743599411882419809.P60
265 (1,5,53) 1061.31271.8344579171.155013410491.
.493389180255291601645532551.3004045135565518822957406769271.
.4113692566646269086681360438319957036345801.P89
266 (2,14,38) 231134317.324253994669893.
.24773683978861921546672349412757344853.C165
267 (1,3,89) 4273.23497.947851.17956819.917319557373542586811.
.9288511699775366433187788427.155472269288059027297936567929679.P81
268 (4) 13301377. C268
269 (1) 69403.31203463.2765713076251.29563472876503.844790045501359501.
.762817040205115840943.C202
270 (2,6,10,18,30,54,90) 2161.1026011881.13611301978718515486861.
.12622131000098804705727124801.102416531950001621967758420265274532941.P50
271 (1) 214091.730613291. C267
272 (16) 237405953.13132082753.2595634903361.
.311878855751101499095418602238443457.C201
273 (1,3,7,13,21,39,91) 588043.40430489183674349857937813199180217357499497.
.6575263262070493794723537878370188894591009298793.P52
274 (2) 2741.308413778021.P269
275 (1,5,25) L.M
L (11L,55L) 109451.7669751.249327078001.1320705477851.
.484953580035490730634734566779401.P37
M (11M,55M) 28948806319554206514033458668643493614401.P64
276 (4,12,92) P184
277 (1) 1109.43718911.228282657507887067649.
.40277403816832163701713758573806839433.
.677446450915060348755445870654443085937.P180
278 (2) 557.7229.224069.4818531445075172246553021289393.
.44444440293051974060919537141568529.C211
279 (1,3,9,31,93) 9012259.1219672319724421680590289140833.622185082524354718003686851166976918099216697074964832543020808326586271.P79
280 (8,40,56) 4481.120499161543956061953521.P174
281 (1) 2165143447416427.73717873044643423196357.
.47677949460728118782533826487424424473.
.46402408546690245400968842648859676155371.842839899538084266198466820541942750943860088703946121840940131686719691460399191375953.P89
282 (2,6,94) 4513.74449.743221153.9367589929.882790848027637.
.50386240544439469245337.
.541280232778157933269788549025666464572420599006025732317.P70
283 (1) 956895449.21535519113007.72176379693191. C258
284 (4) 569.12497.P285
285 (1,3,5,15,19,57,95) 2281.2917899073047729238516802295331.
.6420530775230480256516185608218811668539531217931.P68
286 (2,22,26) 76649.279137.25789193.26212089408649.
.65835490021476935761.5390779113965945529821604718249.P169
287 (1,7,41) 10104697.7754478257. C234
288 (32,96) 1153.2984614810561.785602694273121056085121.P161
289 (1,17) 3469.6359.405179.6719845184674354000239729883051.
.13809514198555273556233360064629771908877014988964567.P188
290 (2,10,58) 551581.22703521.161983561.4383624035501. C200
291 (1,3,97) 1747.69543313187791.718354750537744483.
.1434216758035156452062274787.12624322881812991993463959241.P110
292 (4) 4673.127440856783318855066075619237628626201. C259
293 (1) 587.2605170569440429.30140580360800090029058026244148121.
.3682985778017638025031089403228751074233.C212
294 (2,6,14,42,98) 21757.P171
295 (1,5,59) 6491.P238
296 (8) 593.4317448897.1788997688657006918650513.
.58666781720610399244227419994433.
.9060949789407186960278515603568493413961904897.P186
297 (1,3,9,27) L.M
L (11M,33L,99M) 60212927509792800235219.5343727611107427419946338417467.P41
M (11L,33M,99L) 115564483.P86
298 (2) 1789.3606385337827009.
.254442181550180651601277598631486236645518614349.C243
299 (1,13,23) 599.1956094976608247701896596369. C245
300 (4,12,20,60,100) 601.27903093601.302956332083401.780571892394001.
.504562013892511955344201.P101
-------------------------------------------------------------------------------
319 (1,29) L.M
L (11M) 126069439.54453236653277002250524018661761985258743661.P94
M (11L) 96937721.22395964041133.1674399383651611.24440702406360967.
.4250822076554186563.1362428565267452997267408860021.P45
341 (1,31) L.M
L (11M) 683.13751401821439225165451143629880111.
.1012000371041933382912608396702713889156167.P77
M (11L) 88661.10766053.492922321.644552386633.
.3454061988006506245928197.11635610293174280651716530998551.P69
363 (1,3,11L,11M,33L,33M) L.M
L (121M) 2179.1213873.17156544164914857424669597171794606247.P68
M (121L) 4357.29698483.32054828257.22132988093371.P80
385 (1,5,7,35) L.M
L (11L,55L,77L) 8939701.371071471.518583951271.
.1048947375246657003170213161.P71
M (11M,55M,77M) 5487540521.3474031899426599281.P98
407 (1,37) L.M
L (11L) 82262238908095416625629847487.P159
M (11M) 24421.368743.101730015473692321.1583171273015273165687503920221.
.21787690102053357819275404496594050478419978850603026773289483.P69
429 (1,3,13,39) L.M
L (11L,33M,143M) 349207.361219.P114
M (11M,33L,143L) 105121516501.80026964062240068874678393.
.136781281056972929796341020181077888593676549.P45
451 (1,41) L.M
L (11M) 2707.336017551.8911290961.1072881923818635144449927674819.
.1815484843668506267988330171633365999003.
.547152724762445363229755616341664505869098913767.P69
M (11L) 776075370379457963.8287290957329109961678200239527.P160
473 (1,43) L.M
L (11L) 947.354751.744503.69716417.
.909075700936753324607060003389347319598236051.
.11984437123431823969432655822865428382472038412325377.P100
M (11M) 8000323.368900269.38042842158630893.1285274840618548862537291.
.57335965989876943599721563601.
.637251616253169487561721883573539113866676363414067411.P80
495 (1,3,5,9,15,45) L.M
L (11L,33M,55L,99L,165M) 991.11958211.190193081816052776283014786485321.P83
M (11M,33L,55M,99M,165L) 5367781.16810373035171.21073064227519555351.P86
517 (1,47) L.M
L (11M) 1124993.3667016900282341.983961080031284058011551.
.6853595694861280196431693023336020912080543.P151
M (11L) 613010003.1886657235101.6745592152089407.
