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Factors of Repunit Numbers

Repunit100-20221222.pdf

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Factor of Repunit Numbers site is moved from "http://www.h4.dion.ne.jp/~rep" to this page .

Now factors list and updates are on this web .

Recent update

From everybody :

1355 : c1033 = 64798931224892046095300386296961245938921 * c 992

B1 = 11000000 , sigma = 0:12395092201359388656 , 2019.01.05 , found by yoyo@home

2580L : c 316 = 40577891868500992650677399803808454657267203875748156761 * c 260

B1 = 260000000 , sigma = 0:2155320441625669934 , 2019.01.13 , found by yoyo@home

6380L : c1088 = 2745820043425052285732308383257413452721 * c1048

B1 = 11000000 , sigma = 1168867487 , 2019.01.27 , found by Kurt Beschorner

6100L : c1144 = 69091807550221647412700483018565101 * c1110

B1 = 11000000 , sigma = 0:373158171685814716 , 2019.02.25 , found by yoyo@home

6100L : c1110 = 17729642323320850278883616474935850401 * c1072

B1 = 11000000 , sigma = 0:12691948414942556416 , 2019.02.24 , found by yoyo@home

5742 : c1677 = 1808861312313765194718694286223289 * 26694412701645812093609827243540778173 * c1606

2019.03.02 , found by Alfred Reich

622 : c 223 = 972257004001983078662961403513565995843134142539444914120798476327

* 6233584499738299340076596109269276052417987101388073691610569618213

* P 90

SNFS , 2019.03.13 , found by NFS@Home

8148 : c2260 = 23888331928755038568489169001705089 * c2226

3123 : c2070 = 49295447401007236002837366533239 * c2039

2019.03.22 , found by Alfred Reich

3095 : c2395 = 90443865354658473015839587544568391 * c2360

2019.03.26 , found by Alfred Reich

2248 : c1114 = 1125096610491026258717069231764777 * c1081

2019.04.02 , found by Alfred Reich

2608 : c1285 = 2711533575490636312104255710201930401 * c1249

2019.04.04 , found by Alfred Reich

6138 : c1790 = 4649700678223371354013752098032052413 * c1753

2019.04.06 , found by Alfred Reich

6168 : c2025 = 789623604692467568415491118469360633 * c1989

2019.04.06 , found by Alfred Reich

6188 : c2276 = 5781822105649878089905469839201 * c2245

2019.04.06 , found by Alfred Reich

3453 : c2267 = 60061366931002116328324273314045799654573339003 * c2220

2019.04.08 , found by Alfred Reich

563 : c 545 = 601193188650614249069704703228803510540758119 * c 500

B1 = 110000000 , sigma = 0:16222137679668624593 , 2019.04.11 , found by yoyo@home

7540L : c1337 = 92908918613191880421357495998041 * c1305

2019.04.13 , found by Alfred Reich

8060M : c1400 = 9563613411880480653886428115541468801 * P1363

2019.04.14 , found by Alfred Reich

8420M : c1666 = 961793978153247229732651534445101 * c1633

2019.04.14 , found by Alfred Reich

973 : c 824 = 3715631189441610182664346038535448639 * P 787

B1 = 43000000 , sigma = 0:1221013246906637789 , 2019.05.01 , found by yoyo@home

8220L : c1074 = 6097790664173896352923803646734195061 * c1037

B1 = 11000000 , sigma = 2907575830 , 2019.05.14 , found by Kurt Beschorner

6140L : c1196 = 13250162724903585950689727396593851617218121 * c1153

B1 = 11000000 , sigma = 1403731729 , 2019.05.16 , found by Kurt Beschorner

3375 : c1774 = 9928227087054120839404714671321001 * c1740

2019.06.11 , found by Alfred Reich

4005 : c2113 = 1867328658390232232662140183278161 * c2079

2019.06.11 , found by Alfred Reich

3369 : c2244 = 4087010404483958534982337738286521 * c2211

2019.06.11 , found by Alfred Reich

2029 : c1900 = 245013714487726159144720326081715348604363 * c1859

B1=11000000, sigma=0:12332245062534318460 , 2019.07.03 , found by Bo Chen

1980M : c 187= 1894480662587906626213719003472037744324031299064496778010791034044578628744590947201792481 * P 97

GNFS , 2019.07.07 , found by Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche and Kurt Beschorner

