Riesel conjectures and proofs
Bases that are powers of 2 are shown on a separate page.

Started: Dec. 14, 2007
Last update: June 30, 2023

Compiled by Gary Barnes

Riesel conjectures powers of 2
Riesel conjecture reservations
Sierpinski conjectures
Sierpinski conjectures powers of 2

All n must be >= 1.

k-values with at least one of the following conditions are excluded from the conjectures:
     1.  All n-values have a single trivial factor.
     2.  Make a full covering set with all or partial algebraic factors.

k-values that are a multiple of base (b) and where k-1 is composite are included in the conjectures but excluded from testing.
Such k-values will have the same prime as k / b.

Green = testing through other projects
Gray = conjecture proven

Testing not done through other projects is coordinated at Mersenneforum Conjectures 'R Us.

Base Conjectured Riesel k Covering set k's that make a full covering set with all or partial algebraic factors Trivial k's (factor) Remaining k to find prime
(n testing limit)		 Top 10 k's with largest first primes: k (n) Comments / accounting of all k's
3 63064644938 5, 7, 13, 17, 19, 37, 41, 193, 757   k = = 1 mod 2 (2) 100714 k's remaining at n>=100K.

See k's and test limits at Riesel Base 3 remain.		 676373272 (1072675)
1068687512 (1067484)
1483575692 (1067339)
780548926 (1064065)
1776322388 (1053069)
587137424 (1047373)
1818135848 (1044237)
688002298 (1043910)
1755742784 (1043692)
1328444066 (1039025)		 See all primes for n>25K at prime-riesel-base3-gt-25K.zip.
5 346802 3, 7, 13, 31, 601   k = = 1 mod 2 (2) 56 k's remaining at n=4.3M.

See k's at Riesel Base 5 remain.		 3622 (7558139)
213988 (4138363)
63838 (3887851)
64598 (3769854)
273662 (3493296)
102818 (3440382)
109838 (3168862)
207494 (3017502)
238694 (2979422)
146264 (2953282)		 All k's are being worked on by PrimeGrid's Sierpinski/Riesel Base 5 project.  See k's and test limits at Sierpinski/Riesel Base 5 project stats.

all-ks-riesel-base5.zip
6 84687 7, 13, 31, 37, 97   k = = 1 mod 5 (5) 1597 (5.6M) 36772 (1723287)
43994 (569498)
77743 (560745)
51017 (528803)
57023 (483561)
78959 (458114)
59095 (171929)
48950 (143236)
29847 (141526)
9577 (121099)		 all-ks-riesel-base6.txt
7 408034255082 5, 13, 19, 43, 73, 181, 193, 1201   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 16399 k's remaining for k<=1G at n>=25K.

See k's and test limits at Riesel Base 7 remain.		 1620198 (684923)
7030248 (483691)
7320606 (464761)
5646066 (460533)
9012942 (425310)
3885264 (419940)
5333174 (380887)
4780002 (368053)
9871172 (367701)
328226 (298243)		 See all primes for n>25K at prime-riesel-base7-gt-25K.txt.
9 74 5, 7, 13, 73 All k = m^2 for all n; factors to:
(m*3^n - 1) *
(m*3^n + 1)		 k = = 1 mod 2 (2) none - proven 24 (8)
14 (8)
60 (5)
42 (5)
44 (4)
46 (3)
38 (3)
18 (3)
70 (2)
68 (2)		 k = 4, 16, 36, and 64 proven composite by full algebraic factors.

all-ks-riesel-base9.txt
10 10176 7, 11, 13, 37   k = = 1 mod 3 (3) 4421 (3M) 7019 (881309)
8579 (373260)
6665 (60248)
1935 (51836)
1803 (45882)
1343 (29711)
3356 (13323)
450 (11958)
6588 (5846)
4478 (4817)		 all-ks-riesel-base10.txt
11 862 3, 7, 19, 37   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)		 none - proven 62 (26202)
308 (444)
172 (187)
284 (186)
518 (78)
464 (78)
728 (76)
448 (69)
494 (60)
100 (59)		 all-ks-riesel-base11.txt
12 376 5, 13, 29 (Condition 1):
All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*12^q - 1) *
     (m*12^q + 1)
   odd n:
     factor of 13
(Condition 2):
All k where k = 3*m^2
and m = = 3 or 10 mod 13:
   even n:
     factor of 13
   for odd n let k = 3*m^2
   and let n=2*q-1; factors to:
     [m*2^n*3^q - 1] *
     [m*2^n*3^q + 1]		 k = = 1 mod 11 (11) none - proven 157 (285)
46 (194)
304 (40)
259 (40)
94 (36)
292 (30)
147 (28)
301 (27)
349 (25)
58 (23)		 k = 25, 64 and 324 proven composite by condition 1.

k = 27 and 300 proven composite by condition 2.

all-ks-riesel-base12.txt
13 302 5, 7, 17   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 none - proven 288 (109217)
146 (30)
92 (23)
102 (20)
300 (10)
216 (10)
20 (10)
174 (8)
152 (8)
224 (7)		 all-ks-riesel-base13.txt
14 4 3, 5   k = = 1 mod 13 (13) none - proven 2 (4)
3 (1)		 all-ks-riesel-base14.txt
15 36370321851498 13, 17, 113, 211, 241, 1489, 3877   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)		 14 k's remaining for k<=20M at n>=250K.

See k's and test limits at Riesel Base 15 remain.		 4242104 (728840)
9756404 (527590)
9105446 (496499)
5854146 (428616)
9535278 (375675)
3347624 (347109)
3889018 (275603)
5255502 (257491)
5149158 (249605)
11592838 (214537)		 See all primes for n>25K at Riesel Base 15 primes.
17 86 3, 5, 29   k = = 1 mod 2 (2) none - proven 44 (6488)
36 (243)
10 (117)
26 (110)
58 (35)
46 (25)
70 (19)
54 (16)
74 (12)
42 (12)		 all-ks-riesel-base17.txt
18 246 5, 13, 19   k = = 1 mod 17 (17) none - proven 151 (418)
78 (172)
50 (110)
79 (63)
237 (44)
184 (44)
75 (44)
215 (36)
203 (32)
93 (32)		 all-ks-riesel-base18.txt
19 1119866 5, 7, 13, 127, 181 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*19^q - 1) *
     (m*19^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 19*m^2
and m = = 2 or 3 mod 5:
   [Reverse condition 1]		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 947 k's remaining at n>=100K.

See k's and test limits at Riesel Base 19 remain.		 3224 (217758)
3314 (121512)
899576 (99899)
520266 (99757)
572886 (99635)
916026 (99517)
703454 (99478)
668474 (99400)
1037544 (98582)
680546 (98509)		 k = 12^2, 18^2, 42^2, 48^2, 72^2, 78^2, (etc. pattern repeating every 30m) proven composite by condition 1.

k = 19*12^2, 19*18^2, 19*42^2, 19*48^2, 19*72^2, 19*78^2, (etc. pattern repeating every 30m) proven composite by condition 2.

all-ks-riesel-base19.zip
20 8 3, 7   k = = 1 mod 19 (19) none - proven 2 (10)
6 (2)
5 (2)
7 (1)
4 (1)
3 (1)		 all-ks-riesel-base20.txt
21 560 11, 13, 17   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)		 none - proven 64 (2867)
494 (978)
154 (103)
84 (88)
142 (48)
450 (34)
342 (23)
362 (20)
34 (17)
474 (11)		 all-ks-riesel-base21.txt
22 4461 5, 23, 97   k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 3656 (5M) 3104 (161188)
4001 (36614)
2853 (27975)
1013 (26067)
4118 (12347)
185 (11433)
1335 (11155)
4302 (7653)
3426 (7586)
4440 (5999)		 all-ks-riesel-base22.txt
23 476 3, 5, 53   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)		 404 (2M) 194 (211140)
134 (27932)
394 (20169)
314 (17268)
464 (7548)
230 (6228)
328 (5001)
472 (2379)
326 (1598)
374 (1452)		 all-ks-riesel-base23.txt
24 32336 5, 7, 13, 73, 577 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*24^q - 1) *
     (m*24^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 6*m^2
and m = = 1 or 4 mod 5:
   even n:
     factor of 5
   for odd n let k = 6*m^2
   and let n=2*q-1; factors to:
     [m*2^n*6^q - 1] *
     [m*2^n*6^q + 1]		 k = = 1 mod 23 (23) 68 k's remaining at n=260K.

See k's at Riesel Base 24 remain.		 10171 (259815)
11906 (252629)
23059 (252514)
21411 (252303)
28554 (239686)
20804 (233296)
8894 (210624)
2844 (203856)
25379 (175842)
22604 (169372)		 k = 2^2, 3^2, 7^2, 8^2. 12^2, 13^2, (etc. pattern repeating every 5m where k not = = 1 mod 23) proven composite by condition 1.

k = 6*1^2, 6*4^2, 6*6^2, 6*9^2, 6*11^2, 6*14^2, (etc. pattern repeating every 5m where k not = = 1 mod 23) proven composite by condition 2.

all-ks-riesel-base24.txt
 
25 346802 7, 13, 31, 601 All k = m^2 for all n; factors to:
(m*5^n - 1) *
(m*5^n + 1)		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 100 k's remaining at n>=300K.

See k's and test limits at Riesel Base 25 remain.		 18110 (3779069)
319190 (1943925)
64598 (1884927)
273662 (1746648)
102818 (1720191)
109838 (1584431)
207494 (1508751)
238694 (1489711)
146264 (1476641)
35816 (1472647)		 k = 6^2, 12^2, 18^2, (etc. repeating every 6m) proven composite by full algebraic factors.

k's where k = = 2 mod 3 are being worked on by PrimeGrid's Sierpinski/Riesel Base 5 project.
k's and primes are converted from base 5.

all-ks-riesel-base25.zip
26 149 3, 7, 31, 37   k = = 1 mod 5 (5) none - proven 115 (520277)
32 (9812)
73 (537)
80 (382)
128 (300)
124 (249)
37 (233)
25 (133)
65 (100)
30 (72)		 all-ks-riesel-base26.txt
27 804 5, 7, 73 All k = m^3 for all n; factors to:
(m*3^n - 1) *
(m^2*9^n + m*3^n + 1)		 k = = 1 mod 2 (2)
k = = 1 mod 13 (13)		 706 (5M) 258 (69942)
594 (36624)
684 (6393)
580 (1096)
302 (697)
218 (579)
510 (388)
582 (345)
78 (227)
454 (172)		 k = 8, 64, 216, and 512 proven composite by full algebraic factors.

all-ks-riesel-base27.txt
28 9078 5, 29, 157 (Condition 1):
All k where k = m^2
and m = = 12 or 17 mod 29:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*28^q - 1) *
     (m*28^q + 1)
   odd n:
     factor of 29
(Condition 2):
All k where k = 28*m^2
and m = = 12 or 17 mod 29:
   [Reverse condition 1]		 k = = 1 mod 3 (3) 233 (1M)
1422 (1M)
4322 (1M)
4871 (1M)		 6207 (430803)
5886 (206482)
2319 (65184)
4001 (56146)
5076 (29557)
7367 (23099)
5306 (20994)
8991 (16799)
5133 (7958)
4436 (6242)		 k = 144 and 5625 proven composite by condition 1.

k = 4032 proven composite by condition 2.

all-ks-riesel-base28.txt
29 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)		 none - proven 2 (136) all-ks-riesel-base29.txt
30 4928 13, 19, 31, 67 k = 1369:
   for even n let n=2*q; factors to:
     (37*30^q - 1) *
     (37*30^q + 1)
   odd n:
     covering set 7, 13, 19		 k = = 1 mod 29 (29) 659 (500K)
1024 (500K)
1580 (500K)
1936 (500K)
2293 (500K)
2916 (500K)
3719 (500K)
4372 (500K)
4897 (500K)		 1642 (346592)
239 (337990)
2538 (262614)
249 (199355)
3256 (160619)
225 (158755)
774 (148344)
1873 (50427)
3253 (43291)
25 (34205)		 all-ks-riesel-base30.txt
31 134718 7, 13, 19, 37, 331   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 55758 (3M) 6962 (2863120)
126072 (374323)
43902 (251859)
55940 (197599)
101022 (133208)
37328 (129973)
117690 (108349)
74924 (81381)
131994 (68109)
131240 (46714)		  
33 764 5, 17, 109 (Condition 1):
All k where k = m^2
and m = = 4 or 13 mod 17:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*33^q - 1) *
     (m*33^q + 1)
   odd n:
     factor of 17
(Condition 2):
All k where k = 33*m^2
and m = = 4 or 13 mod 17:
   [Reverse condition 1]		 k = = 1 mod 2 (2) none - proven 732 (19011)
186 (16770)
254 (3112)
562 (3087)
142 (2568)
370 (1628)
272 (1418)
222 (919)
108 (360)
698 (357)		 k = 16 proven composite by condition 1.

k = 528 proven composite by condition 2.
34 6 5, 7   k = = 1 mod 3 (3)
k = = 1 mod 11 (11)		 none - proven 5 (2)
3 (1)
2 (1)		  
35 287860 3, 13, 97, 397   k = = 1 mod 2 (2)
k = = 1 mod 17 (17)		 423 k's remaining at n=100K.

See k's at Riesel Base 35 remain.		 112514 (99908)
212806 (97767)
129428 (97598)
83144 (97498)
250064 (96676)
141466 (96359)
239014 (95455)
56494 (94551)
161554 (94043)
187916 (93860)		  
36 116364 13, 37, 43, 97 All k = m^2 for all n; factors to:
(m*6^n - 1) *
(m*6^n + 1)		 k = = 1 mod 5 (5)
k = = 1 mod 7 (7)		 30 k's remaining at n>=430K.

See k's and test limits at Riesel Base 36 remain.		 102088 (379506)
43809 (340997)
56093 (321585)
73187 (309619)
80883 (297571)
43994 (284749)
33877 (255852)
42623 (245426)
68535 (243900)
92943 (238914)		 k = 2^2, 3^2, 5^2, 7^2, 10^2, 12^2, 17^2, 18^2, 23^2, 25^2, 28^2, 30^2, 32^2, 33^2, 35^2, 37^2, 38^2, 40^2, 42^2, 45^2, 47^2, 52^2, 53^2, 58^2, 60^2, 63^2, 65^2, 67^2, 68^2, 70^2, (etc. pattern repeating every 35m) proven composite by full algebraic factors.
37 7772 5, 19, 137   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 522 (500K)
816 (500K)
1578 (500K)
1614 (500K)
2148 (500K)
2640 (500K)
3972 (500K)
4428 (500K)
5910 (500K)
6752 (500K)
7088 (500K)
7352 (500K)		 4806 (364466)
5376 (289738)
6792 (181029)
284 (128864)
4356 (75913)
5262 (60498)
1842 (41606)
3336 (39794)
3480 (39565)
2606 (39006)		  
38 13 3, 5, 17   k = = 1 mod 37 (37) none - proven 11 (766)
9 (43)
7 (7)
12 (2)
8 (2)
5 (2)
2 (2)
10 (1)
6 (1)
4 (1)		  
39 1352534 5, 7, 223, 1483 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*39^q - 1) *
     (m*39^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 39*m^2
and m = = 2 or 3 mod 5:
   [Reverse condition 1]		 k = = 1 mod 2 (2)
k = = 1 mod 19 (19)		 2134 k's remaining at n>=100K.