.55451364604890843829478778327403507.P169
539 (1,7,49) L.M
L (11L,77L) 54861577.P211
M (11M,77M) C219
561 (1,3,17,51) L.M
L (11L,33M,187M) 4084081.P160
M (11M,33L,187L) C168
583 (1,53) L.M
L (11L) 2333.32695611782383722933302653. C243
M (11M) C271
11^{11h}+1=(11^h+1)L.M, L=A-B, M=A+B, h=2k-1,
A=11^{5h}+5.11^{4h}-11^{3h}-11^{2h}+5.11^h+1,
B=11^k(11^{4h}+11^{3h}-11^{2h}+11^h+1).
Table 12- Factorizations of 12^n-1, n odd, n<300
n Prime Factors
1 11
3 (1) 157
5 (1) 22621
7 (1) 659.4943
9 (1,3) 37.80749
11 (1) 11*.23.266981089
13 (1) 477517.20369233
15 (1,3,5) 61.661.9781
17 (1) 2693651.74876782031
19 (1) 29043636306420266077
21 (1,3,7) 8177824843189
23 (1) 47.39891250417.321218438243
25 (1,5) 303551.12629757106815551
27 (1,3,9) 306829.86769286104133
29 (1) 59.24767.368939.3335672988472972523
31 (1) 373.126883621.23364027983.234187563803
33 (1,3,11) 886381.5999137.661269577
35 (1,5,7) 71.491.806821.6089651.425455031
37 (1) 3933841.196560666553286126588980353347341
39 (1,3,13) 36973.17654521.111704871987697
41 (1) 83.1977898057.97668924760419986491370101198871
43 (1) 431.12313309.13444466603.32359758358562524963364461
45 (1,3,5,9,15) 30781.5234401.21456901.22981681
47 (1) 10617249990997021.4509348865973648037702008076799297
49 (1,7) 77617.27268138641564464649627762762033543154129
51 (1,3,17) 20757613.1510376787258214230993801577
53 (1) 107.743.1694941.29504677.3089222210773.11639817348279944053139101
55 (1,5,11) 5281.442434513819541.5766308324790114380136001
57 (1,3,19) 114001.129733.20526705689989.2141456811167917
59 (1) 22067.33565608845417661253.576319092656266231937955277485160608227
61 (1) 1706293.1000831393.35995548461449237368649937465097120608531155491049
63 (1,3,7,9,21) 708391688852136898302887193094373767489
65 (1,5,13) 131.1932288541.596827590710414051.38346067178495390031121
67 (1) 45464593.16180787699.17577834702049211.P38
69 (1,3,23) 6279903241741823809.P29
71 (1) 5113.19597.P68
73 (1) 50654608967364071.P62
75 (1,3,5,15,25) 601.80342401.P33
77 (1,7,11) 4621.379101493.191199728567.50565974802015289.P25
79 (1) 162109.130479719.P71
81 (1,3,9,27) 5937949.660198074631409.P37
83 (1) 167.997.1993.22079.557889481.35238620437.2731547200091.
.10052468384786123.P28
85 (1,5,17) 1021.22271.4832761.204560684821.5383015065849288291601.P22
87 (1,3,29) 349.1741.74233562929.936727604123432773.P26
89 (1) 179.2137.120863.3163346581.16649789224075621.
.35035317869663569.255053775727906405559.4656868283889935515079
91 (1,7,13) 152705150363039.1091317880778743355464526983.P37
93 (1,3,31) 8929.1261081.16185865453.P45
95 (1,5,19) 191.P76
97 (1) P104
99 (1,3,9,11,33) 397.3169.9143902271574719666671109149.P31
101 (1) 20359133179252403.P92
103 (1) 3709.7417.1309643353.13951770188639477959439.
.226319692803146344014357964333823.P40
105 (1,3,5,7,15,21,35) 2521.126001.9562853581.P34
107 (1) 126047.8368183883.P100
109 (1) P117
111 (1,3,37) P78
113 (1) 227.7450459827983.316093109705519.753692779085581623227.P71
115 (1,5,23) 2531.P92
117 (1,3,9,13,39) 6553.774101091754693.5363939350752581033772013.P35
119 (1,7,17) 239.1429.137089.23082431.P86
121 (1,11) 11*.7019.9971358563.13448069471.
.36801041190212623908408703917306494049155113.P51
123 (1,3,41) P87
125 (1,5,25) 251.13751.118751.P97
127 (1) 88750555799.2597995311343175210111334225450311.P92
129 (1,3,43) 3784861.P85
131 (1) 263.P138
133 (1,7,19) 67033.365876351.153373238287849222871747653.P77
135 (1,3,5,9,15,27,45) 11719914497486992163161.45726761961907655567941.P33
137 (1) 7894763.99485649955791433.
.4270306101158898662140485488376974936909627.P81
139 (1) 32830711631.149723271154501574581.
.13976446202665769757077661403698383112061728500003.P70
141 (1,3,47) 3504133.5136890928835357.P77
143 (1,11,13) 1068975337.28151299084766629509889009.P95
145 (1,5,29) 8458141.152107892171.2833016858862791.P88
147 (1,3,7,21,49) 7622826121.3053140047080689861.
.29014061524726574502110353.P37
149 (1) 11027.1919442572897362836803025134228929025089.P117
151 (1) 16537237851564688924261407041648853990657743.P119
153 (1,3,9,17,51) 613.3673.6128894197.1644982406845777.
.216486853727393579797.53294740218449478902707453.P27
155 (1,5,31) 311.17379312247321.32179535439223966162981.
.504159451473002560362013386812584959284471.P50
157 (1) 3769.896587135133828036528709133.P138
159 (1,3,53) 30529.526468081.564397849.P91
161 (1,7,23) 1933.36709.8820656418738378259508980670038453.P101
163 (1) 3123955328977664272236491.3085088915212385601857770168909.
.55276244920832349213682617306044898442152509401.P74
165 (1,3,5,11,15,33,55) 475350812105401.P72
167 (1) 553194672940916339.P162
169 (1,13) 273854127119.42085870270393.171074557867837392887.
.2236719302927635268499980471.P96
171 (1,3,9,19,57) 2053.25309.P109
173 (1) 347.6229.178537.16520618724247316579377.