8220L : c1037 = 45590288211884086268396615267733422521 * c 999

B1 = 11000000 , sigma = 0:17790716536559808641 , 2019.07.10 , found by yoyo@home

507 : c 200 = 1383906125377990823745051521665361287866249997770983367680122139350699914609150997586781841 * P 110

GNFS , 2019.07.24 , found by Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche and Kurt Beschorner

676 * c 308 = 7249657507840161826942418511086116063748219199832125768043099150081

* 232372119876907280822321391951168183308631299658430083807589307649464986270410218850191981

* P 151

SNFS , 2019.07.28 , found by NFS@home

728 * c 267 = 146922836547557380904624883811070801579636649582426027039761

* 1236386443286416000845205982296310762602996796920706630693450425385353425494707969

* P 127

SNFS , 2019.07.29 , found by NFS@home

2380M : c 347 = 55722909386297024938297392343519300689842174503366122181 * P 292

B1 = 260000000 , sigma = 0:2377822517027304999 , 2019.08.06 , found by yoyo@home

8940M : c1094 = 2647733864525435357868825323065594021 * c1057

B1 = 11000000 , sigma = 2165451346 , 2019.09.28 , found by Kurt Beschorner

1420M : c 274 = 101956533794009284800765131459172391943780858147641273764890861 * c 212

found by ECMNET , 2019.10.03

1417 : c1208 = 55931448966246130071538810222836707 * c1173

B1 = 11000000 , sigma = 3780116918 , 2019.10.14 , found by Kurt Beschorner

1357 : c1268 = 800551567150597779248843185551955662432161 * c1227

B1 = 11000000 , sigma = 0:13842388622860530632 , 2019.10.16 , found by yoyo@home

626 : c 230 = 589855742530873303648997100606906463934277315614405401704255573694516882878454393085805024793769310885400567 * P 122

SNFS , 2019.10.13 , found by NFS@home

2580L : c 260 = 3209681398615442534074101309775547494759396015886801499169945861 * P 197

B1 = 850000000 , sigma = 0:1524063036262106663 , 2020.02.14 , found by yoyo@home

337 : c 268 = 906533749251005245151122204670351312590267105760052002862150546121 * c 202

2020.02.21 , found by Sam Wagstaff

1233 : c 803 = 82953452943096961359732993332153506983079 * c 762

B1 = 43000000 , sigma = 0:10297922851821278427 , 2020.02.23 , found by yoyo@home

1233 : c 762 = 2071133703625587214227323104568507030381670852043 * c 714

B1 = 43000000 , sigma = 0:12155937095413581933 , 2020.05.19 , found by yoyo@home

459 : c 221 = 287743709071765679519005572592282086727787894852332081977696568112925297043603 * P 143

SNFS , 2020.07.24 , found by Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche and Kurt Beschorner

7980L : c 840 = 7852530157762803085617492355913151301 * c 803

B1 = 43000000 , sigma = 0:6858431455024526459 , 2020.09.23 , found by yoyo@home

6580M : c1072 = 5226300854932192952818901175186968159161 * c1032

B1 = 11000000 , sigma = 0:6986030302957500225 , 2020.09.27 , found by yoyo@home

469 : c 396 = 6958997628875965569003769582314963273475677604340583053 * c 342

B1 = 210596123-260000000 , 2020.10.04 , found by yoyo@home

742 : c 235 = 2548171182130492354464113595833821781588064140986874348075459263402328971040215243200625902015381883224397137647 * P 124

SNFS , 2020.10.21 , found by NFS@home

371 : c 255 = 8443278213142643683880850952929502264137832292889910297487445526484776400899484558952278931894560501953983650020256591767199 * P 131

SNFS , 2020.11.08 , found by NFS@home

625 : c 501 = 2782057126261476352728985117193142348250001 * c 458

B1 = 110000000 , sigma = 3811420836399633 , 2020.12.13 , found by Alfred Eichhorn

469 : c 342 = 316237267349250204445544982727458065652184756181185770847813 * c 282

B1 = 260000000 , sigma = 0:16910116206833045390 , 2021.01.12 , found by yoyo@home

519 : c 297 = 25175590297709339047755994593944705119042514299940364907 * P 241

B1 = 850000000 , sigma = 0:15265866885997281733 , 2021.01.26 , found by yoyo@home

337 : c 202 = 10040499610458011332733838420983746051698922310460547466000255532841658478393221611341226016666610043 * P 102