See k's and test limits at Riesel Base 39 remain.		 1225996 (99983)
1164356 (99981)
834506 (99733)
104836 (99645)
903844 (99636)
710586 (99519)
1231836 (99477)
702566 (99381)
432786 (99285)
473068 (99023)		 k = 2^2, 8^2, 12^2, 18^2, 22^2, 28^2, (etc. pattern repeating every 10m where k not = = 1 mod 19) proven composite by condition 1.

k = 39*2^2, 39*8^2, 39*12^2, 39*18^2, 39*22^2, 39*28^2, (etc. pattern repeating every 10m where k not = = 1 mod 19) proven composite by condition 2.
40 3386517 7, 41, 223, 547 (Condition 1):
All k where k = m^2
and m = = 9 or 32 mod 41:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*40^q - 1) *
     (m*40^q + 1)
   odd n:
     factor of 41
(Condition 2):
All k where k = 40*m^2
and m = = 9 or 32 mod 41:
   [Reverse condition 1]
(Condition 3):
All k where k = 10*m^2
and m = = 18 or 23 mod 41:
   even n:
     factor of 41
   for odd n let k = 10*m^2
   and let n=2*q-1; factors to:
     [m*2^n*10^q - 1] *
     [m*2^n*10^q + 1]		 k = = 1 mod 3 (3)
k = = 1 mod 13 (13)		 1117 k's remaining at n=100K.

See k's at Riesel Base 40 remain.		 2672094 (99993)
2391251 (99269)
2076116 (99266)
1003148 (99185)
90488 (98849)
647555 (98803)
1423601 (98702)
1076126 (98628)
1667676 (97433)
2404362 (97146)		 k = 9^2, 114^2, 132^2, 237^2, 255^2, 360^2, (etc. pattern repeating every 123m where k not = = 1 mod 13) proven composite by condition 1.

k = 40*9^2, 40*114^2, 40*132^2, 40*237^2, and 40*255^2 proven composite by condition 2.

k = 10*105^2, 10*351^2, and 10*387^2 proven composite by condition 3.
41 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)		 none - proven 2 (2)
4 (1)		  
42 15137 5, 43, 353   k = = 1 mod 41 (41) 603 (300K)
1049 (300K)
2538 (300K)
4903 (300K)
5118 (300K)
5978 (300K)
6836 (300K)
6964 (300K)
7309 (300K)
8297 (300K)
8341 (300K)
9029 (300K)
9201 (300K)
9633 (300K)
9848 (300K)
11267 (300K)
11781 (300K)
11911 (300K)
11996 (300K)
12125 (300K)
12213 (300K)
12598 (300K)
13288 (300K)
13347 (300K)		 4299 (246132)
12127 (203477)
7051 (188034)
5417 (179220)
13898 (152983)
1633 (128734)
13757 (126934)
7913 (108747)
15024 (104613)
8453 (89184)		  
43 672 5, 11, 37   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 none - proven 308 (624)
12 (203)
450 (162)
494 (148)
476 (101)
104 (77)
560 (70)
384 (48)
188 (37)
230 (34)		  
44 4 3, 5   k == 1 mod 43 (43) none - proven 2 (4)
3 (1)		  
45 22564 7, 19, 23, 109   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)		 2804 (500K)
6094 (500K)
10096 (500K)
15432 (500K)
17918 (500K)		 372 (278559)
10518 (251579)
4210 (235749)
13548 (158941)
24 (153355)
21274 (128858)
1312 (104779)
1264 (64666)
2500 (64011)
7246 (59101)		  
46 8177 29, 47, 73   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 800 (500K)
1317 (500K)
3812 (500K)
4419 (500K)
6060 (500K)
6062 (500K)
7472 (500K)		 6297 (330940)
4580 (225356)
7157 (221981)
7520 (137207)
7848 (103180)
7284 (73716)
3383 (69524)
870 (51699)
2819 (33458)
3147 (27916)		  
47 14 3, 5, 13   k = = 1 mod 2 (2)
k = = 1 mod 23 (23)		 none - proven 4 (1555)
10 (51)
8 (32)
2 (4)
12 (1)
6 (1)		  
48 3226 5, 7, 461   k = = 1 mod 47 (47) 313 (500K)
384 (500K)
909 (500K)
916 (500K)
1093 (500K)
1457 (500K)
1686 (500K)
1877 (500K)
1896 (500K)
1898 (500K)
2071 (500K)
2148 (500K)
2172 (500K)
2402 (500K)
2589 (500K)
2682 (500K)
2927 (500K)
2939 (500K)
3044 (500K)
3067 (500K)		 708 (445477)
2157 (169491)
2549 (169453)
1478 (167541)
2822 (129611)
2379 (116204)
118 (107422)
692 (103056)
1842 (87175)
953 (81493)		  
49 2414 5, 13, 19, 43 All k = m^2 for all n; factors to:
(m*7^n - 1) *
(m*7^n + 1)		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 none - proven 2186 (369737)
1394 (52698)
1266 (36191)
230 (24824)
1706 (16337)
1784 (13480)
786 (6393)
896 (3563)
1314 (3076)
1544 (3026)		 k = 36, 144, 324, 576, 900, 1296, 1764, and 2304 proven composite by full algebraic factors.
50 16 3, 17   k == 1 mod 7 (7) none - proven 14 (66)
13 (19)
5 (12)
11 (6)
6 (6)
2 (2)
12 (1)
10 (1)
9 (1)
7 (1)		  
51 8632534 7, 13, 379, 2551 (Condition 1):
All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*51^q - 1) *
     (m*51^q + 1)
   odd n:
     factor of 13
(Condition 2):
All k where k = 51*m^2
and m = = 5 or 8 mod 13:
   [Reverse condition 1]		 k = = 1 mod 2 (2)
k = = 1 mod 5 (5)		 10432 k's remaining at n>=25K.

See k's and test limits at Riesel Base 51 remain.		 1498550 (49955)
759942 (49811)
1873470 (49791)
1947438 (49754)
2568668 (49707)
2117064 (49607)
1561834 (49583)
160850 (49515)
877070 (49322)
2702894 (49106)		 k = 8^2, 18^2, 60^2, 70^2, 112^2, 122^2, 138^2, 148^2, 190^2, 200^2, 242^2, 252^2, (etc. pattern repeating every 130m) proven composite by condition 1.

k = 51*8^2, 51*18^2, 51*60^2, 51*70^2, 51*112^2, 51*122^2, 51*138^2, 51*148^2, 51*190^2, 51*200^2, 51*242^2, 51*252^2, (etc. pattern repeating every 130m) proven composite by condition 2.
52 85967 5, 53, 541 (Condition 1):
All k where k = m^2
and m = = 23 or 30 mod 53:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*52^q - 1) *
     (m*52^q + 1)
   odd n:
     factor of 53
(Condition 2):
All k where k = 52*m^2
and m = = 23 or 30 mod 53:
   [Reverse condition 1]		 k = = 1 mod 3 (3)
k = = 1 mod 17 (17)		 99 k's remaining at n=100K.

See k's at Riesel Base 52 remain.		 3870 (99193)
8693 (95515)
11394 (94360)
70703 (93799)
39168 (91095)
55119 (90896)
12401 (84322)
71763 (84127)
58407 (81857)
47913 (81807)		 k = 900, 16641, and 35721 proven composite by condition 1.

k = 46800 proven composite by condition 2.
53 5392 3, 5, 281   k = = 1 mod 2 (2)
k = = 1 mod 13 (13)		 64 k's remaining at n=250K.

See k's at Riesel Base 53 remain.		 4404 (235589)
478 (220497)
5174 (199016)
3802 (179867)
208 (158365)
5140 (145173)
3958 (140565)
1628 (138940)
4882 (128251)
2338 (128165)		  
54 21 5, 11 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*54^q - 1) *
     (m*54^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 6*m^2
and m = = 1 or 4 mod 5:
   even n:
     factor of 5
   for odd n let k = 6*m^2
   and let n=2*q-1; factors to:
     [m*3^n*6^q - 1] *
     [m*3^n*6^q + 1]		 k = = 1 mod 53 (53) none - proven 20 (8)
19 (6)
10 (4)
17 (3)
14 (2)
7 (2)
3 (2)
18 (1)
16 (1)
15 (1)		 k = 4 and 9 proven composite by condition 1.

k = 6 proven composite by condition 2.
55 6852 7, 17, 89   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 2330 (500K)
3158 (500K)
3578 (500K)
4878 (500K)
6098 (500K)		 3942 (423771)
5354 (244064)
4640 (201708)
3240 (150226)
5690 (75216)
5286 (56479)
3060 (41775)
608 (25062)
2022 (19568)
1254 (11243)		  
56 20 3, 19   k = = 1 mod 5 (5)
k = = 1 mod 11 (11)
 		 none - proven 14 (26)
10 (23)
18 (4)
17 (4)
7 (3)
8 (2)
5 (2)
2 (2)
19 (1)
15 (1)		  
57 144 5, 13, 29   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
 		 none - proven 54 (157)
100 (109)
124 (31)
88 (27)
38 (20)
128 (16)
34 (12)
94 (7)
80 (7)
98 (6)		  
58 105788 5, 7, 13, 59, 163   k = = 1 mod 3 (3)
k = = 1 mod 19 (19)		 255 k's remaining at n=100K.

See k's at Riesel Base 58 remain.		 43838 (99905)
9696 (98918)
93314 (98883)
30563 (98861)
98366 (95763)
19394 (95453)
29184 (94709)
17463 (93226)
103307 (92620)
49163 (92545)		  
59 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 29 (29)		 none - proven 2 (2)  
60 20558 13, 61, 277 (Condition 1):
All k where k = m^2
and m = = 11 or 50 mod 61:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*60^q - 1) *
     (m*60^q + 1)
   odd n:
     factor of 61
(Condition 2):
All k where k = 60*m^2
and m = = 11 or 50 mod 61:
   [Reverse condition 1]		 k = = 1 mod 59 (59) 36 (250K)
1770 (250K)
4708 (250K)
5317 (250K)
6162 (250K)
6274 (250K)
7060 (250K)
7870 (250K)
8722 (250K)
9454 (250K)
9881 (250K)
11101 (250K)
12061 (250K)
12072 (250K)
12098 (250K)
13297 (250K)
13480 (250K)
14275 (250K)
14851 (250K)
15800 (250K)
17620 (250K)
18972 (250K)
19336 (250K)
19394 (250K)		 12996 (241023)
9212 (199777)
10249 (192067)
19397 (163090)
18965 (150468)
12479 (145725)
5611 (129082)
17185 (116884)
6101 (100167)
1024 (90701)		 k = 121, 2500, 5184, 12321, and 17689 proven composite by condition 1.

k = 7260 proven composite by condition 2.
61 13484 7, 13, 31, 97   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 9642 (1M)
10572 (1M)		 1520 (287837)
10968 (102738)
198 (41855)
1644 (31715)
6168 (29180)
404 (18637)
8958 (17644)
11150 (13014)
6230 (12684)
12450 (12564)		  
62 8 3, 7   k = = 1 mod 61 (61) none - proven 3 (59)
4 (9)
6 (2)
5 (2)
2 (2)
7 (1)		  
63 187258666 5, 13, 37, 109, 3907   k = = 1 mod 2 (2)
k = = 1 mod 31 (31)		 177330 k's remaining at n=25K.

See k's at Riesel Base 63 remain.		 5189954 (25000)
1625398 (25000)
164097056 (24999)
105140986 (24999)
74448672 (24999)
49821932 (24999)
39348182 (24999)
136482716 (24998)
91621778 (24998)
78114558 (24998)		  
65 10 3, 11   k = = 1 mod 2 (2) none - proven 8 (10)
4 (9)
2 (4)
6 (1)		  
66 101954772 7, 17, 37, 67, 73, 613   k = = 1 mod 5 (5)
k = = 1 mod 13 (13)		 66553 k's remaining at n=25K.

See k's and test limits at Riesel Base 66 remain.		 37114584 (25005)
62598184 (24999)
31164044 (24998)
80012272 (24997)
833823 (24997)
91875750 (24995)
58804628 (24995)
14547242 (24993)
95244855 (24991)
67306928 (24991)		  
67 3144 5, 17, 449 All k where k = m^2
and m = = 4 or 13 mod 17:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*67^q - 1) *
     (m*67^q + 1)
   odd n:
     factor of 17		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 11 (11)		 1274 (400K)
2228 (400K)
2846 (400K)		 1886 (177962)
242 (105312)
2906 (41890)
128 (10592)
2244 (6600)
902 (3669)
1070 (3006)
494 (2953)
2492 (2730)
2922 (1932)		 k = 900 proven composite by partial algebraic factors.
68 22 3, 23   k = = 1 mod 67 (67) none - proven 7 (25395)
5 (13574)
11 (198)
8 (62)
10 (53)
3 (10)
14 (4)
2 (4)
9 (3)
20 (2)		  
69 6 5, 7 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*69^q - 1) *
     (m*69^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 17 (17)		 none - proven 2 (1) k = 4 proven composite by partial algebraic factors.
70 6176 13, 29, 71   k = = 1 mod 3 (3)
k = = 1 mod 23 (23)		 1776 (1M)
2202 (1M)		 5468 (864479)
729 (28625)
2699 (15455)
5925 (8850)
2621 (6247)
1461 (4034)
434 (3820)
2859 (3627)
5537 (3448)
6107 (3043)		  
71 1132052528 3, 13, 37, 73, 109, 1657, 2521   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 7 (7)		 8960 k's remaining for k<=1M at n=2.5K. To be shown later. 630014 (2500)
934054 (2499)
477574 (2499)
580814 (2496)
6260 (2496)
449392 (2495)
346234 (2495)
86518 (2495)
409792 (2493)
613550 (2492)		  
72 293 5, 17, 73   k = = 1 mod 71 (71) none - proven 4 (1119849)
79 (28009)
291 (26322)
116 (13887)
118 (4599)
67 (4308)
197 (3256)
24 (2648)
11 (2445)
18 (1494)		  
73 408 5, 13, 37 All k where k = m^2
and m = = 6 or 31 mod 37:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*73^q - 1) *
     (m*73^q + 1)
   odd n:
     factor of 37		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 none - proven 242 (2280)
302 (874)
122 (196)
200 (162)
48 (73)
404 (69)
54 (63)
222 (62)
42 (50)
26 (50)		 k = 36 proven composite by partial algebraic factors.
74 4 3, 5   k = = 1 mod 73 (73) none - proven 2 (132)
3 (2)		  
75 4086 7, 13, 19, 61   k = = 1 mod 2 (2)
k = = 1 mod 37 (37)		 856 (500K)
968 (500K)
1388 (500K)
1538 (500K)
3320 (500K)
3592 (500K)
3628 (500K)
3742 (500K)		 2490 (209649)
3708 (137166)
3362 (105670)
2854 (47919)
1312 (45281)
3284 (36123)
2148 (33163)
2336 (26174)
2304 (11585)
2500 (9629)		  
76 120 7, 11   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 none - proven 83 (1354)
90 (190)
113 (113)
27 (40)
87 (24)
20 (22)
102 (16)
15 (11)
65 (10)
54 (10)		  
77 14 3, 13   k = = 1 mod 2 (2)
k = = 1 mod 19 (19)		 none - proven 2 (14)
12 (2)
8 (2)
10 (1)
6 (1)
4 (1)		  
78 90059 5, 79, 1217   k = = 1 mod 7 (7)
k = = 1 mod 11 (11)		 63 k's remaining at n=100K.

See k's at Riesel Base 78 remain.		 3633 (94500)
68571 (91386)
51476 (88677)
78053 (84433)
58412 (83824)
45661 (73022)
11412 (72798)
72638 (70230)
23462 (69162)
23543 (62677)		  
79 1965996 5, 7, 43, 6163 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*79^q - 1) *
     (m*79^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 79*m^2
and m = = 2 or 3 mod 5:
   [Reverse condition 1]		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 13 (13)		 4993 k's remaining at n=100K.