.133631610959030020559251207363442895201402950558413165227170111.P90
175 (1,5,7,25,35) 2453984000813135412614651.P106
177 (1,3,59) 6373.472683457.29664964237.48253224577.215006774581.
.2245657505577169.247679421927970902164473.P42
179 (1) 359.23242390265122325064379304298589468949738258002565951689210803734501431778880443.P111
181 (1) 56473.188954578048573195547226930925499.P158
183 (1,3,61) 7321.7756968162619561.P110
185 (1,5,37)
6441085856120368040593352248224844221696350548901425367127551.P95
187 (1,11,17) 7824829.6367170107.5272292087965614119.P138
189 (1,3,7,9,21,27,63) P117
191 (1) 383.2293.5576463887.492394777262152830140779120613620261.P154
193 (1) 6563.143593.876772490946684644304688840806507849770157877.45217442809188335376258573027831301630813739280371078165650059881162723213257.P77
195 (1,3,5,13,15,39,65) 24263325716698381.457644272256236018195571421.P61
197 (1) 1159476869764471212326146050644254795037901851473126597328861230702273.P143
199 (1) 11941.50445745393.534989935052173.452633703528239603.
.2408107039243923308111.
.2312692670375121170444589429146936204459886179063617714050658717.P82
201 (1,3,67) 492853.337362557588033581.
.2340033136012362062475950746729856638028655463932144793.P65
203 (1,7,29) 2437.2032540343.168010120865329.
.4038644506148119439397242761.P127
205 (1,5,41) 50860501.61708179551.109423722071.594458960231.1272168094511.
.59114755745455413432518951.802612658538701099788630604070125125897621.P52
207 (1,3,9,23,69) 123373.46359329929201.80965151313250177.P107
209 (1,11,19) 419.167246399.19043506626213169.2877972269567413524001.
.131258359076578876173923.4714073727036453202094931887.P95
211 (1) 98327.599663.8960574127139.1374686882866127.
.11442157099782185036780447859311.
.389491106120076990268950453219202572305807.P116
213 (1,3,71) 853.668821.5938441.14726274721.593597578469053.P111
215 (1,5,43) 1456536066158565295403081451401133852690051756454912868460861932571472151310875724311.P98
217 (1,7,31) 5077606871.30847829203283.3621684771405978346406298479029.P141
219 (1,3,73) 877.384229369.13036824921402558973.P125
221 (1,13,17) 443.9640021.52016377765223.141523296304179193.
.27267433046893619404631197.2767487366128813243478189568387004020073.P102
223 (1) 1423187.23385119.14130288853.43954882455277.
.1006249991892868346686216789.P176
225 (1,3,5,9,15,25,45,75) 2363726892633483756321124302681778344117301.P88
227 (1) 147551.256057.152574419.1267583437.110565744056955405733.
.65427844998422797036464287486758625198640908952234347.P144
229 (1) 76487. C242
231 (1,3,7,11,21,33,77) 793717.1053467722693.237808105253287801.
.1285249260419549776349461.P71
233 (1) 467.31223.78863682072342587129533815443. C215
235 (1,5,47) 4982941.11664037157021516682204241.
.17622268090118561496454088499627774029883062124055059841.P112
237 (1,3,79) 6637.114598432057.1286930998217149714369.
.27567862476721705741499814127507129428735247904137980751231873.P71
239 (1) 479.17585764699549862561020053258920461069906105666613231. C202
241 (1) C260
243 (1,3,9,27,81) 19880317.P168
245 (1,5,7,35,49) 34167708909181.1100673907592638009772080006291497491.P132
247 (1,13,19) 263303.320113.45198395571733. C209
249 (1,3,83) 1417303413610237.825176156498150775878180145483505039849.P123
251 (1) 503.195781.289444667.1155793163468786851614675409281577.
.548481679382194709448031861812868591262551381.P176
253 (1,11,23) 23*.3037.1696862399.P224
255 (1,3,5,15,17,51,85) 79561.31144681.419335261.50540765443957214580241.P95
257 (1) 27262561. C269
259 (1,7,37) 8807.13683163257201265013663.
.27061148352191633314197974751800952154655200940479609.P155
261 (1,3,9,29,87) 44956729.17638236042841.P161
263 (1) 1933972763996644233329899026760057.P250
265 (1,5,53) 44512772676958707670636861.13540628227343143513585152841.P171
267 (1,3,89) 1069.28837.138151576813.
.46992000437847692882153515791466203156562909.
.38377631790110438168929289924771541551278936312860162633912589.P67
269 (1) 139343.210448392071.435969870238402935098824427.
.867262062344332574857370903987335252122781.C205
271 (1) 128684351.82563258586244744645506795146107567270927259291623. C234
273 (1,3,7,13,21,39,91) 1513979377.55088522581.127471845172490875057.
.4058519934585456806481289.P91
275 (1,5,11,25,55) 3301.9965388674060051.23481556650628451.
.2238729366218120051.342057173738154343151.
.1253637273890699938095461437151.
.20730228394927104240276793781652047312213543451167483401.P56
277 (1) 14607061984967. C285
279 (1,3,9,31,93) 7357522785371991109.P176
281 (1) 563.397897. C294
283 (1) 9039254891. C295
285 (1,3,5,15,19,57,95) 110621041.3070127161.
.1060198543142555940529623642541.154501946388922582618190838253261.
.670944760331657801031002660478241.P43
287 (1,7,41) 1754535469.154051237757089.P236
289 (1,17) 7401450291499674166985824937646679091649406429. C248
291 (1,3,97) 31915708783183821611425247734471919077.
.2720790319906484616848247043137589307514425929.P125
293 (1) 587.70321.1266949011911677. C293
295 (1,5,59) 6491.18432781.552959784071. C228
297 (1,3,9,11,27,33,99) 84349.
.283060719736432770539523360816216456291213229.P145
299 (1,13,23) 599.150697.320800091.3733087268543387.
.1500398624174864772818715119622474419.