GNFS , 2021.01.30 , found by Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche and Kurt Beschornor

2231 : c2002 = 127269517286008733272752480463187 * c1970

B1 = 11000000 , sigma = 0:2945844318283144 , 2021.03.24 , found by Kurt Beschornor

1285 : c 971 = 16125873110496868884553362758627283290407985434481 * P 922

B1 = 43000000 , sigma = 0:8766000215669500 , 2021.04.12 , found by Kurt Beschornor

485 : c 305 = 3905050584750719584997916596589271839372757118110949321 * c 251

B1 = 260000000 , sigma = 0:13910476698621796582 , 2021.04.23 , found by yoyo@home

11220M : c1267 = 16930380233308606707892880902447984978624096501 * c1220

B1 = 43000000 , sigma = 0:863078287696667 , 2021.05.07 , found by Kurt Beschornor

7500L : c 932 = 48207545174782975493383750875127027725001 * c 891
B1 = 43000000 , sigma = 0:7630000256316624 , 2021.06.02 , found by Kurt Beschorner
5700M : c 711 = 214098531848960682375313931062057408227354489641401 * c 660
B1 = 43000000 , sigma = 0:1218120574389352 , 2021.06.09 , found by Kurt Beschorner
10180M : c2000 = 618469348886528986386736868045981 * P1967
B1 = 11000000 , sigma = 0:138044562091769 , 2021.06.11 , found by Kurt Beschorner
1740M : c 204 = 38500497070688096027556817882565728990416892548263819672284096593431517949011701136219584563960572421 * P 103
GNFS , 2021.06.27 , found by Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche and Kurt Beschorner
1269 : c 814 = 541520087299201982040396188910708534378319 * c 773
B1 = 43000000 , sigma = 0:932524933627175 , 2021.07.11 , found by Kurt Beschorner

1008 : c 249 = 11824792503914776383865492901019100670460517256833712771719617457 *P 185

SNFS , 2021.08.23 , found by Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche and Kurt Beschorner

5002 : c2401 = 522346250245015592799109827193626997 * c2365

B1 = 11000000 , sigma = 0:7715223337182973 , 2021.10.28 , found by Kurt Beschorner

5002 : c2365 = 9257979664211852962861062975013161250901383 * c2322

B1 = 11000000 , sigma = 0:1183374437285197 , 2021.11.03 , found by Kurt Beschorner

1789 : c1726 = 64056025886889373277419436256019351 * c1691

B1 = 11000000 , sigma = 0:2109008035502416 , 2021.11.24 , found by Kurt Beschorner

1789 : c1691 = 105700953104805896168083326362115409 * c1656

B1 = 11000000 , sigma = 0:1163849328483425 , 2021.11.24 , found by Kurt Beschorner

888 : c 258 = 78423397189035946058321607200546180176617061948406580747828212881 * P 193

SNFS , 2021.12.23 , found by Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche and Kurt Beschorner

890 : c 195 = 80855294634541341009709576571189264494703351351547829906051 * P 136

B1 = 11000000 , sigma = 110000000 , sigma = 2898407432 , 2022.01.07 , found by Ray Chandler

942 : c 274 = 46362291155014458662283849816585346934219100138220618375160747209 * c 209

B1 = 110000000 , sigma = 3574469845 , 2022.01.23 , found by Ray Chandler

1293 : c 842 = 81462499223765124189973519762431164923148551627 * c 795

B1 = 43000000 , sigma = 0:5078991612991630 , 2022.04.04 , found by Kurt Beschorner

323 : c 271 = 1000889286725563474405662045911093540900908710082344227506919162972107

* 2024740873938190513425266673474911634048354422503451267887726938473483

* P 132

SNFS , 2022.04.19 , found by NFSNET

718 : c 329 = 2731764846587782091546914066524656594612608438032609803989298453 * c 265

2022.04.24 , found by Sam Wagstaff

1441 : c1239 = 1314434306697830924275628881502710792058563 * c1197

B1 = 11000000 , sigma = 0:281840436550688 , 2022.04.30 , found by Kurt Beschorner

646 : c 242 = 298705372736554351789156294144090138390916509553983003911433879637774413 * P 170

SNFS , 2022.05.06 , found by NFSNET

1780L : c 268 = 7660395383708237627973789216434577857253936548886784731800803873631881 * P 198