See k's at Riesel Base 79 remain.		 265616 (99911)
1318598 (99763)
587234 (99744)
1632864 (99736)
458588 (99519)
749774 (99290)
1306286 (99243)
403134 (99218)
1360556 (99097)
1133436 (99085)		 k = 12^2, 18^2, 42^2, 48^2, 72^2, 78^2, (etc. pattern repeating every 30m where k not = = 1 mod 13) proven composite by condition 1.

k = 79*18^2, 79*42^2, 79*48^2, 79*72^2, 79*78^2, 79*102^2, 79*108^2, 79*132^2, and 79*138^2 proven composite by condition 2.
80 253 3, 37, 173   k = = 1 mod 79 (79) 31 (500K)
214 (500K)		 10 (423715)
170 (148256)
106 (16237)
154 (9753)
46 (5337)
232 (2997)
157 (2613)
169 (1959)
45 (1156)
218 (776)		  
81 74 7, 13, 73 All k = m^2 for all n; factors to:
(m*9^n - 1) *
(m*9^n + 1)		 k = = 1 mod 2 (2)
k = = 1 mod 5 (5)		 none - proven 42 (99)
18 (15)
30 (12)
60 (4)
40 (4)
24 (4)
14 (4)
58 (3)
72 (2)
48 (2)		 k = 4 and 64 proven composite by full algebraic factors.
82 22326 5, 83, 269   k = = 1 mod 3 (3) 66 k's remaining at n=100K.

See k's at Riesel Base 82 remain.		 15978 (99999)
21429 (96772)
18989 (96049)
17592 (83837)
22233 (75716)
12912 (74869)
5811 (72615)
16091 (65850)
18576 (64927)
4482 (63245)		  
83 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 41 (41)		 none - proven 2 (8)
6 (2)
4 (1)		  
84 16 5, 17 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*84^q - 1) *
     (m*84^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 83 (83) none - proven 14 (8)
11 (7)
8 (4)
12 (3)
15 (1)
13 (1)
10 (1)
7 (1)
6 (1)
5 (1)		 k = 4 and 9 proven composite by partial algebraic factors.
85 398534880 37, 43, 193, 2437   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 449684 k's remaining at n=2.5K. To be shown later. 396487112 (2500)
393117938 (2500)
392266922 (2500)
388605318 (2500)
386794730 (2500)
386014482 (2500)
385829696 (2500)
383492532 (2500)
379989594 (2500)
377578226 (2500)		  
86 28 3, 29   k = = 1 mod 5 (5)
k = = 1 mod 17 (17)		 none - proven 23 (112)
14 (38)
27 (14)
2 (10)
25 (9)
22 (5)
19 (5)
4 (5)
20 (2)
17 (2)		  
87 1660 7, 11, 13, 19   k = = 1 mod 2 (2)
k = = 1 mod 43 (43)		 172 (500K)
384 (500K)
562 (500K)
672 (500K)
714 (500K)
848 (500K)
862 (500K)
1132 (500K)
1154 (500K)
1418 (500K)		 1112 (143809)
1004 (76524)
1628 (42252)
472 (33116)
186 (30922)
536 (21534)
958 (17047)
898 (14455)
758 (13638)
508 (9016)		  
88 9702 13, 19, 31, 89 All k where k = m^2
and m = = 34 or 55 mod 89:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*88^q - 1) *
     (m*88^q + 1)
   odd n:
     factor of 89		 k = = 1 mod 3 (3)
k = = 1 mod 29 (29)		 1247 (500K)
2010 (500K)
2258 (500K)
2493 (500K)
2744 (500K)
3641 (500K)
4572 (500K)
5112 (500K)
5121 (500K)
5307 (500K)
6101 (500K)
6329 (500K)
6353 (500K)
6498 (500K)
6759 (500K)
7842 (500K)
7911 (500K)
7968 (500K)
8990 (500K)		 9326 (209654)
3168 (205764)
6393 (170870)
2013 (159972)
5606 (139558)
7386 (133598)
3773 (129945)
1782 (124030)
3819 (110272)
8810 (106956)		 No k's proven composite by algebraic factors.
89 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)		 none - proven 2 (60)  
90 27 7, 13 All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*90^q - 1) *
     (m*90^q + 1)
   odd n:
     factor of 13		 k = = 1 mod 89 (89) none - proven 6 (20)
11 (10)
10 (10)
13 (6)
15 (5)
12 (4)
7 (4)
24 (3)
20 (2)
17 (2)		 k = 25 proven composite by partial algebraic factors.
91 229058 23, 41, 101   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 35 k's remaining at n=200K.

See k's at Riesel Base 91 remain.		 28340 (195704)
85860 (177483)
219582 (169845)
189174 (165374)
199334 (162612)
5544 (146013)
197778 (125101)
146304 (124389)
97868 (121877)
103524 (121187)		  
92 32 3, 31   k = = 1 mod 7 (7)
k = = 1 mod 13 (13)		 none - proven 28 (99)
13 (35)
18 (26)
20 (6)
6 (6)
17 (4)
5 (4)
25 (3)
30 (2)
26 (2)		  
93 612 5, 47, 173   k = = 1 mod 2 (2)
k = = 1 mod 23 (23)		 424 (1M) 452 (65264)
284 (1863)
234 (1132)
92 (476)
46 (434)
270 (408)
474 (357)
212 (270)
518 (153)
122 (126)		  
94 39 5, 19 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*94^q - 1) *
     (m*94^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 31 (31)		 29 (1M) 14 (154)
24 (12)
26 (9)
36 (7)
18 (6)
33 (5)
27 (5)
2 (5)
35 (2)
12 (2)		 k = 9 proven composite by partial algebraic factors.
95 2510 3, 7, 13, 1303 k = 324:
   for even n let n=2*q; factors to:
     (18*95^q - 1) *
     (18*95^q + 1)
   odd n:
     covering set 7, 13, 229		 k = = 1 mod 2 (2)
k = = 1 mod 47 (47)		 632 (500K)
844 (500K)
1268 (500K)
1408 (500K)
1516 (500K)
1562 (500K)
1780 (500K)
1876 (500K)		 1414 (482691)
692 (316400)
1234 (300749)
448 (180933)
400 (174167)
46 (162025)
1628 (117720)
1336 (50225)
148 (41269)
1640 (29978)		  
96 38995 7, 67, 97, 1303 All k where k = m^2
and m = = 22 or 75 mod 97:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*96^q - 1) *
     (m*96^q + 1)
   odd n:
     factor of 97		 k = = 1 mod 5 (5)
k = = 1 mod 19 (19)		 30 k's remaining at n=100K.

See k's at Riesel Base 96 remain.		 3769 (92879)
28907 (89447)
13528 (86114)
19882 (82073)
37155 (76817)
9160 (71178)
5179 (66965)
32960 (60312)
7565 (59052)
4754 (56909)		 k = 484 proven composite by partial algebraic factors.
97 26354 5, 7, 13, 37, 73   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 132 k's remaining at n=100K.

See k's at Riesel Base 97 remain.		 8 (192335)
15152 (97082)
4346 (96442)
12132 (94245)
19424 (89672)
18914 (87535)
16122 (87073)
17402 (86494)
4892 (86458)
22274 (85941)		  
98 10 3, 11   k = = 1 mod 97 (97) none - proven 5 (10)
7 (3)
4 (3)
8 (2)
2 (2)
9 (1)
6 (1)
3 (1)		  
99 144 5, 13, 129 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*99^q - 1) *
     (m*99^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 7 (7)		 none - proven 124 (302)
90 (300)
28 (108)
14 (106)
40 (70)
24 (62)
100 (25)
66 (11)
104 (8)
132 (7)		 k = 4 proven composite by partial algebraic factors.
100 750 7, 13, 37 All k = m^2 for all n; factors to:
(m*10^n - 1) *
(m*10^n + 1)		 k = = 1 mod 3 (3)
k = = 1 mod 11 (11)		 none - proven 653 (717513)
74 (44709)
450 (5979)
302 (2132)
470 (1957)
630 (1691)
690 (1310)
557 (332)
467 (263)
666 (224)		 k = 9, 36, 81, 225, 324, 576, and 729 proven composite by full algebraic factors.
101 118 3, 17   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)		 none - proven 108 (28320)
68 (5410)
74 (966)
64 (559)
28 (113)
8 (112)
14 (104)
82 (87)
114 (61)
2 (42)		  
102 1635 7, 19, 79   k = = 1 mod 101 (101) 191 (500K)
207 (500K)
1082 (500K)
1369 (500K)		 1451 (188973)
1208 (178632)
653 (117255)
1607 (82644)
254 (58908)
1527 (49462)
1037 (43460)
32 (43302)
1296 (37715)
142 (22025)		  
103 1158 5, 7, 13, 19, 97 All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*103^q - 1) *
     (m*103^q + 1)
   odd n:
     factor of 13		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 17 (17)		 924 (1M) 584 (131076)
906 (77843)
612 (6047)
248 (3833)
234 (3705)
866 (2391)
1148 (2090)
300 (1805)
726 (1599)
636 (1166)		 No k's proven composite by algebraic factors.
104 4 3, 5   k = = 1 mod 103 (103) none - proven 2 (68)
3 (1)		  
105 170606 37, 53, 149 (Condition 1):
All k where k = m^2
and m = = 23 or 30 mod 53:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*105^q - 1) *
     (m*105^q + 1)
   odd n:
     factor of 53
(Condition 2):
All k where k = 105*m^2
and m = = 23 or 30 mod 53:
   [Reverse condition 1]		 k = = 1 mod 2 (2)
k = = 1 mod 13 (13)		 47 k's remaining at n=100K.

See k's at Riesel Base 105 remain.		 106582 (92330)
67186 (89208)
97292 (86636)
47872 (85065)
96088 (84744)
158418 (83223)
13302 (79410)
133194 (77197)
158404 (74353)
63672 (73281)		 k = 900, 5776, 18496, 33124, 58564, 82944, 121104 and 155236 proven composite by condition 1.

k = 94500 proven composite by condition 2.
106 1626615 17, 107, 661   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 7 (7)		 590 k's remaining at n=100K.

See k's at Riesel Base 106 remain.		 1473362 (99999)
131823 (99664)
1270110 (99656)
1146185 (99225)
353315 (98717)
1221834 (98651)
464487 (98583)
305484 (98120)
575463 (98015)
1062639 (97718)		  
107 686 3, 5, 229   k = = 1 mod 2 (2)
k = = 1 mod 53 (53)		 100 (500K)
200 (500K)
208 (500K)
250 (500K)
358 (500K)
382 (500K)
404 (500K)
436 (500K)
508 (500K)
536 (500K)
568 (500K)
596 (500K)
632 (500K)		 116 (455562)
118 (314663)
88 (273915)
172 (242649)
614 (129616)
104 (102608)
592 (66989)
130 (56601)
356 (31002)
2 (21910)		  
108 13406 7, 13, 61, 109 (Condition 1):
All k where k = m^2
and m = = 33 or 76 mod 109:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*108^q - 1) *
     (m*108^q + 1)
   odd n:
     factor of 109
(Condition 2):
All k where k = 3*m^2
and m = = 20 or 89 mod 109:
   even n:
     factor of 109
   for odd n let k = 3*m^2
   and let n=2*q-1; factors to:
     [m*6^n*3^q - 1] *
     [m*6^n*3^q + 1]		 k = = 1 mod 107 (107) 75 k's remaining at n=100K.

See k's at Riesel Base 108 remain.		 10322 (88080)
1999 (85188)
7557 (84180)
11882 (81547)
3439 (79524)
4686 (79010)
1159 (77107)
3573 (76352)
1465 (75209)
2148 (75018)		 k = 1089 and 5776 proven composite by condition 1.

k = 1200 proven composite by condition 2.
109 144 5, 11   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 84 (1M) 60 (3883)
92 (167)
128 (96)
38 (91)
18 (90)
98 (26)
126 (25)
8 (19)
56 (15)
114 (12)		  
110 38 3, 37 All k where k = m^2
and m = = 6 or 31 mod 37:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*110^q - 1) *
     (m*110^q + 1)
   odd n:
     factor of 37		 k = = 1 mod 109 (109) none - proven 23 (78120)
17 (2598)
37 (1689)
9 (77)
11 (42)
10 (17)
2 (16)
31 (9)
5 (6)
22 (5)		 k = 36 proven composite by partial algebraic factors.
111 12018 7, 61, 101   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 11 (11)		 2024 (479K)
2612 (479K)
3244 (479K)
4320 (479K)
7622 (479K)
7748 (479K)		 2582 (338032)
9710 (248035)
3438 (189659)
8884 (75375)
9444 (72601)
9344 (71404)
11374 (69540)
2092 (41902)
6972 (41496)
11272 (37082)		  
112 3843 5, 13, 113 All k where k = m^2
and m = = 15 or 98 mod 113:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*112^q - 1) *
     (m*112^q + 1)
   odd n:
     factor of 113		 k = = 1 mod 3 (3)
k = = 1 mod 37 (37)		 1662 (500K)
3327 (500K)		 948 (173968)
1268 (50536)
3414 (46200)
2319 (39352)
758 (35878)
3389 (24768)
3528 (20066)
1353 (7751)
498 (6038)
9 (5717)		 k = 225 proven composite by partial algebraic factors.
113 20 3, 19   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)		 none - proven 14 (308)
16 (5)
12 (3)
4 (3)
18 (2)
2 (2)
10 (1)
6 (1)		  
114 24 5, 23 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*114^q - 1) *
     (m*114^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 113 (113) none - proven 3 (63)
11 (27)
18 (21)
22 (20)
20 (3)
19 (2)
17 (2)
14 (2)
10 (2)
23 (1)		 k = 4 and 9 proven composite by partial algebraic factors.
115 78966 17, 29, 389 (Condition 1):
All k where k = m^2
and m = = 12 or 17 mod 29:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*115^q - 1) *
     (m*115^q + 1)
   odd n:
     factor of 29
(Condition 2):
All k where k = 115*m^2
and m = = 12 or 17 mod 29:
   [Reverse condition 1]		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 19 (19)		 48 k's remaining at n=100K.

See k's at Riesel Base 115 remain.		 66488 (84399)
8322 (81658)
75662 (80051)
42450 (71826)
38540 (68594)
36686 (66631)
72266 (59649)
29958 (55851)
51882 (51815)
70152 (49377)		 k = 144, 26244, and 34596 proven composite by condition 1.

k = 16560 proven composite by condition 2.
116 14 3, 13   k = = 1 mod 5 (5)
k = = 1 mod 23 (23)		 none - proven 9 (249)
5 (156)
2 (32)
13 (15)
10 (11)
12 (2)
8 (2)
7 (1)
4 (1)
3 (1)		  
117 6432 5, 37, 59   k = = 1 mod 2 (2)
k = = 1 mod 29 (29)		 1358 (300K)
3128 (300K)
3440 (300K)
3480 (300K)
4476 (300K)
4898 (300K)
5014 (300K)
5486 (300K)		 5840 (96286)
3368 (53482)
1956 (32421)
6034 (30641)
222 (26806)
4306 (19706)
6214 (17248)
2888 (13796)
3154 (11963)
2112 (11296)		  
118 50 7, 17   k = = 1 mod 3 (3)
k = = 1 mod 13 (13)		 none - proven 29 (599)
18 (393)
6 (210)
8 (85)
42 (30)
41 (26)
48 (18)
5 (15)
39 (8)
15 (7)		  
119 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 59 (59)		 none - proven 2 (28)  
121 3294 7, 19, 37 All k = m^2 for all n; factors to:
(m*11^n - 1) *
(m*11^n + 1)		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 none - proven 2622 (810960)
3110 (48054)
174 (16667)
62 (13101)
1122 (10705)
2868 (3697)
2690 (3012)
438 (1445)
872 (1340)
2718 (838)		 k = 144, 324, 900, 1764, and 2304 proven composite by full algebraic factors.
122 14 3, 5, 13   k = = 1 mod 11 (11) none - proven 13 (43)
8 (26)
11 (10)
2 (6)
10 (3)
6 (2)
5 (2)
3 (2)
9 (1)
7 (1)		  
123 154 5, 17, 31   k = = 1 mod 2 (2)
k = = 1 mod 61 (61)		 24 (816K) 86 (176510)
98 (1666)
148 (1213)
102 (180)
44 (161)
142 (140)
72 (108)
16 (75)
88 (73)
108 (66)		  
124 3730449 5, 7, 2179, 5167 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*124^q - 1) *
     (m*124^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 31*m^2
and m = = 1 or 4 mod 5:
   even n:
     factor of 5
   for odd n let k = 31*m^2
   and let n=2*q-1; factors to:
     [m*2^n*31^q - 1] *
     [m*2^n*31^q + 1]		 k = = 1 mod 3 (3)
k = = 1 mod 41 (41)		 54450 k's remaining at n>=10K.