.10257808708998033162862892522269646365380529.C174
Table 12+ Factorizations of 12^n+1, n<=300
L,M for n=6k-3<=597
n Prime Factors
1 13
2 5.29
3 (1) L.M
L 7
M 19
4 89.233
5 (1) 19141
6 (2) 20593
7 (1) 211.13063
8 17.97.260753
9 (1,3L,3M) L.M
L 1657
M 1801
10 (2) 5*.85403261
11 (1) 57154490053
12 (4) 193.2227777
13 (1) 13*.79.36037.222379
14 (2) 673.13156924369
15 (1,5) L.M
L (3M) 31.421
M (3L) 35671
16 153953.1200913648289
17 (1) 2551.66900193189411
18 (2,6) 73.122138321401
19 (1) 3307.8209.905265296671
20 (4) 41.521.127921.67657441
21 (1,7) L.M
L (3M) 1885339
M (3L) 7*.43.17011
22 (2) 2377.3697.6337.68368660537
23 (1) 829.12421.49489630860836437
24 (8) 7681.40609.592734049
25 (1,5) 1951.60601.73951.438472201
26 (2) 53.677.2200289654266792155913
27 (1,3L,3M,9L,9M) L.M
L 109.47336293
M 271.487.39097
28 (4) 79493013628273739882868481
29 (1) 1402596253.1084876017544880450377
30 (2,6,10) 186168115009253521
31 (1) 1263499.173420475484059478781201647
32 769.44450180997616192602560262634753
33 (1,11) L.M
L (3L) 67.199.1453.5479
M (3M) 39105782299
34 (2) 79471453801.427152748915310957418697
35 (1,5,7) 86121235964912696227980301
36 (4,12) 2231857.3684845809.9666387937
37 (1) 5250079.4150805645839.30023720899326796981
38 (2) 1977673.176477034940417.2016864235215616489
39 (1,13) L.M
L (3L) 859.17793645013
M (3M) 313.17991125491
40 (8) 34182189107670005092862256297738241
41 (1) 12301.1684652527.13657436942593.47936660465075191
42 (2,6,14) 80048881834094656438235281
43 (1) 71209.372060253.10273420681.7177727914895266742809
44 (4) 67651673.217245283970973197278039678825711337
45 (1,3L,3M,5,15L,15M) L.M
L (9M) 181.47263556341
M (9L) 9298142299081
46 (2) 302669957628317561107372328495588758678132736113
47 (1) 18049.12349627.21622395121.8405516927437711741762092271
48 (16) 7489.3122881.1461573322938242802306049
49 (1,7) 8356734198817312279063.253265324522131745115559
50 (2,10) 5*.101.1201.700936801.2334798291701.14807687049800501
51 (1,17) L.M
L (3M) 307.380355066717049
M (3L) 103.3077130526103089
52 (4) 288913.25265657.865727447657645665290857439836665912121
53 (1) 3181.33073.77366539.14861828970617714166257633556559606415803
54 (2,6,18) 433.3889.42729553.165042892009.59686188135337
55 (1,5,11) 331.6271.164018234982236911.46768482029635739671
56 (8) 113.2129.244721.527633.22232950788588289.9150512297530943809
57 (1,19) L.M
L (3M) 19*.884986147755302617
M (3L) 229.62701.3178598581687
58 (2) 29*.1277.378509.9533379150437.507127415651053993.39821279284774257217
59 (1) 709.1063.25232402089.21271304642628211.892931082048097905588129990661
60 (4,12,20) 241.141841649932724596178535977341201
61 (1) 111997.7361466337.5188602220069.P38
62 (2) 617521.26825115448057.87873272984241400393.P26
63 (1,3L,3M,7,21L,21M) L.M
L (9M) 127.79277059.2537121133
M (9L) 27764103747580691401
64 36097.81281.69619841.73389730593973249.P35
65 (1,5,13) 37831.52960051.P40
66 (2,6,22) 109297.219649.1717321.P27
67 (1) 44623.2291803.P61
68 (4) 137.17019338113.P57
69 (1,23) L.M
L (3L) 139.277.8419.22542577.129512587
M (3M) 348670382471247108491803
70 (2,10,14) 71874601.10365509281.1612092376073761.5298455664688950121
71 (1) 48058613330617.P62
72 (8,24) 577.2752993.15670947324691873.P27
73 (1) 439.346059859.6325722879776491.P51
74 (2) 149.48989.417509.21617621.13721476576343266613693.P36
75 (1,5,25) L.M
L (3L,15M) 151.2251.1696501.6625387201
M (3M,15L) 395251.9733315100252251
76 (4) 7889080897.143529155542303647618953713.P42
77 (1,7,11) 463.P63
78 (2,6,26) 3247609.23709901801.P35
79 (1) 5434599708664429598203.270354982362100782692527.P39
80 (16) 2081.2478806527025281.214538593513800809975201.P28
81 (1,3L,3M,9L,9M,27L,27M) L.M
L 163.811.1621.641065152502677063709
M P30
82 (2) P87
83 (1) 499.8305623819547.5277826961453441457872455753.P46
84 (4,12,28) 337.10753.284065793761.P34
85 (1,5,17) 235111.32182021.182593435609480192119451.P33
86 (2) 173.195049.1260760517.247819688992536197.881572852017880141483757.P33
87 (1,29) L.M
L (3M) P31
M (3L) 2032959451.1390046661396154093141
88 (8) 2481601.6188868577.49514757601.8200539405448794297995729.P35
89 (1) 7477.572511347126394968679427.P68
90 (2,6,10,18,30) 1653489395093881.33276147172349761.114859125525232035721
91 (1,7,13) 1093.44773.2322926580703.2620222710234691381.P40
92 (4) 23369.36433.44805941084686008411833430562841.P55
93 (1,31) L.M
L (3M) 5209.24221034391.1188277798029874021
M (3L) P33
94 (2) 941.1129.6581.56078144420933.1645156433564398201.
.19141017664453895628642529.P33
95 (1,5,19) 251831088886489381.P61
96 (32) 1153.2689.4993.22273.3124609.3531754753.P39
97 (1) 322429.P99
98 (2,14) 197.81667460066590930293917.P66
99 (1,3L,3M,11,33L,33M) L.M
L (9L) 5690162377645219.43504476926662819
M (9M) 2971.P29
100 (4,20) 15601.55201.9880627023929801.P62
101 (1) 1213.21211.P101
102 (2,6,34) 409.615782161.P58
103 (1) 1237.289765369.1003041977479.13561251678157.987452638049443.