B1 = 2200000000 , sigma = 1:532322200 , 2022.05.27 , found by Wagstaff

4700L : c 882 = 45356719338814489536408951887817301 * c 847

B1 = 43000000 , sigma = 1704111251554519 , 2022.06.21 , found by Kurt Beschorner

878 : c 361 = 3127889058329352843751138723028784195008863188510913210373 * P 303

2022.09.19 , found by Sam Wagstaff

2580M : c 275 = 5450116210658743893234594584043237507827598349697948371796539141 * P 211

B1 = 2900000000 , sigma = 0:10511886308721671557 , 2022.10.01 , found by yoyo@home

12180L : c1337 = 2750865191314983385202411742967911795988441 * c1295

B1 = 11000000 , sigma = 0:3511433398072626 , 2022.10.11 , found by Kurt Beschorner

1290 : c 279 = 46918389192417684252494192977798983971157315180037905073531 * c220

B1=2900000000, sigma=0:15756483711164029501 , 2022.10.19 , found by yoyo@home

7380L : c 954 = 18083439727099436159112817133086310461 * c 917

B1 = 43000000 , sigma = 2954795763367013 , 2022.10.27 , found by Kurt Beschorner

1389 : c 878 = 39307144309365706756279849773434495203 * P 840

B1 = 43000000 , sigma = 1509003123809924 , 2022.11.01 , found by Kurt Beschorner

497 : c 366 = 4247178976042868082665679915673747026882614569 * P 321

B1 = 850000000 , sigma = 0:17252997664838270985 , 2022.11.24 , found by yoyo@home

1212 : c 322 = 10498042566741901780282937616325375954902715561 * P 276

B1 = 850000000 , sigma = 0:3738033742963211035 , 2022.12.06 , found by yoyo@home

1315 : c 953 = 193413247904674241324507425343532732791 * P 915

B1 = 43000000 , sigma = 0:7414637162882108 , 2022.12.13 , found by Kurt Beschorner

1381 : c1340 = 71236855295678591990160932434313161 * c1305

B1 = 11000000 , sigma = 6012605352570225 , 2022.12.15 , found by Kurt Beschorner

537 : c 334 = 2167451486375064397900184401899510260456269195385135677227157 * c 274

B1 = 850000000 , sigma = 0:5910846903816997764 , 2022.12.17 , found by yoyo@home

From me :

(My search range is R802..R998 and R1620L..R1980M)

816 : c 242 = 3178246571075235723080972275640135632212436318968968029466533249264048115754831736073020454216579035062833710671458881 * P 125

SNFS , 2020.04.05

1620L : c 185 = 216228542818328308783433809596084627890392881018159564738348653328755727601 * P 110

SNFS , 2021.05.15

834 : c 205 = 84191134295847459088496323909951690425296390505413654926185730285872463 * P 134

SNFS , 2021.07.28

890 : c 255 = 630859966703635424146382843107732835487998079409968772589281 * c 195

B1 = 300000000 , sigma = 2:7216577815049336811 , 2021.08.30

846 : c 249 = 8147270298945964118744634040617462692098679807835492529 * P 194

SNFS , 2021.10.18

852 : c 257 = 791145568078856137872408096636314622331869565265096415358925771275309

* 843407644889588409015473024758866665298118138956929263554289382634028509255935457469

* P 105

SNFS , 2022.04.12

892 : c 321 = 6159486985016013075067913427429040588111855293215481915322769 * P 260

B1 = 300000000 , sigma = 2:10607718275885008793 , 2022.09.10

880 : c 295 = 62716385987763617906038889384985304875217698799039986699716641 * P 234

B1 = 300000000 , sigma = 2:10560429264819151247 , 2022.12.04

1940M : c 344 = 5571625642084498030602199756991965375293044719417529765342701 * c 283

B1 = 300000000 , sigma = 2:13803433046389983180 , 2022.12.20

PLEASE CHECK THIS TO AVOID DUPLICATION .

IT MAKES NO SENSE THAT TWO OR MORE PEOPLE DO THE SAME NUMBER .

My search range is Phi(802,10) ... Phi(998,10) where even n and Phi(1620L,10) ... Phi(1980M,10) .

Below Phi(n,10)'s are under computation ;

990 -> SNFS

ECM for 16 numbers at B1 = 3e8 ;

802 , 806 , 824 , 826 , 832 , 868 , 874 , 946 , 950 , 954 , 970 , 978 , 984 , 1660L , 1940L , 1940M