See k's and test limits at Riesel Base 124 remain.		 28586 (24975)
19176 (24963)
42446 (24921)
96176 (24861)
25586 (24749)
95484 (24710)
63249 (24668)
86094 (24628)
43851 (24389)
73194 (24366)		 k = 3^2, 12^2, 18^2, 27^2, 33^2, 42^2, (etc. pattern repeating every 15m where k not = = 1 mod 41) proven composite by condition 1.

k = 31*6^2, 31*9^2, 31*21^2, 31*24^2, 31*36^2, 31*39^2, (etc. pattern repeating every 15m where k not = = 1 mod 41) proven composite by condition 2.
125 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 31 (31)		 none - proven 6 (24)
2 (2)
4 (1)		  
126 2767077 13, 19, 127, 829   k = = 1 mod 5 (5) 4532 k's remaining at n=25K.

See k's at Riesel Base 126 remain.		 783948 (24993)
2010375 (24990)
2709635 (24985)
2034224 (24976)
1942803 (24971)
2529014 (24959)
2585304 (24948)
997980 (24945)
2726244 (24908)
2334075 (24908)		  
129 14 5, 13 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*129^q - 1) *
     (m*129^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2) none - proven 12 (228)
10 (1)
8 (1)
6 (1)
2 (1)		 k = 4 proven composite by partial algebraic factors.
130 2443673 7, 31, 131, 811   k = = 1 mod 3 (3)
k = = 1 mod 43 (43)		 4115 k's remaining at n=25K.

See k's at Riesel Base 130 remain.		 403481 (24997)
1400214 (24987)
554114 (24958)
1846167 (24956)
273443 (24954)
1677812 (24949)
612417 (24949)
2204316 (24947)
200285 (24935)
2171177 (24907)		  
131 10 3, 11   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 13 (13)		 none - proven 8 (196)
2 (4)
4 (1)		  
132 20 7, 19   k = = 1 mod 131 (131) none - proven 18 (62)
3 (38)
8 (11)
19 (9)
4 (3)
13 (2)
7 (2)
6 (2)
17 (1)
16 (1)		  
133 3684 5, 29, 67   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 11 (11)		 926 (600K) 1004 (238300)
2988 (75001)
872 (50411)
1554 (19992)
2748 (9421)
2486 (6646)
2798 (6240)
2250 (5962)
1080 (5071)
282 (2571)		  
134 4 3, 5   k = = 1 mod 7 (7)
k = = 1 mod 19 (19)		 none - proven 2 (2)
3 (1)		  
135 3112 7, 17, 61, 229 (Condition 1):
All k where k = m^2
and m = = 4 or 13 mod 17:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*135^q - 1) *
     (m*135^q + 1)
   odd n:
     factor of 17
(Condition 2):
All k where k = 135*m^2
and m = = 4 or 13 mod 17:
   [Reverse condition 1]		 k = = 1 mod 2 (2)
k = = 1 mod 67 (67)		 240 (300K)
1038 (300K)
1240 (300K)
1786 (300K)
2328 (300K)
2930 (300K)		 2060 (252066)
662 (174116)
996 (159478)
2702 (115472)
1206 (58842)
2622 (55334)
868 (44467)
2872 (40864)
2370 (18851)
928 (11538)		 k = 16, 900 and 1444 proven composite by condition 1.

k = 2160 proven composite by condition 2.
136 90693 7, 43, 61, 137 All k where k = m^2
and m = = 37 or 100 mod 137:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*136^q - 1) *
     (m*136^q + 1)
   odd n:
     factor of 137		 k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 51 k's remaining at n=100K.

See k's at Riesel Base 136 remain.		 64028 (97970)
17948 (93193)
12605 (84371)
14715 (79844)
88254 (76152)
9848 (74282)
63293 (63646)
34662 (60921)
83900 (58077)
66993 (53958)		 k = 56169 proven composite by partial algebraic factors.
137 22 3, 23   k = = 1 mod 2 (2)
k = = 1 mod 17 (17)		 none - proven 16 (231)
20 (8)
10 (5)
14 (4)
12 (2)
8 (2)
2 (2)
6 (1)
4 (1)		  
138 1806 5, 13, 139   k = = 1 mod 137 (137) 408 (300K)
688 (300K)
831 (300K)
1074 (300K)
1743 (300K)		 421 (272919)
773 (249730)
372 (103160)
1368 (66926)
1087 (55582)
1258 (54256)
557 (52295)
359 (47249)
291 (35886)
9 (35685)		  
139 6 5, 7   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 23 (23)		 none - proven 2 (1)  
140 46 3, 47   k = = 1 mod 139 (139) none - proven 38 (448)
11 (108)
5 (30)
29 (18)
32 (16)
14 (16)
33 (12)
40 (9)
41 (8)
17 (8)		  
142 12 11, 13   k = = 1 mod 3 (3)
k = = 1 mod 47 (47)		 none - proven 3 (26)
11 (14)
8 (7)
6 (3)
9 (1)
5 (1)
2 (1)		  
143 1226 3, 5, 409   k = = 1 mod 2 (2)
k = = 1 mod 71 (71)		 206 (500K)
284 (500K)
410 (500K)
482 (500K)
494 (500K)
536 (500K)
884 (500K)
892 (500K)
968 (500K)
1094 (500K)
1124 (500K)
1162 (500K)
1186 (500K)
1198 (500K)		 682 (203335)
250 (181829)
506 (175854)
502 (171279)
656 (106282)
1004 (89560)
688 (64933)
1042 (54527)
434 (54504)
316 (22437)		  
144 59 5, 29 All k = m^2 for all n; factors to:
(m*12^n - 1) *
(m*12^n + 1)		 k = = 1 mod 11 (11)
k = = 1 mod 13 (13)		 none - proven 39 (964)
30 (519)
46 (97)
58 (35)
2 (24)
57 (20)
15 (10)
54 (8)
44 (6)
26 (5)		 k = 4, 9, 16, 25, 36, and 49 proven composite by full algebraic factors.
145 257324 7, 19, 73, 157 All k where k = m^2
and m = = 27 or 46 mod 73:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*145^q - 1) *
     (m*145^q + 1)
   odd n:
     factor of 73		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 120 k's remaining at n=100K.

See k's at Riesel Base 145 remain.		 11930 (99169)
142890 (98911)
145748 (97861)
120524 (96609)
147150 (96275)
226308 (85213)
88358 (81300)
244170 (80349)
51852 (80319)
65516 (79686)		 k = 36864 and 60516 proven composite by partial algebraic factors.
146 8 3, 7   k = = 1 mod 5 (5)
k = = 1 mod 29 (29)		 none - proven 5 (30)
2 (16)
4 (5)
3 (3)
7 (1)		  
147 79956 5, 37, 2161 (Condition 1):
All k where k = m^2
and m = = 6 or 31 mod 37:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*147^q - 1) *
     (m*147^q + 1)
   odd n:
     factor of 37
(Condition 2):
All k where k = 3*m^2
and m = = 5 or 32 mod 37:
   even n:
     factor of 37
   for odd n let k = 3*m^2
   and let n=2*q-1; factors to:
     [m*7^n*3^q - 1] *
     [m*7^n*3^q + 1]		 k = = 1 mod 2 (2)
k = = 1 mod 73 (73)		 166 k's remaining at n=100K.

See k's at Riesel Base 147 remain.		 26750 (97936)
6158 (96375)
15514 (96148)
6474 (92352)
946 (89286)
50516 (89146)
33928 (88946)
76484 (88361)
64172 (88086)
17204 (86716)		 k = 36, 4624, 6400, 20164, 23716, 46656, and 51984 proven composite by condition 1.

k = 3072, 5292, 33708, and 40368 proven composite by condition 2.
148 5214 5, 13, 149 All k where k = m^2
and m = = 44 or 105 mod 149:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*148^q - 1) *
     (m*148^q + 1)
   odd n:
     factor of 149		 k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 1743 (300K)
3012 (300K)
4757 (300K)
4844 (300K)		 4701 (213315)
3954 (175188)
1256 (158963)
3171 (63359)
4191 (44097)
746 (39249)
3428 (28485)
4634 (26677)
801 (23003)
1052 (20835)		 No k's proven composite by algebraic factors.
149 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 37 (37)		 none - proven 2 (4)  
150 49074 7, 31, 103, 151   k = = 1 mod 149 (149) 71 k's remaining at n=100K.

See k's at Riesel Base 150 remain.		 17554 (99646)
32797 (97430)
32399 (96963)
37966 (96107)
10505 (93910)
42643 (93875)
5674 (92155)
6492 (90168)
32135 (90000)
31409 (89441)		  
151 349922 13, 19, 877   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 365 k's remaining at n=320K.

See k's at Riesel Base 151 remain.		 74270 (315734)
275102 (311399)
144912 (310514)
164978 (309413)
10880 (302997)
202064 (302700)
193020 (301686)
78792 (294324)
128448 (284308)
318564 (283711)		  
152 16 3, 17   k = = 1 mod 151 (151) none - proven 14 (343720)
2 (796)
13 (23)
11 (14)
5 (12)
10 (5)
3 (3)
15 (2)
8 (2)
12 (1)		  
153 34 7, 11   k = = 1 mod 2 (2)
k = = 1 mod 19 (19)		 none - proven 12 (21659)
22 (23)
32 (8)
4 (3)
30 (2)
26 (2)
10 (2)
6 (2)
2 (2)
28 (1)		  
154 216 5, 31 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*154^q - 1) *
     (m*154^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 17 (17)		 none - proven 6 (1989)
63 (1743)
39 (326)
114 (210)
24 (106)
74 (82)
14 (78)
29 (62)
54 (30)
179 (24)		 k = 9 and 144 proven composite by partial algebraic factors.
155 14 3, 13   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 11 (11)		 none - proven 2 (2)
10 (1)
6 (1)
4 (1)		  
157 3554 5, 17, 79   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 13 (13)		 1026 (500K)
1296 (500K)
3098 (500K)
3104 (500K)		 1974 (118956)
1346 (102793)
2558 (31648)
2126 (30626)
2216 (21521)
2058 (16127)
3396 (13282)
2892 (12188)
2118 (11811)
3294 (9976)		  
158 52 3, 53   k = = 1 mod 157 (157) 29 (500K)
44 (500K)		 47 (273942)
34 (5223)
46 (147)
41 (94)
38 (74)
39 (49)
7 (39)
9 (35)
20 (34)
8 (20)		  
159 516 5, 7, 13, 103 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*159^q - 1) *
     (m*159^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 79 (79)		 none - proven 172 (561319)
234 (47174)
274 (22786)
394 (7348)
376 (2997)
412 (2790)
206 (1545)
364 (1176)
44 (1140)
146 (961)		 k = 4, 64, 144, 324, and 484 proven composite by partial algebraic factors.
160 183 7, 23   k = = 1 mod 3 (3)
k = = 1 mod 53 (53)		 116 (600K) 149 (7715)
20 (7570)
68 (3534)
132 (656)
180 (507)
108 (320)
36 (261)
56 (116)
179 (76)
53 (73)		  
161 3154 3, 13, 17, 41   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)		 194 (300K)
344 (300K)
378 (300K)
428 (300K)
448 (300K)
892 (300K)
1240 (300K)
1438 (300K)
1730 (300K)
1988 (300K)
2042 (300K)
2200 (300K)
2878 (300K)
3008 (300K)		 1262 (249078)
2452 (220943)
1504 (213809)
1754 (85972)
2294 (77542)
2998 (77319)
1600 (52191)
190 (51683)
800 (43732)
2572 (41617)		  
162 3259 5, 163, 181   k = = 1 mod 7 (7)
k = = 1 mod 23 (23)		 2118 (500K)
2841 (500K)		 2018 (194314)
2954 (95124)
1308 (82803)
1607 (28018)
58 (13758)
2809 (12303)
423 (8898)
3098 (8723)
653 (8335)
1781 (8327)		  
163 372 7, 19, 67   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 254 (600K) 144 (49401)
86 (48778)
102 (6690)
146 (1418)
246 (814)
158 (797)
42 (775)
368 (368)
204 (208)
128 (174)		  
164 4 3, 5   k = = 1 mod 163 (163) none - proven 2 (2)
3 (1)		  
165 646 7, 13, 43   k = = 1 mod 2 (2)
k = = 1 mod 41 (41)		 none - proven 484 (22073)
400 (7105)
144 (5869)
450 (3515)
204 (1195)
582 (395)
498 (197)
326 (133)
170 (101)
588 (93)		  
166 127754 7, 13, 43, 167   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 11 (11)		 91 k's remaining at n=100K.

See k's at Riesel Base 166 remain.		 77787 (92470)
95024 (90229)
60048 (79571)
100584 (74518)
74507 (72420)
32337 (71241)
222 (67989)
31259 (67089)
126513 (65703)
22668 (63231)		  
167 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 83 (83)		 none - proven 4 (1865)
6 (34)
2 (8)		  
168 4744 5, 13, 17, 73 (Condition 1):
All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*168^q - 1) *
     (m*168^q + 1)
   odd n:
     factor of 13
(Condition 2):
All k where k = 42*m^2
and m = = 3 or 10 mod 13:
   even n:
     factor of 13
   for odd n let k = 42*m^2
   and let n=2*q-1; factors to:
     [m*2^n*42^q - 1] *
     [m*2^n*42^q + 1]		 k = = 1 mod 167 (167) 41 k's remaining at n=100K.

See k's at Riesel Base 168 remain.		 1689 (68676)
3309 (63795)
4471 (54466)
4185 (53498)
2846 (50670)
1717 (38259)
1829 (34296)
2885 (34186)
2942 (33546)
2523 (31457)		 k = 25, 64, 324, 441, 961, 1156, 1936, 2209, 3249, and 3600 proven composite by condition 1.

k = 378 and 4200 proven composite by condition 2.
169 186 5, 17 All k = m^2 for all n; factors to:
(m*13^n - 1) *
(m*13^n + 1)		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 none - proven 24 (2586)
54 (1108)
26 (151)
44 (52)
30 (17)
146 (15)
102 (10)
126 (7)
84 (6)
20 (5)		 k = 144 proven composite by full algebraic factors.
170 20 3, 19   k = = 1 mod 13 (13) none - proven 2 (166428)
8 (15422)
18 (360)
11 (108)
5 (38)
13 (13)
9 (7)
7 (3)
4 (3)
17 (2)		  
171 112790 7, 13, 37, 43, 67   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 17 (17)		 75 k's remaining at n=100K.