.237720321284227801429.P38
104 (8) 3946177.235590161.2394253229201412644716539488455823024969393.P47
105 (1,5,7,35) L.M
L (3L,15M,21M) P26
M (3M,15L,21L) 1471.641761.133835330443229101
106 (2) 8693.35617.317789.1386570848451637577834086609.P72
107 (1) 643.192601.44075082436603.69912077218155300056899.P70
108 (4,12,36) 2593.182696316061009932535899288044215009.P40
109 (1) P117
110 (2,10,22) 190966927558661.P73
111 (1,37) L.M
L (3L) 223.2221.17276929.P27
M (3M) 16651.P35
112 (16) 140897.P99
113 (1) 13528813.800189839.P105
114 (2,6,38) 457.19739195005084795112797936193449.P44
115 (1,5,23) 1381.21391.13644729896474641.233290498320197431.P55
116 (4) 18097.10161601.112121388095793449.P93
117 (1,3L,3M,13,39L,39M) L.M
L (9L) P39
M (9M) 937.3846087181.P27
118 (2) 2489616072661321.
.87940176560868762457974039344527150684272220289857.P60
119 (1,7,17) 12853.799536900947360848804232005031172803108911069.P55
120 (8,24,40) 148589761.297499056050881.P47
121 (1,11) 727.9888121.353182139722763737.2394580881055996074990901.P67
122 (2) 149780377.35025797988529.P108
123 (1,41) L.M
L (3M) 6768262271978677.P28
M (3L) 2631304807.31383200376667.305115772972736748643
124 (4) 1489.2729.29347118548682214281.15838950898364499433201.P82
125 (1,5,25) 21751.73233751.
.49155455682299488607091202165523262609092033251.P50
126 (2,6,14,18,42) 2254746358873.1264490050687509371770918441.P39
127 (1) 7621.1373887.2567179.2580485967752214559759.
.3297733393711855795526315949469237174164031.P56
128 257.P136
129 (1,43) L.M
L (3M) 53923.3227839.52929369769.145096636623818195367871
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130 (2,10,26) 1301.25993663579055640467321336114621.
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135 (1,3L,3M,5,9L,9M,15L,15M,45L,45M) L.M
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136 (8) 17*.6529.277169.3145763540507811991784369.
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137 (1) 823.2467.55897.660067.13105969.446465191.4726519476067642779241.
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138 (2,6,46) P95
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141 (1,47) L.M
L (3L) P50
M (3M) 283.4231.161869.37144759.148353433.25952349017122640990797
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147 (1,7,49) L.M
L (3L,21M) 7*.883.3410989.57537510254151061.1744201069246727869
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148 (4) 4681523916811354897444073089020189848257.
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153 (1,3L,3M,17,51L,51M) L.M
L (9M) 919.53684863381.P39
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155 (1,5,31) 7578569533699283401.
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156 (4,12,52) 1873.P101
157 (1) 22716788413945698967.55986003890075009071.354451872726804327183679.
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158 (2) 317.15723744461.77554200461.1829338999401677.3110065141987323841.P112
159 (1,53) L.M
L (3M) 3499.11131.8326360951.P39
M (3L) 202222243.P49
160 (32) 1601.199715619558540486533761.P112
161 (1,7,23) 10627.334783723.3089670921499.329018796407371519.
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162 (2,6,18,54) 1297.P114
163 (1) 601245191936553406609.10922727889921079239009.
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165 (1,5,11,55) L.M
L (3M,15L,33M) 89101.1094369431.P30
M (3L,15M,33L) 1321.2070234581811001.3124194314678732463656071
166 (2) 211153.631820237.3983031033485223917.
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169 (1,13) 13*.4057.8145943651.15886110302730924472087.
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170 (2,10,34) 6121.4049858983776261992381.P113
171 (1,3L,3M,19,57L,57M) L.M
L (9M) 22573.1438529448862747.9010459894204410841.61881711307123989727
M (9L) P59
172 (4) 41281.130527361.362288744135700314075987061907939467040578292513.P122
173 (1) 1039.43597.21397333.
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174 (2,6,58) 171488833.25273969801.3038990284303129343488010161.P75
175 (1,5,7,25,35) 11172001.10624525041914118138301.
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176 (16) 353.16612884494783675297.415303366879530983041.
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177 (1,59) L.M
L (3L) 9375882931.12198432901.8125059831313561.P27
M (3M) 16993.56136259.P51
178 (2) 2159497.238672013.1202622621437.2946583977087010969.720167766050900193760846961135216805551800888406370139983414556549013.P76
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180 (4,12,20,36,60) 15121.P100
181 (1) 79279.1685473.49673641.119643173667024481.P159
182 (2,14,26) P156
183 (1,61) L.M
L (3L) 1278439.5110459.29285491.13154655247.978408452143.P23
M (3M) 367.733.563215815517.662381962579.22163333263957.P23
184 (8) 4049.421361.972098497.20107997297.391181626599457.
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185 (1,5,37) 6764688113022994226918648862368728289461094728017674281.P101
186 (2,6,62) 12115297.21280495849.21936211819491841.
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187 (1,11,17) 22441.4595713.477945682530691.1834077939520927.
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188 (4) 2633.4513.1015825593725032363561079258932013657.
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189 (1,3L,3M,7,9L,9M,21L,21M,63L,63M) L.M
L (27M) 2647.462137131.17680996718533.423070985265769.2062205895072564361
M (27L) 379.757.P53
190 (2,10,38) 649612661.51845827441.2084161597163899364720952131893201.P103
191 (1) 613020613.6303137521.251052583513.419680716841.
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192 (64) 7668481.33943279743151873.
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193 (1) P208
194 (2) 389.1655597.1202992061.33645879781724447427004153.P164
195 (1,5,13,65) L.M
L (3M,15L,39M) 2341.145341745837081.P35
M (3L,15M,39L) 14821.P48
196 (4,28) 25873.148728721.93960767325881.1311501490634441.
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197 (1) 155014378153.704293061363422089216865009818481.P168
198 (2,6,18,22,66) 79201.587999017.137815904137033.
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199 (1) 467102924796427.31911250188907711.3445743855122791226122392817.
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200 (8,40) 401.29424001.108271601.1633440001.80645261636342801.
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201 (1,67) L.M
L (3M) 305632468535298708448383841573.P42
M (3L) 8067337.8725118568091.P52
202 (2) 999105185203320570913016600688374300679389933.