See k's at Riesel Base 171 remain.		 55008 (93265)
112664 (92686)
31002 (90264)
55312 (89116)
53018 (86740)
39690 (86597)
31050 (77135)
39820 (71361)
57180 (70673)
32194 (65957)		  
172 1262 7, 13, 109 All k where k = m^2
and m = = 80 or 93 mod 173:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*172^q - 1) *
     (m*172^q + 1)
   odd n:
     factor of 173		 k = = 1 mod 3 (3)
k = = 1 mod 19 (19)		 219 (300K)
387 (300K)
1140 (300K)		 576 (132695)
693 (61919)
672 (12306)
1118 (8572)
632 (8400)
788 (7291)
701 (6919)
768 (6808)
864 (6228)
1158 (5755)		 No k's proven composite by algebraic factors.
173 28 3, 29   k = = 1 mod 2 (2)
k = = 1 mod 43 (43)		 22 (1M) 14 (172)
24 (29)
20 (4)
2 (4)
10 (3)
26 (2)
18 (2)
12 (2)
8 (2)
6 (2)		  
174 6 5, 7 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*174^q - 1) *
     (m*174^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 173 (173) none - proven 5 (2)
3 (1)
2 (1)		 k = 4 proven composite by partial algebraic factors.
176 58 3, 59   k = = 1 mod 5 (5)
k = = 1 mod 7 (7)		 none - proven 34 (79)
53 (16)
32 (12)
25 (9)
4 (9)
35 (6)
20 (6)
2 (6)
54 (5)
42 (5)		  
177 268 5, 13, 89   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)		 none - proven 64 (340147)
36 (2957)
242 (1953)
44 (1711)
266 (1270)
228 (315)
200 (288)
58 (219)
172 (200)
148 (98)		  
178 87 13, 19, 43   k = = 1 mod 3 (3)
k = = 1 mod 59 (59)		 none - proven 80 (3268)
11 (177)
6 (118)
21 (89)
57 (47)
14 (44)
51 (18)
3 (14)
83 (13)
66 (13)		  
179 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 89 (89)		 none - proven 2 (2)  
180 7674582 7, 31, 181, 1051 (Condition 1):
All k where k = m^2
and m = = 19 or 162 mod 181:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*180^q - 1) *
     (m*180^q + 1)
   odd n:
     factor of 181
(Condition 2):
All k where k = 5*m^2
and m = = 67 or 114 mod 181:
   even n:
     factor of 181
   for odd n let k = 5*m^2
   and let n=2*q-1; factors to:
     [m*6^n*5^q - 1] *
     [m*6^n*5^q + 1]		 k = = 1 mod 179 (179) 110328 k's remaining at n=2.5K. To be shown later. 6911474 (2500)
6621509 (2500)
6270700 (2500)
6152204 (2500)
5853556 (2500)
5427018 (2500)
5049031 (2500)
4753348 (2500)
4709004 (2500)
4362742 (2500)		 k = 361, 26244, 40000, 117649, 145161, 274576, 315844, 497025, 552049, 784996, 853776, 1138489, 1221025, 1557504, 1653796, 2042041, 2152089, 2715904, 3345241, 3888784, 4040100, 4635409, 4800481, 5447556, 5626384, 6325225, 6517809, 7268416, and 7474756 proven composite by condition 1.

k = 22445, 64980, 307520, 435125, 920205, 1132880, 1860500, 2158245, 3128405, 3511220, 4723920, 5191805, 6647045, and 7200000 proven composite by condition 2.
181 300 7, 13   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 168 (600K) 272 (178)
284 (123)
210 (107)
258 (38)
174 (38)
14 (29)
170 (25)
62 (24)
264 (23)
194 (22)		  
182 62 3, 61   k = = 1 mod 181 (181) none - proven 43 (502611)
26 (990)
29 (632)
54 (329)
7 (209)
44 (152)
58 (127)
47 (122)
59 (96)
40 (41)		  
183 208 5, 17, 23   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 13 (13)		 none - proven 114 (1116)
68 (110)
206 (78)
166 (78)
102 (40)
26 (37)
186 (21)
198 (17)
100 (13)
42 (11)		  
184 36 5, 37 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*184^q - 1) *
     (m*184^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 61 (61)		 none - proven 11 (15)
24 (8)
14 (8)
3 (6)
35 (2)
33 (2)
32 (2)
29 (2)
20 (2)
18 (2)		 k = 9 proven composite by partial algebraic factors.
185 32 3, 31   k = = 1 mod 2 (2)
k = = 1 mod 23 (23)		 none - proven 10 (6783)
30 (14)
20 (10)
12 (8)
8 (8)
26 (6)
14 (4)
22 (3)
16 (3)
2 (2)		  
186 67 11, 17   k = = 1 mod 5 (5)
k = = 1 mod 37 (37)		 none - proven 12 (112717)
32 (388)
43 (44)
44 (14)
35 (13)
52 (11)
58 (9)
42 (7)
49 (5)
9 (5)		  
187 3524 5, 13, 47   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 31 (31)		 1182 (300K)
1598 (300K)
1926 (300K)
3338 (300K)		 2868 (212559)
2492 (100021)
2210 (27237)
2400 (16396)
3236 (8617)
3432 (7193)
3054 (4708)
422 (3502)
234 (2544)
2718 (2147)		  
188 8 3, 7   k = = 1 mod 11 (11)
k = = 1 mod 17 (17)		 none - proven 6 (950)
5 (40)
7 (7)
2 (2)
4 (1)
3 (1)		  
189 56 5, 19 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*189^q - 1) *
     (m*189^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 47 (47)		 none - proven 34 (2286)
50 (555)
52 (33)
38 (19)
24 (14)
54 (6)
44 (6)
14 (4)
26 (3)
6 (3)		 k = 4 proven composite by partial algebraic factors.
190 626861 13, 89, 191, 1753   k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 554 k's remaining at n=25K.

See k's at Riesel Base 190 remain.		 341672 (24869)
235721 (24827)
27312 (24808)
453725 (24761)
257607 (24704)
250925 (24652)
120992 (24533)
75617 (24413)
617897 (24310)
551280 (24219)		  
191 260 3, 29, 37   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 19 (19)		 204 (500K)
254 (500K)		 222 (6271)
152 (5704)
212 (5068)
64 (3323)
68 (3150)
92 (1370)
2 (970)
184 (277)
190 (263)
50 (188)		  
192 13897 5, 73, 193 All k where k = m^2
and m = = 81 or 112 mod 193:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*192^q - 1) *
     (m*192^q + 1)
   odd n:
     factor of 193		 k = = 1 mod 191 (191) 113 k's remaining at n=100K.

See k's at Riesel Base 192 remain.		 10909 (89859)
2486 (88582)
49 (88335)
2258 (86531)
7511 (85174)
12732 (85108)
12807 (84820)
9344 (83216)
1023 (78795)
2423 (77515)		 k = 6561 and 12544 proven composite by partial algebraic factors.
193 80802 5, 97, 149 All k where k = m^2
and m = = 22 or 75 mod 97:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*193^q - 1) *
     (m*193^q + 1)
   odd n:
     factor of 97		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 232 k's remaining at n=100K.

See k's at Riesel Base 193 remain.		 34296 (97549)
40464 (96552)
37502 (93942)
11384 (93660)
16346 (92666)
31970 (92615)
9408 (91974)
39600 (91399)
43856 (87433)
49898 (87398)		 k = 46656 proven composite by partial algebraic factors.
194 4 3, 5   k = = 1 mod 193 (193) none - proven 2 (42)
3 (3)		  
196 2215067 41, 197, 937 All k = m^2 for all n; factors to:
(m*14^n - 1) *
(m*14^n + 1)		 k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 13 (13)		 1992 k's remaining at n=25K.

See k's at Riesel Base 196 remain.		 771732 (24939)
1480667 (24879)
891818 (24770)
496047 (24755)
1848225 (24735)
1407327 (24735)
823658 (24719)
965910 (24676)
491097 (24603)
1255679 (24589)		 k = 3^2, 15^2, 18^2, 30^2, 33^2, 42^2, 45^2, 48^2, 57^2, 60^2, 63^2, 72^2, 75^2, 78^2, 87^2, 93^2, 102^2, 108^2, 117^2, 120^2, 123^2, 132^2, 135^2, 138^2, 147^2, 150^2, 153^2, 162^2, 165^2, 177^2, 180^2, 192^2, 195^2, (etc. pattern repeating every 195m) proven composite by full algebraic factors.
197 10 3, 11   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)		 none - proven 2 (2)
6 (1)
4 (1)		  
198 3662 7, 13, 433   k = = 1 mod 197 (197) 29 k's remaining at n=100K.

See k's at Riesel Base 198 remain.		 2661 (95399)
1284 (73379)
807 (50662)
2791 (48837)
2187 (43879)
2388 (43718)
848 (40132)
947 (36807)
3420 (35891)
1922 (31592)		  
199 13224 5, 7, 13, 433 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*199^q - 1) *
     (m*199^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 11 (11)		 43 k's remaining at n=100K.

See k's at Riesel Base 199 remain.		 656 (96495)
10304 (95542)
2756 (91263)
3176 (80841)
10566 (70197)
2204 (69888)
3714 (66858)
4044 (57548)
12644 (56436)
7544 (49834)		 k = 324, 1764, 2304, 5184, 10404, and 11664 proven composite by partial algebraic factors.
200 68 3, 67   k = = 1 mod 199 (199) none - proven 38 (131900)
58 (102363)
53 (45666)
51 (44252)
23 (31566)
19 (29809)
13 (12053)
37 (597)
62 (126)
16 (89)		  
201 3669230 7, 19, 101, 2137 All k where k = m^2
and m = = 10 or 91 mod 101:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*201^q - 1) *
     (m*201^q + 1)
   odd n:
     factor of 101		 k = = 1 mod 2 (2)
k = = 1 mod 5 (5)		 9769 k's remaining at n=25K.

See k's at Riesel Base 201 remain.		 2980884 (24990)
2187724 (24968)
1460594 (24942)
2679334 (24927)
2909292 (24923)
16204 (24918)
2831558 (24915)
244120 (24915)
3269268 (24912)
2481084 (24894)		 k = 100, 36864, 44944, 636804, 669124, 1000000, 1040400, 1444804, 1493284, 3268864, and 3341584 proven composite by partial algebraic factors.
202 57 7, 29   k = = 1 mod 3 (3)
k = = 1 mod 67 (67)		 none - proven 8 (155771)
3 (262)
53 (260)
15 (201)
20 (70)
24 (24)
14 (17)
2 (17)
27 (16)
36 (9)		  
203 14 3, 5, 13   k = = 1 mod 2 (2)
k = = 1 mod 101 (101)		 none - proven 2 (4)
12 (3)
8 (2)
10 (1)
6 (1)
4 (1)		  
204 81 5, 41 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*204^q - 1) *
     (m*204^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 51*m^2
and m = = 1 or 4 mod 5:
   even n:
     factor of 5
   for odd n let k = 51*m^2
   and let n=2*q-1; factors to:
     [m*2^n*51^q - 1] *
     [m*2^n*51^q + 1]		 k = = 1 mod 7 (7)
k = = 1 mod 29 (29)		 none - proven 79 (10346)
54 (10188)
53 (1040)
46 (59)
35 (58)
16 (23)
24 (20)
74 (6)
77 (5)
70 (5)		 k = 4, 9, and 49 proven composite by condition 1.

k = 51 proven composite by condition 2.
205 8450016 7, 13, 103, 2011   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 17 (17)		 33171 k's remaining at n=2.5K. To be shown later. 8351394 (2500)
8003408 (2500)
7246164 (2500)
5113088 (2500)
4062122 (2500)
2402976 (2500)
7677420 (2499)
6121176 (2499)
5767040 (2499)
4390962 (2499)		  
206 22 3, 23   k = = 1 mod 5 (5)
k = = 1 mod 41 (41)		 none - proven 5 (108)
7 (59)
20 (20)
10 (7)
19 (5)
17 (4)
12 (4)
8 (4)
18 (3)
9 (3)		  
207 38572 5, 7, 13, 157, 181 (Condition 1):
All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*207^q - 1) *
     (m*207^q + 1)
   odd n:
     factor of 13
(Condition 2):
All k where k = 23*m^2
and m = = 2 or 11 mod 13:
   even n:
     factor of 13
   for odd n let k = 23*m^2
   and let n=2*q-1; factors to:
     [m*3^n*23^q - 1] *
     [m*3^n*23^q + 1]		 k = = 1 mod 2 (2)
k = = 1 mod 103 (103)		 280 k's remaining at n=100K.

See k's at Riesel Base 207 remain.		 27650 (96826)
15196 (95894)
5524 (92860)
5602 (92258)
6966 (91555)
29436 (91355)
5952 (89637)
34932 (87105)
25414 (85756)
20122 (85006)		 k = 64, 324, 1156, 1936, 3600, 4900, 7396, 9216, 12544, 14884, 19044, 21904, 26896, 30276, and 36100 proven composite by condition 1.

k = 92, 13248, and 18032 proven composite by condition 2.
208 56 11, 19   k = = 1 mod 3 (3)
k = = 1 mod 23 (23)		 none - proven 53 (80)
18 (74)
32 (24)
54 (8)
29 (7)
12 (7)
30 (6)
2 (6)
45 (5)
35 (5)		  
209 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 13 (13)		 none - proven 2 (6)  
210 80176412 13, 73, 109, 211, 607   k = = 1 mod 11 (11)
k = = 1 mod 19 (19)		 239583 k's remaining at n=2.5K. To be shown later. 80147083 (2500)
79436250 (2500)
78628387 (2500)
76482476 (2500)
76380897 (2500)
75608558 (2500)
75357493 (2500)
74417167 (2500)
72430760 (2500)
72220528 (2500)		  
211 5058 13, 31, 37 All k where k = m^2
and m = = 23 or 30 mod 53:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*211^q - 1) *
     (m*211^q + 1)
   odd n:
     factor of 53		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 7 (7)		 2172 (300K)
2810 (300K)
3714 (300K)
4910 (300K)		 2778 (6794)
3590 (4534)
1218 (3804)
1028 (3593)
1602 (2539)
4904 (2490)
2348 (2410)
128 (1567)
2102 (1485)
32 (1469)		 k = 900 proven composite by partial algebraic factors.
212 70 3, 71   k = = 1 mod 211 (211) 14 (300K)
36 (300K)
53 (300K)
67 (300K)		 44 (62692)
37 (35493)
4 (34413)
13 (2807)
28 (1507)
26 (518)
51 (355)
3 (282)
25 (161)
66 (139)		  
213 534 5, 13, 107   k = = 1 mod 2 (2)
k = = 1 mod 53 (53)		 294 (600K) 522 (37299)
352 (8827)
36 (6429)
368 (2797)
304 (2281)
102 (1398)
472 (860)
104 (541)
128 (533)
496 (499)		  
214 44 5, 43 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*214^q - 1) *
     (m*214^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 71 (71)		 11 (1M) 42 (2230)
23 (78)
29 (44)
30 (17)
33 (14)
41 (11)
38 (10)
39 (4)
32 (4)
8 (4)		 k = 9 proven composite by partial algebraic factors.
215 15358 3, 29, 797   k = = 1 mod 2 (2)
k = = 1 mod 107 (107)		 237 k's remaining at n=100K.