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203 (1,7,29) 183261006686578338416027276079312207309847974270158525000765859448404747943.P108
204 (4,12,68) 184417.P133
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206 (2) 62213.1416140785427637803934557.503180154307434770432679706302037067307897625131184321636580213235326705711837.P114
207 (1,3L,3M,23,69L,69M) L.M
L (9L) 20287.668400059773.1772111891947545658642828177.P28
M (9M) 7867.104743.322093.37384201.827427439.376160757697.P29
208 (16) 369409.150150683842116870889052227704005935987543824478574753.100858744670924022520300656806373879413356193345689138600802795572647361.P78
209 (1,11,19) 2585746747.687821113425007553547034151213073599660116001176060480000065641507924137633216221421.P102
210 (2,6,10,14,30,42,70) 76441.P99
211 (1) 5416110502063771552032127.P202
212 (4) 104926293459735752969.P205
213 (1,71) L.M
L (3L) 1279.7243.529352523153057469.P52
M (3M) 2557.95262284863.P61
214 (2) 2141.1574087767398010009.4317337289784510701.
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215 (1,5,43) 338053531.18734395231.68595346231.1431737954334448711.
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216 (8,24,72) 2395814278787283747215883470689.
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217 (1,7,31) 4140361.75722731456257718300696150377235672232328849654282900426005002694557558207.P114
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219 (1,73) L.M
L (3L) 2596979075258143.39415223202308615565360103.P37
M (3M) 3067.570271380155140435027.3370272948856354464883.P32
220 (4,20,44) 91961.1851672241.2757802256166761.
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221 (1,13,17) 1074061.5107908870536771352457.P180
222 (2,6,74) 40849.640249.9022993753.42957790001471664291686050194961.
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223 (1) 2672516856853.P228
224 (32) 449.3137.3870580673.7168793748481.7382222489336492114312129.
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225 (1,3L,3M,5,15L,15M,25,75L,75M) L.M
L (9L,45M) 21601.76113001.2991403880190867231178651.P29
M (9M,45L) 511201.294634605912782337115596451.P33
226 (2) 32931747749.P232
227 (1) 19998034891.1080368358052272077617. C213
228 (4,12,76) P156
229 (1) 50839.52973555989.31835342204569.285741264675509431.
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230 (2,10,46) 461.5840221773191621.P172
231 (1,7,11,77) L.M
L (3M,21L,33M) 2311.4159.8622307.161409762520777.P37
M (3L,21M,33L) 33468683678431.62442345339067.P38
232 (8) 25057.252881.2848033.
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233 (1) 1399.2797.P244
234 (2,6,18,26,78) 28081.20614377630228200209.
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235 (1,5,47) 307381.248288311.43018304761.19882592550980069311.P155
236 (4) 629177.4407098760913.128360515998721.
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237 (1,79) L.M
L (3M) 3480424159.850419722408989.671737391081542963.P42
M (3L) 10903.12799.1283119.40320873507469.P57
238 (2,14,34) 6597418695917224851239065051873.
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239 (1) 32983.9982666982947861015602992869.P225
240 (16,48,80) 20161.13536885121.P124
241 (1) 871002439.97990658323.77318076925617721.1705313384546509819192987.
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242 (2,22) 3554981.37111000225385280564173.
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243 (1,3L,3M,9L,9M,27L,27M,81L,81M) L.M
L 18111923839.661044417041377.P63
M 745572861233573041.169763894591993350021.P50
244 (4) 22076633.28066350243530852751023005817.
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245 (1,5,7,35,49) 17601781.2345555521.73840856020821121.P148
246 (2,6,82) 16729.910201.2085926490367660753.P145
247 (1,13,19) 7411.53930531844080329285477423.
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248 (8) 18353.1022396369.P246
249 (1,83) L.M
L (3L) 17431.128983.1734037.6751461025693.P61
M (3M) 39343.3990098666304739.38114783021552038563632809.P43
250 (2,10,50) 5*.69001.279001.53700001.
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251 (1) 52711.4761717879067.P253
252 (4,12,28,36,84) 1009.86689.111831553.P140
253 (1,11,23) 1921789.4534267.43170403.454179529.
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254 (2) 509.6089827801.996677731569883050073730015953. C230
255 (1,5,17,85) L.M
L (3L,15M,51M) 177317320711.19838799892671391.P42
M (3M,15L,51L) 5101.20443746737883023759876091151.P38
256 8253953.295278642689.5763919006323142831065059613697. C228
257 (1) 77101.P272
258 (2,6,86) 1033.162935257.101391687543594481273.
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259 (1,7,37) 665113.15995146399.916996836381815091928033. C194
260 (4,20,52) 3121.5388241.293307933575801.2424551213039281.
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261 (1,3L,3M,29,87L,87M) L.M
L (9M) 523.1567.7503751.116786539.3145595491.27322991191.
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M (9L) 6079335356606159341.23174012541969149929713611504191.P41
262 (2) 519880117895761861778014698107089761958364381.P236
263 (1) 1192969.77987323260962631796122148363.P248
264 (8,24,88) 235489.8181889.11268322561.15811594657.58862348161.
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265 (1,5,53) 17571334218807733191229900337510167923931. C185
266 (2,14,38) 130873.228587958649.1670794414661.
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267 (1,89) L.M
L (3M) 36313.112959868327042355869.P71
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268 (4) 549937.3637389718220784599165177.
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269 (1) 39240999619.110816967917297862522156297245628727144567.P238
270 (2,6,10,18,30,54,90) 149543333664755078865961.
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271 (1) 237170491971748845802701622792973710308943. C250
272 (16) 326530547629297173770673642387809.
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273 (1,7,13,91) L.M
L (3M,21L,39M) 3823.9829.434406883.P62
M (3L,21M,39L) 547.11393929.91343993722014854143544819053.P39
274 (2) 2741.7667314103399781339196386463901.
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275 (1,5,11,25,55) 715580251.732573601.926029501.
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276 (4,12,92) 3313.1901089.71994082180323625969.45369831937439015559361.P138
277 (1) 1663.9973.2351731.25882977075102049597.735248617074033784609.
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278 (2) 557.32345857.2011860695151193.
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279 (1,3L,3M,31,93L,93M) L.M
L (9M) 3907.282349.20594141185056607117.P69
M (9L) 1117.2151005303694648538345119623059499317.P58
280 (8,40,56) 13441.1434161.179846307761.3310008098362561.