See k's at Riesel Base 215 remain.		 10876 (98509)
7288 (96217)
284 (95532)
11182 (93555)
13504 (93093)
2704 (90573)
10784 (90468)
4796 (88856)
14536 (87503)
3290 (83852)		  
216 92 7, 31 All k = m^3 for all n; factors to:
(m*6^n - 1) *
(m^2*36^n + m*6^n + 1)		 k = = 1 mod 5 (5)
k = = 1 mod 43 (43)		 none - proven 55 (1004)
69 (774)
83 (426)
49 (377)
48 (26)
10 (21)
79 (19)
67 (11)
57 (11)
9 (11)		 k = 8, 27, and 64 proven composite by full algebraic factors.
217 4688 5, 17, 109 All k where k = m^2
and m = = 33 or 76 mod 109:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*217^q - 1) *
     (m*217^q + 1)
   odd n:
     factor of 109		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 1376 (500K)
2642 (500K)		 3792 (255934)
4416 (227937)
458 (199724)
1290 (133478)
1106 (90905)
438 (36640)
50 (36180)
2226 (27255)
1268 (27102)
3506 (15762)		 No k's proven composite by algebraic factors.
218 74 3, 73   k = = 1 mod 7 (7)
k = = 1 mod 31 (31)		 53 (500K)
59 (500K)		 4 (23049)
72 (6352)
37 (5867)
23 (3966)
49 (2419)
35 (1734)
9 (177)
26 (170)
62 (140)
46 (67)		  
219 34 5, 11 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*219^q - 1) *
     (m*219^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 109 (109)		 none - proven 16 (423)
14 (32)
10 (18)
2 (15)
8 (10)
12 (9)
6 (5)
18 (3)
32 (2)
24 (2)		 k = 4 proven composite by partial algebraic factors.
220 324 13, 17   k = = 1 mod 3 (3)
k = = 1 mod 73 (73)		 none - proven 305 (17494)
233 (5978)
285 (3572)
186 (1828)
39 (1708)
246 (1100)
284 (816)
92 (719)
155 (490)
11 (405)		  
221 38 3, 37   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 11 (11)		 32 (600K) 20 (230)
2 (18)
14 (16)
10 (15)
28 (9)
18 (4)
30 (2)
8 (2)
24 (1)
22 (1)		  
222 88530 7, 31, 43, 223   k = = 1 mod 13 (13)
k = = 1 mod 17 (17)		 258 k's remaining at n=100K.

See k's at Riesel Base 222 remain.		 13681 (99483)
31886 (98783)
39024 (97844)
71359 (96932)
73959 (95983)
74009 (95875)
67054 (92945)
76039 (92791)
6831 (92698)
45687 (92012)		  
223 54704 5, 7, 4973   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 37 (37)		 402 k's remaining at n=100K.

See k's at Riesel Base 223 remain.		 52050 (99907)
47552 (98659)
27824 (98544)
13278 (98542)
33776 (98445)
20376 (97134)
39834 (96643)
12186 (95650)
372 (94855)
25782 (94747)		  
224 4 3, 5   k = = 1 mod 223 (223) none - proven 2 (108)
3 (34)		  
225 168032 17, 113, 1489 All k = m^2 for all n; factors to:
(m*15^n - 1) *
(m*15^n + 1)		 k = = 1 mod 2 (2)
k = = 1 mod 7 (7)		 128 k's remaining at n=100K.

See k's at Riesel Base 225 remain.		 113084 (97080)
136222 (96922)
135202 (95293)
50060 (95099)
88724 (94530)
51362 (92170)
155070 (91011)
122154 (90273)
159966 (88618)
10048 (87778)		 k = 2^2, 4^2, 10^2, 12^2, 14^2, 16^2, 18^2, 24^2, 26^2, 28^2, (etc. pattern repeating every 14m) proven composite by full algebraic factors.
226 158447 7, 211, 227, 349   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 509 k's remaining at n=25K.

See k's at Riesel Base 226 remain.		 51765 (24739)
78114 (24217)
118934 (24183)
47225 (24097)
38735 (24096)
17594 (24053)
85632 (23999)
138840 (23697)
55560 (23644)
64979 (23325)		  
227 20 3, 19   k = = 1 mod 2 (2)
k = = 1 mod 113 (113)		 none - proven 14 (872)
18 (66)
2 (12)
8 (4)
12 (2)
16 (1)
10 (1)
6 (1)
4 (1)		  
228 16718 5, 37, 229 (Condition 1):
All k where k = m^2
and m = = 107 or 122 mod 229:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*228^q - 1) *
     (m*228^q + 1)
   odd n:
     factor of 229
(Condition 2):
All k where k = 57*m^2
and m = = 15 or 214 mod 229:
   even n:
     factor of 229
   for odd n let k = 57*m^2
   and let n=2*q-1; factors to:
     [m*2^n*57^q - 1] *
     [m*2^n*57^q + 1]		 k = = 1 mod 227 (227) 121 k's remaining at n=100K.

See k's at Riesel Base 228 remain.		 14177 (99474)
10041 (98461)
12211 (95815)
3773 (94689)
7827 (93095)
15173 (88888)
12048 (87086)
10849 (85593)
5766 (83570)
8701 (81210)		 k = 11449 and 14884 proven composite by condition 1.

k = 12825 proven composite by condition 2.
229 24 5, 23   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 19 (19)		 none - proven 14 (1366)
12 (21)
18 (3)
8 (1)
6 (1)
2 (1)		  
230 8 3, 7   k = = 1 mod 229 (229) none - proven 5 (42)
2 (14)
6 (2)
3 (2)
7 (1)
4 (1)		  
231 151584 13, 29, 61, 67 (Condition 1):
All k where k = m^2
and m = = 12 or 17 mod 29:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*231^q - 1) *
     (m*231^q + 1)
   odd n:
     factor of 29
(Condition 2):
All k where k = 231*m^2
and m = = 12 or 17 mod 29:
   [Reverse condition 1]		 k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 23 (23)		 55 k's remaining at n=100K.

See k's at Riesel Base 231 remain.		 150544 (96779)
130414 (83729)
70152 (80073)
21210 (78681)
97932 (78100)
69628 (77468)
98744 (75752)
12848 (71597)
107098 (71283)
77728 (70648)		 k = 144, 16384, 48400, 77284, 91204, and 129600 proven composite by condition 1.

k = 33264 proven composite by condition 2.
232 501417 5, 233, 2153 All k where k = m^2
and m = = 89 or 144 mod 233:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*232^q - 1) *
     (m*232^q + 1)
   odd n:
     factor of 233		 k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 11 (11)		 884 k's remaining at n=25K.

See k's at Riesel Base 232 remain.		 19901 (24982)
298644 (24932)
249233 (24880)
457719 (24839)
211959 (24733)
325148 (24728)
207491 (24685)
88937 (24674)
445031 (24673)
265929 (24628)		 k = 308025 proven composite by partial algebraic factors.
233 14 3, 13   k = = 1 mod 2 (2)
k = = 1 mod 29 (29)		 10 (600K) 2 (8620)
12 (22)
6 (10)
4 (3)
8 (2)		  
234 46 5, 47 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*234^q - 1) *
     (m*234^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 26*m^2
and m = = 1 or 4 mod 5:
   even n:
     factor of 5
   for odd n let k = 26*m^2
   and let n=2*q-1; factors to:
     [m*3^n*26^q - 1] *
     [m*3^n*26^q + 1]		 k = = 1 mod 233 (233) 6 (600K) 41 (43)
34 (36)
19 (32)
17 (24)
44 (18)
11 (15)
38 (8)
33 (8)
21 (7)
40 (6)		 k = 4 and 9 proven composite by condition 1.

k = 26 proven composite by condition 2.
235 5378 7, 19, 139   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 13 (13)		 294 (300K)
1926 (300K)
2598 (300K)
2832 (300K)
3194 (300K)
3788 (300K)
4778 (300K)		 4998 (260170)
4190 (257371)
3336 (166287)
1136 (83633)
30 (56835)
2148 (50099)
4032 (35848)
3270 (34802)
5112 (19247)
5118 (16834)		  
236 80 3, 79   k = = 1 mod 5 (5)
k = = 1 mod 47 (47)		 none - proven 78 (402022)
67 (42381)
59 (1786)
4 (939)
45 (672)
65 (270)
17 (228)
25 (91)
50 (82)
72 (55)		  
237 50 7, 17 All k where k = m^2
and m = = 4 or 13 mod 17:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*237^q - 1) *
     (m*237^q + 1)
   odd n:
     factor of 17		 k = = 1 mod 2 (2)
k = = 1 mod 59 (59)		 none - proven 22 (6053)
8 (527)
42 (322)
48 (18)
38 (10)
10 (6)
34 (4)
14 (4)
46 (3)
36 (3)		 k = 16 proven composite by partial algebraic factors.
238 5415261 5, 239, 11329   k = = 1 mod 3 (3)
k = = 1 mod 79 (79)		 57141 k's remaining at n=2.5K. To be shown later. 5365565 (2500)
4248917 (2500)
3485364 (2500)
2948072 (2500)
2662952 (2500)
2638013 (2500)
1892073 (2500)
1746077 (2500)
1251329 (2500)
4936337 (2499)		  
239 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 17 (17)		 none - proven 2 (10)  
240 2952972 7, 13, 17, 19, 73, 241 (Condition 1):
All k where k = m^2
and m = = 64 or 177 mod 241:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*240^q - 1) *
     (m*240^q + 1)
   odd n:
     factor of 241
(Condition 2):
All k where k = 15*m^2
and m = = 15 or 226 mod 241:
   even n:
     factor of 241
   for odd n let k = 15*m^2
   and let n=2*q-1; factors to:
     [m*4^n*15^q - 1] *
     [m*4^n*15^q + 1]		 k = = 1 mod 239 (239) 56648 k's remaining at n=2.5K. To be shown later. 2034615 (2500)
1599865 (2500)
1015975 (2500)
902553 (2500)
749303 (2500)
747613 (2500)
666939 (2500)
267261 (2500)
261655 (2500)
2481084 (2499)		 k = 4096, 31329, 93025, 174724, 298116, 434281, 619369, 810000, 1056784, 1301881, 1610361, 1909924, 2280100, and 2634129 proven composite by condition 1.

k = 3375, 766140, and 983040 proven composite by condition 2.
241 15918 11, 113, 257   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 1682 (500K)
2168 (500K)
4014 (500K)
4082 (500K)
4610 (500K)
5312 (500K)
5864 (500K)
6128 (500K)
8504 (500K)
9362 (500K)
9998 (500K)
12044 (500K)
12270 (500K)
12924 (500K)
14202 (500K)
14354 (500K)		 14772 (485468)
8460 (387047)
8700 (350384)
11210 (339153)
9602 (295318)
2960 (197729)
4520 (168994)
3488 (143451)
10284 (112678)
9822 (109156)		  
242 14 3, 5, 13   k = = 1 mod 241 (241) none - proven 11 (8386)
10 (43)
13 (11)
8 (4)
9 (3)
5 (2)
3 (2)
2 (2)
12 (1)
7 (1)		  
243 11896 7, 13, 61, 271 (Condition 1):
All k where k = m^2
and m = = 11 or 50 mod 61:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*243^q - 1) *
     (m*243^q + 1)
   odd n:
     factor of 61
(Condition 2):
All k where k = 3*m^2
and m = = 23 or 38 mod 61:
   even n:
     factor of 61
   for odd n let k = 3*m^2
   and let n=2*q-1; factors to:
     [m*9^n*3^q - 1] *
     [m*9^n*3^q + 1]
(Condition 3):
All k = m^5 for all n; factors to:
(m*3^n - 1) *
(m^4*81^n + m^3*27^n + m^2*9^n + m*3^n + 1)		 k = = 1 mod 2 (2)
k = = 1 mod 11 (11)		 31 k's remaining at n=210K.

See k's at Riesel Base 243 remain.		 3636 (192141)
7972 (183300)
8100 (160159)
1418 (128582)
11192 (127798)
6772 (120339)
9974 (102911)
7102 (97952)
8066 (93714)
7654 (82880)		 k = 2500 and 5184 proven composite by condition 1.

k = 4332 proven composite by condition 2.

k = 32 and 7776 proven composite by condition 3.
244 6 5, 7   k = = 1 mod 3 (3) none - proven 5 (7)
3 (5)
2 (1)		  
245 40 3, 41   k = = 1 mod 2 (2)
k = = 1 mod 61 (61)		 none - proven 8 (500)
26 (212)
28 (205)
22 (101)
38 (38)
10 (37)
14 (30)
6 (7)
4 (5)
32 (4)		  
246 77 13, 19 All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*246^q - 1) *
     (m*246^q + 1)
   odd n:
     factor of 13		 k = = 1 mod 5 (5)
k = = 1 mod 7 (7)		 none - proven 27 (23989)
14 (203)
69 (58)
75 (38)
17 (34)
49 (29)
59 (26)
70 (25)
39 (23)
30 (17)		 k = 25 proven composite by partial algebraic factors.
247 469184 5, 17, 31, 1009   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 41 (41)		 1913 k's remaining at n=25K.

See k's at Riesel Base 247 remain.		 269916 (24990)
429504 (24968)
139302 (24892)
337434 (24692)
357372 (24641)
414810 (24624)
380772 (24618)
168422 (24594)
436958 (24558)
390216 (24530)		  
248 82 3, 83   k = = 1 mod 13 (13)
k = = 1 mod 19 (19)		 none - proven 56 (32638)
74 (20344)
59 (18716)
7 (3179)
10 (2793)
28 (1413)
76 (1319)
61 (1037)
52 (655)
36 (489)		  
249 14256 5, 7, 13, 29, 37 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*249^q - 1) *
     (m*249^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 249*m^2
and m = = 2 or 3 mod 5:
   [Reverse condition 1]		 k = = 1 mod 2 (2)
k = = 1 mod 31 (31)		 133 k's remaining at n=100K.

See k's at Riesel Base 249 remain.		 8564 (95200)
1624 (91784)
1812 (84698)
7146 (80627)
11684 (77336)
10536 (74657)
12436 (73285)
11234 (71748)
8224 (71446)
3294 (68326)		 k = 2^2, 8^2, 12^2, 18^2, 22^2, 28^2, 38^2, 42^2, 48^2, 52^2, 58^2, 62^2, 68^2, 72^2, 78^2, 82^2, 88^2, 98^2, 102^2, 108^2, 112^2, and 118^2 proven composite by condition 1.

k = 249*2^2 proven composite by condition 2.
250 682217 7, 13, 251, 1609   k = = 1 mod 3 (3)
k = = 1 mod 83 (83)		 3699 k's remaining at n=10K.

See k's at Riesel Base 250 remain.		 19202 (9989)
264291 (9985)
81006 (9982)
332060 (9968)
454245 (9961)
280632 (9961)
74153 (9961)
462900 (9959)
183020 (9958)
337749 (9956)		  
251 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)		 none - proven 4 (271)
2 (2)		  
252 45 11, 23   k = = 1 mod 251 (251) none - proven 8 (6287)
23 (399)
36 (123)
31 (62)
32 (52)
4 (7)
16 (5)
39 (4)
33 (4)
38 (3)		  
253 1904 5, 127, 173   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 1854 (1M) 1652 (92631)
1650 (67010)
408 (34273)
578 (3428)
258 (2972)
662 (1771)
1526 (902)
1472 (782)
1844 (760)
434 (511)		  
254 4 3, 5   k = = 1 mod 11 (11)
k = = 1 mod 23 (23)		 none - proven 2 (2866)
3 (1)		  
255 205022 7, 13, 19, 61, 97   k = = 1 mod 2 (2)
k = = 1 mod 127 (127)		 360 k's remaining at n=57K.

See k's at Riesel Base 255 remain.		 152990 (57192)
98522 (56433)
29706 (56039)
66910 (55524)
23074 (55464)
117944 (55297)
198398 (54976)
74972 (54747)
178404 (54467)
170018 (54348)		  
257 44 3, 43   k = = 1 mod 2 (2) none - proven 42 (58)
2 (22)
18 (20)
4 (15)
28 (11)
26 (10)
14 (8)
24 (5)
20 (4)
40 (3)		  
258 36 7, 37   k = = 1 mod 257 (257) none - proven 6 (212134)
22 (8471)
14 (2624)
9 (105)
26 (59)
2 (28)
30 (27)
19 (27)
13 (20)
15 (11)		  
259 14 5, 13   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 43 (43)		 none - proven 12 (48)
8 (5)
2 (2)
6 (1)		  
260 28 3, 29   k = = 1 mod 7 (7)
k = = 1 mod 37 (37)		 none - proven 10 (2103)
7 (825)
20 (326)
2 (120)
26 (100)
24 (12)
23 (12)
21 (9)
19 (9)
25 (7)		  
261 13061094 7, 79, 131, 859   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 13 (13)		 58155 k's remaining at n=2.5K. To be shown later. 11634394 (2500)
10308164 (2500)
6264812 (2500)
5603550 (2500)
4933448 (2500)
2805354 (2500)
1474432 (2500)
12630452 (2499)
12000550 (2499)
10796804 (2499)		  
262 27351 5, 7, 13, 103, 263   k = = 1 mod 3 (3)
k = = 1 mod 29 (29)		 118 k's remaining at n=100K.

See k's at Riesel Base 262 remain.		 9120 (99664)
21951 (99430)
14492 (98753)
12623 (95954)
23246 (93125)
6648 (91980)
4104 (91956)
14906 (88099)
16989 (86060)
21080 (83670)		  
263 10 3, 11   k = = 1 mod 2 (2)
k = = 1 mod 131 (131)		 none - proven 8 (2)
6 (2)
2 (2)
4 (1)		  
264 54 5, 53 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*264^q - 1) *
     (m*264^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 263 (263) none - proven 24 (2096)
36 (375)
16 (217)
41 (47)
50 (26)
3 (18)
28 (16)
33 (13)
44 (10)
15 (7)		 k = 4, 9, and 49 proven composite by partial algebraic factors.
265 20 7, 19   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 11 (11)		 none - proven 8 (71)
18 (2)
6 (2)
2 (2)
14 (1)		  
266 88 3, 89   k = = 1 mod 5 (5)
k = = 1 mod 53 (53)		 none - proven 64 (26843)
23 (1684)
85 (1615)
87 (354)
20 (198)
50 (114)
47 (56)
28 (23)
80 (20)
17 (20)		  
267 1432662 5, 67, 7129   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 19 (19)		 5761 k's remaining at n=10K.

See k's at Riesel Base 267 remain.		 1001236 (9998)
681726 (9997)
1091366 (9994)
462012 (9992)
1219544 (9988)
644184 (9972)
1397958 (9967)
1255596 (9963)
396926 (9963)
751048 (9958)		  
268 1344 5, 17, 269   k = = 1 mod 3 (3)
k = = 1 mod 89 (89)		 267 (500K)
408 (500K)
599 (500K)
806 (500K)
863 (500K)
1101 (500K)
1136 (500K)
1143 (500K)
1296 (500K)		 291 (452750)
872 (251714)
1061 (229202)
632 (113226)
1194 (81459)
954 (64839)
467 (36859)
884 (36621)
720 (24307)
758 (18193)		  
269 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 67 (67)		 none - proven 2 (20)  
270 21681 7, 13, 37, 271 k = 3600:
   for even n let n=2*q; factors to:
     (60*270^q - 1) *
     (60*270^q + 1)
   odd n:
     covering set 7, 13, 37		 k = = 1 mod 269 (269) 69 k's remaining at n=100K.

See k's at Riesel Base 270 remain.		 4573 (99828)
9296 (93802)
4 (89661)
11580 (87864)
15213 (85053)
5359 (84972)
2588 (81676)
10817 (81410)
4195 (80151)
9825 (80094)		  
271 50389004 11, 17, 31, 41, 251, 6301 (Condition 1):
All k where k = m^2
and m = = 4 or 13 mod 17:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*271^q - 1) *
     (m*271^q + 1)
   odd n:
     factor of 17
(Condition 2):
All k where k = 271*m^2
and m = = 4 or 13 mod 17:
   [Reverse condition 1]		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 320252 k's remaining at n=2.5K. To be shown later. 49475490 (2500)
49389390 (2500)
48937100 (2500)
48746510 (2500)
48741192 (2500)
48659592 (2500)
45923870 (2500)
43799904 (2500)
43405470 (2500)
43355898 (2500)		 k = 30^2, 72^2, 132^2, 378^2, 438^2, 480^2, 540^2, 582^2, 642^2, 888^2, 948^2, 990^2, (etc. pattern repeating every 510m) proven composite by condition 1.

k = 271*30^2, 271*72^2, 271*132^2, and 271*378^2 proven composite by condition 2.
272 8 3, 7   k = = 1 mod 271 (271) none - proven 6 (148426)
5 (8)
2 (6)
7 (5)
3 (2)
4 (1)		  
273 7262 5, 29, 137   k = = 1 mod 2 (2)
k = = 1 mod 17 (17)		 136 (300K)
156 (300K)
962 (300K)
1758 (300K)
2072 (300K)
3424 (300K)
3756 (300K)
5226 (300K)
5802 (300K)		 138 (224093)
4794 (135632)
4522 (129019)
3254 (122768)
6702 (96743)
4396 (87951)
6980 (72300)
4086 (60454)
4614 (60372)
488 (59024)		  
274 21 5, 11 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*274^q - 1) *
     (m*274^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 13 (13)		 none - proven 12 (51)
5 (4)
11 (3)
6 (3)
20 (1)
18 (1)
17 (1)
3 (1)
2 (1)		 k = 9 proven composite by partial algebraic factors.
275 22 3, 23   k = = 1 mod 2 (2)
k = = 1 mod 137 (137)		 4 (600K) 16 (54825)
20 (8)
8 (8)
18 (5)
2 (4)
6 (3)
14 (2)
12 (1)
10 (1)		  
276 1552307 7, 13, 277, 5881 (Condition 1):
All k where k = m^2
and m = = 60 or 217 mod 277:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*276^q - 1) *
     (m*276^q + 1)
   odd n:
     factor of 277
(Condition 2):
All k where k = 69*m^2
and m = = 120 or 157 mod 277:
   even n:
     factor of 277
   for odd n let k = 69*m^2
   and let n=2*q-1; factors to:
     [m*2^n*69^q - 1] *
     [m*2^n*69^q + 1]		 k = = 1 mod 5 (5)
k = = 1 mod 11 (11)		 12601 k's remaining at n=2.5K. To be shown later. 699147 (2500)
380992 (2500)
196665 (2500)
1293318 (2499)
1010902 (2499)
585260 (2499)
406347 (2499)
178207 (2499)
469763 (2498)
1387408 (2498)		 k = 3600, 47089, 113569, 1098304, and 1364224 proven composite by condition 1.

k = 993600 proven composite by condition 2.
277 7088 7, 13, 19, 139   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 23 (23)		 84 (300K)
764 (300K)
1178 (300K)
1808 (300K)
1908 (300K)
2064 (300K)
2640 (300K)
2642 (300K)
2690 (300K)
3032 (300K)
3896 (300K)
4082 (300K)
4428 (300K)
4512 (300K)
4586 (300K)
5118 (300K)
5238 (300K)
5378 (300K)
6486 (300K)
6822 (300K)		 5916 (252878)
1616 (242731)
5954 (120147)
2766 (114778)
4016 (109211)
2538 (85188)
5882 (74049)
6918 (59328)
6008 (50658)
5196 (47499)		  
278 14 3, 5, 13   k = = 1 mod 277 (277) none - proven 2 (43908)
4 (175)
5 (34)
11 (26)
3 (21)
10 (15)
9 (15)
12 (4)
7 (3)
8 (2)		  
279 6 5, 7 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*279^q - 1) *
     (m*279^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 139 (139)		 none - proven 2 (1) k = 4 proven composite by partial algebraic factors.
281 328 3, 47   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 7 (7)		 38 (500K)
314 (500K)		 272 (162232)
112 (133589)
170 (50358)
284 (1232)
252 (1106)
304 (535)
194 (340)
94 (253)
34 (209)
200 (170)		  
282 19139 5, 7, 13, 37, 109   k = = 1 mod 281 (281) 229 k's remaining at n=100K.

See k's at Riesel Base 282 remain.		 9027 (98973)
1999 (98840)
3617 (95568)
8659 (94640)
10419 (87352)
17278 (86908)
4384 (85848)
18965 (84625)
58 (82974)
2382 (82845)		  
283 218042 5, 7, 71, 73, 1069   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 47 (47)		 1118 k's remaining at n=25K.

See k's at Riesel Base 283 remain.		 8 (164768)
150914 (24976)
118616 (24873)
21152 (24808)
196404 (24707)
14342 (24486)
168264 (24460)
128988 (24446)
9018 (24441)
164082 (24403)		  
284 4 3, 5   k = = 1 mod 283 (283) none - proven 2 (416)
3 (30)		  
285 12 11, 13   k = = 1 mod 2 (2)
k = = 1 mod 71 (71)		 none - proven 4 (71)
10 (2)
8 (2)
6 (1)
2 (1)		  
286 83 7, 41   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 19 (19)		 none - proven 9 (163)
72 (8)
53 (6)
48 (6)
45 (4)
63 (3)
50 (3)
30 (3)
12 (3)
80 (2)		  
287 14276 3, 5, 17, 457   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)
k = = 1 mod 13 (13)		 156 k's remaining at n=100K.

See k's at Riesel Base 287 remain.		 12656 (98870)
4666 (98063)
1658 (91104)
5122 (90193)
3926 (88302)
7214 (78864)
5126 (76594)
11894 (73556)
4208 (73292)
1646 (72086)		  
288 613 5, 17, 53 (Condition 1):
All k where k = m^2
and m = = 4 or 13 mod 17:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*288^q - 1) *
     (m*288^q + 1)
   odd n:
     factor of 17
(Condition 2):
All k where k = 2*m^2
and m = = 3 or 14 mod 17:
   even n:
     factor of 17
   for odd n let k = 2*m^2
   and let n=2*q-1; factors to:
     [m*12^n*2^q - 1] *
     [m*12^n*2^q + 1]		 k = = 1 mod 7 (7)
k = = 1 mod 41 (41)		 339 (500K)
509 (500K)		 478 (3250)
137 (2319)
207 (2251)
47 (1198)
182 (1070)
84 (972)
304 (928)
117 (878)
346 (745)
381 (621)		 k = 16 and 441 proven composite by condition 1.

k = 18 and 392 proven composite by condition 2.
289 86 5, 29 All k = m^2 for all n; factors to:
(m*17^n - 1) *
(m*17^n + 1)		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 none - proven 44 (3244)
26 (55)
84 (14)
54 (8)
74 (6)
60 (6)
42 (6)
24 (6)
68 (4)
38 (4)		 k = 36 proven composite by full algebraic factors.
290 98 3, 97   k = = 1 mod 17 (17) none - proven 64 (96385)
19 (51591)
71 (49360)
81 (45303)
31 (5025)
32 (4512)
74 (4270)
82 (495)
48 (415)
47 (300)		  
291 16410 7, 61, 199 All k where k = m^2
and m = = 27 or 46 mod 73:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*291^q - 1) *
     (m*291^q + 1)
   odd n:
     factor of 73		 k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 29 (29)		 32 k's remaining at n=100K.

See k's at Riesel Base 291 remain.		 5630 (82805)
8292 (81139)
7912 (78780)
13360 (72937)
4454 (70811)
5608 (70369)
2410 (65589)
12552 (50923)
11250 (50912)
8514 (49961)		 k = 10000 proven composite by partial algebraic factors.
292 34682 5, 7, 13, 19, 79 All k where k = m^2
and m = = 138 or 155 mod 293:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*292^q - 1) *
     (m*292^q + 1)
   odd n:
     factor of 293		 k = = 1 mod 3 (3)
k = = 1 mod 97 (97)		 219 k's remaining at n=100K.

See k's at Riesel Base 292 remain.		 6381 (95011)
5963 (91183)
26343 (89838)
6639 (89757)
22854 (89052)
9824 (88733)
19904 (88371)
10314 (86704)
32558 (86618)
12893 (86099)		 k = 19044 proven composite by partial algebraic factors.
293 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 73 (73)		 none - proven 6 (6)
2 (2)
4 (1)		  
294 119 5, 59 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*294^q - 1) *
     (m*294^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 6*m^2
and m = = 1 or 4 mod 5:
   even n:
     factor of 5
   for odd n let k = 6*m^2
   and let n=2*q-1; factors to:
     [m*7^n*6^q - 1] *
     [m*7^n*6^q + 1]		 k = = 1 mod 293 (293) none - proven 60 (5973)
116 (1605)
31 (743)
44 (466)
84 (268)
92 (182)
109 (130)
36 (69)
112 (42)
99 (42)		 k = 4, 9, 49, and 64 proven composite by condition 1.

k = 6 and 96 proven composite by condition 2.
295 664484 37, 53, 821 All k where k = m^2
and m = = 6 or 31 mod 37:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*295^q - 1) *
     (m*295^q + 1)
   odd n:
     factor of 37		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 880 k's remaining at n=25K.

See k's at Riesel Base 295 remain.		 229940 (24963)
9806 (24853)
390956 (24829)
11136 (24774)
12548 (24689)
280608 (24683)
627596 (24674)
660708 (24600)
354006 (24596)
18788 (24567)		 k = 51984, 191844, 202500, 435600, and 451584 proven composite by partial algebraic factors.
296 10 3, 11   k = = 1 mod 5 (5)
k = = 1 mod 59 (59)		 none - proven 2 (36)
4 (27)
8 (16)
5 (8)
7 (3)
9 (1)
3 (1)		  
297 130076 5, 7, 67, 97, 149 All k where k = m^2
and m = = 44 or 105 mod 149:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*297^q - 1) *
     (m*297^q + 1)
   odd n:
     factor of 149		 k = = 1 mod 2 (2)
k = = 1 mod 37 (37)		 678 k's remaining at n=25K.

See k's at Riesel Base 297 remain.		 87864 (24988)
127042 (24922)
32764 (24772)
54388 (24632)
82472 (24548)
10744 (24516)
64574 (24445)
52352 (24412)
84334 (24375)
121988 (24322)		 k = 1936, 64516, and 116964 proven composite by partial algebraic factors.
298 116 13, 23   k = = 1 mod 3 (3)
k = = 1 mod 11 (11)		 27 (300K)
92 (300K)
105 (300K)		 66 (62275)
30 (10338)
36 (6571)
2 (4202)
9 (93)
38 (92)
44 (83)
102 (70)
60 (48)
53 (37)		  
299 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 149 (149)		 none - proven 2 (4)  
300 85 7, 43   k = = 1 mod 13 (13)
k = = 1 mod 23 (23)		 none - proven 81 (12793)
83 (624)
42 (516)
75 (174)
74 (106)
13 (98)
6 (96)
62 (52)
33 (29)
3 (26)		  
301 1152584 89, 151, 509   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 734 k's remaining at n=25K.

See k's at Riesel Base 301 remain.		 103434 (24924)
756584 (24868)
821268 (24824)
1094328 (24800)
582408 (24787)
788628 (24717)
685088 (24607)
316928 (24599)
166632 (24548)
539924 (24476)		  
302 13 3, 5, 17   k = = 1 mod 7 (7)
k = = 1 mod 43 (43)		 none - proven 5 (98)
11 (74)
2 (6)
9 (5)
3 (4)
4 (3)
12 (1)
10 (1)
7 (1)
6 (1)		  
303 85368 5, 17, 19, 97, 401   k = = 1 mod 2 (2)
k = = 1 mod 151 (151)		 1077 k's remaining at n=25K.