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281 (1) 3373.3033765575099117203012703463019696531217971429.P254
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283 (1) 6793.26125011969600077440822326298215406946517643673341327.
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284 (4) 569.201073.18016283364319433.78319571337276201426695657. C252
285 (1,5,19,95) L.M
L (3L,15M,57M) 7172881.P71
M (3M,15L,57L) 571.19381.103171.P66
286 (2,22,26) 37181.411841.1616473.176854393.P235
287 (1,7,41) 1081918770619.10096181520132121.525089549882812111.
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288 (32,96) 869481096087367307680259568769.762385251001265057189995310431603114317281219969948523309880786700037910469408257.P97
289 (1,17) 3469.30750530058706268489212711. C265
290 (2,10,58) 24847854821. C232
291 (1,97) L.M
L (3L) 3526932999432884537573363232678175415119.P65
M (3M) 11266918213.12836508951473917.P78
292 (4) 48473.P307
293 (1) 10896414032857. C303
294 (2,6,14,42,98) 5881.37633.316469915422174112372447362321249.P141
295 (1,5,59) 1497624254461.142419925980091.P225
296 (8) 593.17016616129.6728113966001.P285
297 (1,3L,3M,9L,9M,11,33L,33M,99L,99M) L.M
L (27L) P98
M (27M) 11287.19603.13261051.28701487.80724945709.2885974552146329029.P45
298 (2) 300044489495789. C305
299 (1,13,23) 760657.932507653507.9995633493847.
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300 (4,12,20,60,100) 1807485601.5103924628562576406001.
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303 (1,101) L.M
L (3M) 607.231493.298759.526860472918622027980214644731465727.P59
M (3L) 1487513659.69438508211723922167864504908608149557.P62
309 (1,103) L.M
L (3M) 619.999571839499.P96
M (3L) 2473.13597.63774677479.P92
315 (1,3L,3M,5,7,15L,15M,21L,21M,35,105L,105M) L.M
L (9L,45M,63M) 52291.2979271.1438494751.6797462485591.P45
M (9M,45L,63L) 631.P75
321 (1,107) L.M
L (3L) 57139.875689.2404291.9335323.387551764771.P79
M (3M) 2783005579153.15708961636372282803822883.P77
327 (1,109) L.M
L (3L) 505613287.P109
M (3M) 111298869849168513847.63451209239592760254614461129411419614827.P56
333 (1,3L,3M,37,111L,111M) L.M
L (9L) 124543.119810607463.615366154824465215271421.P77
M (9M) 47287.71263.2616651769743883.P92
339 (1,113) L.M
L (3M) 764110694773033.73282934361847577401.1147032708195514473009031.P62
M (3L) 2793740569392459675945343.P97
345 (1,5,23,115) L.M
L (3M,15L,69M) 691.24581965534907417117282311.P67
M (3L,15M,69L) 96801166741.4912523136523783944565190673920491013101.P45
351 (1,3L,3M,9L,9M,13,39L,39M,117L,117M) L.M
L (27L) 17551.129169.314132679901.17719478069541690622753.
.501073941779111566528388153767.P44
M (27M) 18253.10182380153167.5557307465977957.1287078033734511273919.P63
357 (1,7,17,119) L.M
L (3L,21M,51M) 595588813.53179121411533282455104389.
.7444967386325111267663723410113529.P35
M (3M,21L,51L) 3571.8895013.26108923931329.1485478883324335621849.P59
363 (1,11,121) L.M
L (3L,33L) 11617.1902847.4240567.233011560739.
.17590776403036520999000083528813789198205653.P48
M (3M,33M) 2179.116574547.P108
369 (1,3L,3M,41,123L,123M) L.M
L (9M) 739.136531.3642031.5752711.1423355095922941.
.374072153370327840457698722983.P64
M (9L) 14627161.105843637766088877609.
.3270052699297600797400421230129564000055047.P60
375 (1,5,25,125) L.M
L (3M,15L,75M) 862768857355002751.26061802206090827529591526287333751.P56
M (3L,15M,75L) 751.1861999501.P96
381 (1,127) L.M
L (3M) 1524763.12721529803.206375981018136378198643.
.22179455009646313890461937208319215171.P59
M (3L) 2287.970789.409795207580354851.1480444859343993091644952608883.
.1140932738223148258864544522278327.P47
387 (1,3L,3M,43,129L,129M) L.M
L (9M) 6967.4388268096716033913973672130408161496791.
.202923202077686203277513231859003158873473.P52
M (9L) 5419.34057.51859.607848517.11281513627.169315811495745796632187.P81
393 (1,131) L.M
L (3L) 787.288931243.7853352071229031.
.3540037548679408652606516870379751.P80
M (3M) 47161.540200509.173461409377.P116
399 (1,7,19,133) L.M
L (3L,21M,57M) 7928131.1262555546640315313.P92
M (3M,21L,57L) 332767.17706929602633139191.1062177777127068280484149.P68
405 (1,3L,3M,5,9L,9M,15L,15M,27L,27M,45L,45M,135L,135M) L.M
L (81M) 171947421803819953791091.500131074548916716314179353131.P64
M (81L) 9230674951.P107
411 (1,137) L.M
L (3M) 32059.88630068743448247758082010402431935794978004066530299.P90
M (3L) 139729711658022289818417409915604887567.P109
417 (1,139) L.M
L (3M) 1669.15013.110923.208501.
.5638888896763019486450225237314251285030538064074261.P80
M (3L) 3964837.P143
423 (1,3L,3M,47,141L,141M) L.M
L (9L) 103169155868277226048549.10455277041391964392381265548669243.
.381846165419473573914787041977491293397073551.P48
M (9M) 554977.
.49428368266998575771508427851382501624434884685008412777493.P85
429 (1,11,13,143) L.M
L (3L,33L,39L) 3729230661964237.P114
M (3M,33M,39M) 274233961.593967524131726603.159504077463298584589.
.43450210975084947437977.P61
435 (1,5,29,145) L.M
L (3L,15M,87M) 69872836351.887257418543475083551.P89
M (3M,15L,87L) 3628562344662781538711332722241635752511217245360661.P70
441 (1,3L,3M,7,21L,21M,49,147L,147M) L.M
L (9L,63M) 3529.11467.69710998267.162145535833.1208862422525899.P92
M (9M,63L) 47629.312229.3819943.147915811.400268955783439.
.80563595863991546010661115881806884967004027.P53
447 (1,149) L.M
L (3M) 24268594204567449579226886929351661652137901703954781860703146532721181.P90
M (3L) 13411.3740497.27760489.
.2085436050830101868627222971448078347771532442559785477511.P85
453 (1,151) L.M
L (3M) 7345054738129351972681432555641148061413364808769116545344488307.P98
M (3L) 1348129.2092861.112341266088109835884435114483.
.3206046355269404360980173532840459.7154409726952489428326850247389343.P54
459 (1,3L,3M,9L,9M,17,51L,51M,153L,153M) L.M
L (27M) 6427.8263.3290873941.
.4772949043296938327540555652344566627901623072447285275681332599.P75
M (27L) 2583416323.1848577259045898983521.P125
465 (1,5,31,155) L.M
L (3L,15M,93M) 33661195621.7608436297012031616889789008167761321.P82
M (3M,15L,93L) 31*.4853358451.P119
471 (1,157) L.M
L (3L) 44704452965167992989021059.
.3373910943552318560566312255270898933180978334214232817297798982057.P77
M (3M) 7537.15073.12453241.35010373.74479461399093993433.
.31289406059597855950513457417424955206259.P86
477 (1,3L,3M,53,159L,159M) L.M
L (9M) P169
M (9L) 6679.126563242535798869117.12127245100359565505374301335436857963786417904384880169071412408713919.P75
483 (1,7,23,161) L.M
L (3M,21L,69M) 967.P140
M (3L,21M,69L)
607006142583726902226615046763509882376974181278444022803.P86
489 (1,163) L.M
L (3M) 13693.53791.73351.
.1589450798887141029369915280596841501323098573956641339782791.P101
M (3L) 1929515761.636076523128573.617979037622870188705978539097764755562007183462574733638849717988229201.P80
495 (1,3L,3M,5,11,15L,15M,33L,33M,55,165L,165M) L.M
L (9M,45L,99M) 53639866668586533056821906301274295479310292221.P83
M (9L,45M,99L) 991.4241102915611.19211052014551.931826707797528452251.P80
501 (1,167) L.M
L (3L) P180
M (3M) 97174963.P171
507 (1,13,169) L.M
L (3L,39L) 2029.24337.75037.38915923723.P146
M (3M,39M) 70981.19818208177.142020168733.
.44962084852792428976301085987770964908163039004483.P93
513 (1,3L,3M,9L,9M,19,57L,57M,171L,171M) L.M
L (27M) 76041217116941473.P158
M (27L) 105856254362071.20424500075336986891104565020294665487061027.
.48621554404118655538174883189588506054052233.P74
519 (1,173) L.M
L (3M) 2163193.1392394853916259.77800409639814848538397771424169207356806135954509605930376319347717201490361707.P85
M (3L) 108298213841149.P172
525 (1,5,7,25,35,175) L.M
L (3M,15L,21L,75M,105M) 720301.113023051.P116
M (3L,15M,21M,75L,105L) 1051.6301.17851.6442801.
.137674063225843198051259632503102522001.P74
531 (1,3L,3M,59,177L,177M) L.M
L (9L) 70631031907.1641292827443365429.P159
M (9M) 273997.P183
537 (1,179) L.M
L (3L) 16111.61676889995993664538489477189609.
.395990847983499230629473507336067593585583.
.6553202059289007592766882635476749822940266122999.P66
M (3M) 17619052443834679.P176
543 (1,181) L.M
L (3L) 2278429.1945994562603443515808503234371445892786518320911083354368578944419107392783511986751617.P101
M (3M) 1087.2472823.7842135398918588368969.872467473285058707693422089.
.13080055006360860550237644443085429757.
.210113748844700144917711383538967015427673.P58
549 (1,3L,3M,61,183L,183M) L.M
L (9L) 7687.358789069.P182
M (9M) 354960413514937.26896003358908279221661679473939478241981255703.
.322410908070969630339041359359164154612901586904078700184707.P74
555 (1,5,37,185) L.M
L (3M,15L,111M) 7771881751691625037690129926078250918116885996408721.P104
M (3L,15M,111L) 3109111.38689265837367032644023417953163545911.P112
561 (1,11,17,187) L.M
L (3M,33M,51L) 1123.32562842234539.78324649527879819109.
.301185864380214605485651.1058569077572449333936789312141.P83
M (3L,33L,51M) 10099.4496981131825488660800158938461828526815530233607.P120
567 (1,3L,3M,7,9L,9M,21L,21M,27L,27M,63L,63M,189L,189M) L.M
L (81M) 28390394386299961.809314740206179298645509353511.
.5230055597704998513749511222169.
.563331271783469665535306255634948806914286843491.P50
M (81L) 40278547.1954561267.32835102679.16351687657198086505701607.P123
573 (1,191) L.M
L (3L) 60344482942982897615998724470855285226949321551984117995141479519932977.P135
M (3M) 2213558629224791673406902242107.
.4073110572177402880358023433665428834389887.P132
579 (1,193) L.M
L (3L) 208441.6439316280967.35135274085230907447.
.212633762985937736199663727.
.114016331193920092225584659338086215629841839071424207154308069.P82
M (3M) 1140068969221082768792175765231766327060329518346066867530983.P147
585 (1,3L,3M,5,13,15L,15M,39L,39M,65,195L,195M) L.M
L (9M,45L,117M) 1171.44022421.8778178115705076853830510781.
.30191929647961734821233855062192311705657444483644561.P65
M (9L,45M,117L) 11950124941.16644914911.866757827669435037422729371.
.91264931872794338368056566736419162905070295091.P62
591 (1,197) L.M
L (3M) 1638089365033813.394269001208982069133.674591191048755553063.P155
M (3L) 89833.389945631679504093322073487.1139807681135944776240219053639595390947513666853190760367107498802022946752383776898613.P94
597 (1,199) L.M
L (3M) 3583.65817972421.110693643337.406687074361.
.94502328581673515370642457513.P148
M (3L) 3127087.762655517470452162449734755292117546105489225453443649619017774346819409553725976907519534883432257137.P106
12^{3h}+1=(12^h+1)L.M, L=12^h-2^h.3^k+1, M=12^h+2^h.3^k+1, h=2k-1.