See k's at Riesel Base 303 remain.		 4 (198357)
2 (40174)
65744 (24957)
47468 (24949)
40422 (24935)
24756 (24830)
39064 (24632)
85102 (24571)
45688 (24413)
59376 (24309)		  
304 426 5, 61 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*304^q - 1) *
     (m*304^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 19*m^2
and m = = 2 or 3 mod 5:
   even n:
     factor of 5
   for odd n let k = 19*m^2
   and let n=2*q-1; factors to:
     [m*4^n*19^q - 1] *
     [m*4^n*19^q + 1]		 k = = 1 mod 3 (3)
k = = 1 mod 101 (101)		 131 (300K)
284 (300K)
294 (300K)
389 (300K)
404 (300K)
411 (300K)		 339 (136846)
374 (33968)
111 (22367)
341 (21621)
234 (19860)
359 (18894)
390 (17571)
194 (11540)
72 (7592)
416 (6747)		 k = 9, 144, and 324 proven composite by condition 1.

k = 171 proven composite by condition 2.
305 16 3, 17   k = = 1 mod 2 (2)
k = = 1 mod 19 (19)		 none - proven 4 (3)
14 (2)
8 (2)
6 (2)
2 (2)
12 (1)
10 (1)		  
306 39295 7, 37, 199, 307   k = = 1 mod 5 (5)
k = = 1 mod 61 (61)		 70 k's remaining at n=100K.

See k's at Riesel Base 306 remain.		 9757 (99242)
38564 (96037)
34794 (92317)
25445 (90812)
32132 (84472)
6232 (83797)
26317 (83083)
37852 (82223)
36928 (76377)
37824 (75225)		  
307 8 5, 7, 13   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 17 (17)		 none - proven 6 (26262)
2 (1)		  
308 104 3, 103   k = = 1 mod 307 (307) 7 (300K)
43 (300K)
67 (300K)
74 (300K)
89 (300K)		 52 (95851)
59 (63148)
94 (11543)
71 (6262)
100 (1213)
2 (990)
82 (763)
87 (670)
69 (503)
22 (259)		  
309 94 5, 31 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*309^q - 1) *
     (m*309^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 11 (11)		 none - proven 14 (2164)
74 (1298)
24 (174)
6 (73)
28 (68)
82 (51)
26 (35)
54 (30)
44 (30)
70 (27)		 k = 4 proven composite by partial algebraic factors.
310 363869 7, 13, 17, 37, 311   k = = 1 mod 3 (3)
k = = 1 mod 103 (103)		 1470 k's remaining at n=25K.

See k's at Riesel Base 310 remain.		 338741 (24999)
108893 (24922)
221990 (24841)
100878 (24812)
231144 (24809)
228429 (24796)
172391 (24790)
363563 (24713)
208230 (24574)
75161 (24570)		  
311 14 3, 13   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 31 (31)		 none - proven 12 (146)
4 (5)
8 (2)
2 (2)
10 (1)		  
312 173401 5, 7, 19, 277, 313 All k where k = m^2
and m = = 25 or 288 mod 313:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*312^q - 1) *
     (m*312^q + 1)
   odd n:
     factor of 313		 k = = 1 mod 311 (311) 3577 k's remaining at n=10K.

See k's at Riesel Base 312 remain.		 4 (51565)
75254 (10000)
26614 (9984)
33856 (9979)
154829 (9968)
115892 (9949)
157457 (9945)
4358 (9942)
20504 (9929)
126981 (9926)		 k=625, 82944, and 114244 proven composite by partial algebraic factors.
313 8634 5, 97, 157 All k where k = m^2
and m = = 28 or 129 mod 157:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*313^q - 1) *
     (m*313^q + 1)
   odd n:
     factor of 157		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 13 (13)		 188 (300K)
2298 (300K)
3924 (300K)
4280 (300K)
4338 (300K)
4358 (300K)
6086 (300K)
6428 (300K)
7976 (300K)		 7188 (245886)
5724 (232269)
7092 (202412)
4482 (201622)
5754 (155768)
7244 (142223)
5666 (132354)
2034 (90007)
4734 (69331)
366 (68982)		 No k's proven composite by algebraic factors.
314 4 3, 5   k = = 1 mod 313 (313) none - proven 2 (74)
3 (1)		  
315 900 13, 19, 31   k = = 1 mod 2 (2)
k = = 1 mod 157 (157)		 64 (500K)
552 (500K)		 400 (225179)
256 (18845)
614 (4965)
80 (2825)
638 (2389)
710 (2304)
342 (2143)
438 (1601)
326 (865)
558 (663)		  
316 287520 13, 19, 31, 317 All k where k = m^2
and m = = 114 or 203 mod 317:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*316^q - 1) *
     (m*316^q + 1)
   odd n:
     factor of 317		 k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 7 (7)		 175 k's remaining at n=100K.

See k's at Riesel Base 316 remain.		 50313 (99453)
268098 (98915)
234579 (98670)
13205 (98214)
264624 (97143)
281970 (95718)
31938 (95696)
128585 (94554)
78777 (93285)
43778 (91974)		 No k's proven composite by algebraic factors.
317 14 3, 5, 13   k = = 1 mod 2 (2)
k = = 1 mod 79 (79)		 none - proven 4 (119)
2 (10)
8 (2)
12 (1)
10 (1)
6 (1)		  
318 144 11, 29   k = = 1 mod 317 (317) 122 (1M) 128 (131133)
78 (33813)
67 (17435)
117 (14403)
111 (1643)
54 (1432)
23 (989)
98 (198)
32 (108)
44 (68)		  
319 1526 5, 17, 41 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*319^q - 1) *
     (m*319^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 53 (53)		 614 (300K)
1356 (300K)
1506 (300K)		 276 (160971)
1266 (85179)
1244 (51654)
626 (45687)
1496 (39721)
86 (19361)
944 (15678)
834 (7174)
606 (7141)
804 (7110)		 k = 144 and 324 proven composite by partial algebraic factors.
320 106 3, 107   k = = 1 mod 11 (11)
k = = 1 mod 29 (29)		 73 (500K)
103 (500K)		 53 (115706)
42 (13743)
10 (9645)
82 (7189)
24 (1618)
74 (1524)
66 (1234)
61 (537)
58 (443)
5 (232)		  
321 22 7, 23   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)		 8 (600K) 20 (1406)
18 (4)
14 (1)
12 (1)
10 (1)
4 (1)
2 (1)		  
322 18 17, 19   k = = 1 mod 3 (3)
k = = 1 mod 107 (107)		 none - proven 8 (10)
3 (3)
17 (2)
15 (2)
14 (1)
12 (1)
11 (1)
9 (1)
6 (1)
5 (1)		  
323 93896 3, 5, 10433   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 23 (23)		 1836 k's remaining at n=25K.

See k's at Riesel Base 323 remain.		 3184 (24999)
83324 (24996)
3952 (24955)
92564 (24836)
34706 (24822)
29330 (24812)
53696 (24730)
46886 (24678)
68456 (24654)
39742 (24551)		  
324 14 5, 13 All k = m^2 for all n; factors to:
(m*18^n - 1) *
(m*18^n + 1)		 k = = 1 mod 17 (17)
k = = 1 mod 19 (19)		 none - proven 11 (149)
12 (4)
10 (3)
6 (3)
13 (1)
8 (1)
7 (1)
6 (1)
5 (1)
3 (1)		 k = 4 and 9 proven composite by full algebraic factors.
326 110 3, 109   k = = 1 mod 5 (5)
k = = 1 mod 13 (13)		 50 (600K) 35 (174298)
98 (4562)
74 (4278)
59 (1500)
47 (1328)
52 (1119)
99 (848)
73 (771)
64 (395)
108 (198)		  
327 696 5, 17, 41   k = = 1 mod 2 (2)
k = = 1 mod 163 (163)		 38 (772K)
204 (772K)
370 (772K)		 346 (55078)
308 (52903)
62 (43088)
458 (30208)
664 (27823)
484 (10207)
302 (6734)
450 (5778)
276 (3245)
368 (1898)		  
328 48 7, 47   k = = 1 mod 3 (3)
k = = 1 mod 109 (109)		 8 (1M) 41 (31734)
20 (20962)
35 (6603)
9 (605)
42 (447)
2 (80)
32 (22)
24 (4)
47 (3)
21 (3)		  
329 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 41 (41)		 none - proven 2 (2)  
330 16527822 13, 331, 8377   k = = 1 mod 7 (7)
k = = 1 mod 47 (47)		 99767 k's remaining at n=2.5K. To be shown later. 16491743 (2500)
16396665 (2500)
14927167 (2500)
12191560 (2500)
10774711 (2500)
10709395 (2500)
10474264 (2500)
10094837 (2500)
8853051 (2500)
8846841 (2500)		  
331 470030 7, 13, 19, 83, 1889   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 11 (11)		 486 k's remaining at n=100K.

See k's at Riesel Base 331 remain.		 426444 (98961)
148514 (98406)
170232 (98332)
63918 (96544)
92030 (95621)
213132 (95611)
221708 (95085)
432492 (94916)
94760 (94328)
369048 (93526)		  
332 38 3, 37 All k where k = m^2
and m = = 6 or 31 mod 37:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*332^q - 1) *
     (m*332^q + 1)
   odd n:
     factor of 37		 k = = 1 mod 331 (331) 18 (600K) 28 (66159)
37 (16001)
7 (15221)
8 (13204)
16 (4617)
14 (1208)
9 (945)
32 (822)
23 (258)
26 (106)		 k = 36 proven composite by partial algebraic factors.
333 502 5, 13, 167   k = = 1 mod 2 (2)
k = = 1 mod 83 (83)		 16 (1M) 302 (90815)
14 (69297)
254 (20036)
226 (14714)
258 (8969)
102 (4540)
272 (4032)
368 (2658)
246 (2389)
90 (1864)		  
334 66 5, 67 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*334^q - 1) *
     (m*334^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 37 (37)		 14 (600K) 26 (6027)
53 (505)
30 (136)
48 (66)
59 (60)
36 (53)
56 (47)
65 (11)
47 (10)
44 (10)		 k = 9 proven composite by partial algebraic factors.
335 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 167 (167)		 none - proven 4 (3)
6 (2)
2 (2)		  
336 63018 17, 29, 337 All k where k = m^2
and m = = 148 or 189 mod 337:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*336^q - 1) *
     (m*336^q + 1)
   odd n:
     factor of 337		 k = = 1 mod 5 (5)
k = = 1 mod 67 (67)		 67 k's remaining at n=100K.

See k's at Riesel Base 336 remain.		 3688 (98616)
11244 (96803)
34540 (96494)
2697 (94053)
18427 (89084)
16338 (87527)
32079 (86609)
34982 (78524)
51268 (74057)
44393 (73161)		 k = 21904 proven composite by partial algebraic factors.
337 378 5, 13, 41 All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*337^q - 1) *
     (m*337^q + 1)
   odd n:
     factor of 13		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 38 (500K)
222 (500K)		 194 (33268)
248 (9935)
350 (4454)
368 (3740)
224 (149)
296 (118)
62 (106)
170 (89)
54 (60)
216 (53)		 k = 324 proven composite by partial algebraic factors.
338 74 3, 5, 73   k = = 1 mod 337 (337) 5 (300K)
22 (300K)
44 (300K)
56 (300K)		 71 (56314)
7 (42867)
40 (2603)
70 (797)
67 (407)
25 (285)
37 (175)
18 (156)
72 (144)
4 (111)		  
339 16 5, 17 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*339^q - 1) *
     (m*339^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 13 (13)		 none - proven 6 (121)
12 (3)
10 (1)
8 (1)
2 (1)		 k = 4 proven composite by partial algebraic factors.
340 32 11, 31   k = = 1 mod 3 (3)
k = = 1 mod 113 (113)		 none - proven 2 (60)
18 (22)
20 (12)
24 (4)
23 (3)
9 (3)
30 (2)
27 (2)
21 (2)
29 (1)		  
341 20 3, 19   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 17 (17)		 none - proven 8 (4966)
10 (447)
14 (344)
2 (36)
4 (3)
12 (1)		  
342 629 5, 7, 157   k = = 1 mod 11 (11)
k = = 1 mod 31 (31)		 193 (300K)
267 (300K)
393 (300K)
400 (300K)
407 (300K)
477 (300K)		 216 (106298)
25 (35729)
69 (32956)
244 (29020)
288 (19567)
461 (17290)
127 (16569)
582 (13629)
321 (10314)
314 (4864)		  
343 1676 5, 13, 43 All k = m^3 for all n; factors to:
(m*7^n - 1) *
(m^2*49^n + m*7^n + 1)		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 19 (19)		 314 (300K)
1248 (300K)
1334 (300K)
1370 (300K)
1422 (300K)		 516 (68693)
1416 (24073)
636 (19713)
528 (17076)
1544 (4637)
558 (2856)
1070 (2710)
1238 (2030)
474 (1387)
1638 (1360)		 k = 8, 216, and 512 proven composite by full algebraic factors.
344 4 3, 5   k = = 1 mod 7 (7) none - proven 2 (4)
3 (1)		  
346 2119475 7, 31, 347, 1291   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 23 (23)		 19648 k's remaining at n=2.5K. To be shown later. 1417463 (2500)
1068345 (2500)
1914899 (2499)
1878083 (2499)
1593854 (2499)
1299492 (2499)
125508 (2499)
25433 (2499)
1999760 (2498)
1997159 (2498)		  
347 28 3, 29   k = = 1 mod 2 (2)
k = = 1 mod 173 (173)		 22 (600K) 14 (4616)
2 (522)
24 (384)
26 (18)
18 (10)
16 (9)
12 (5)
8 (4)
4 (3)
20 (2)		  
348 18496 5, 53, 349 All k where k = m^2
and m = = 136 or 213 mod 349:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*348^q - 1) *
     (m*348^q + 1)
   odd n:
     factor of 349		 k = = 1 mod 347 (347) 143 k's remaining at n=100K.

See k's at Riesel Base 348 remain.		 6421 (98465)
6431 (96325)
2892 (95830)
6061 (95087)
7274 (93928)
18444 (92600)
16976 (92145)
15128 (91514)
14023 (88813)
12622 (85696)		 No k's proven composite by algebraic factors.
349 6 5, 7   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 29 (29)		 none - proven 2 (15)  
350 14 3, 13   k = = 1 mod 349 (349) none - proven 5 (40)
2 (14)
11 (12)
8 (10)
7 (9)
9 (5)
12 (4)
13 (1)
10 (1)
6 (1)		  
351 27708 11, 229, 269   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 7 (7)		 3364 (300K)
4900 (300K)
5884 (300K)
6214 (300K)
8174 (300K)
8722 (300K)
9074 (300K)
12110 (300K)
14334 (300K)
15872 (300K)
19040 (300K)
22452 (300K)
24608 (300K)
27358 (300K)
27642 (300K)		 20802 (172225)
24388 (165187)
6898 (144173)
2232 (142466)
2760 (106776)
6304 (101001)
13982 (87657)
3948 (76432)
6458 (59547)
25378 (55867)		  
352 2426 7, 61, 97 All k where k = m^2
and m = = 42 or 311 mod 353:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*352^q - 1) *
     (m*352^q + 1)
   odd n:
     factor of 353		 k = = 1 mod 3 (3)
k = = 1 mod 13 (13)		 354 (300K)
389 (300K)
414 (300K)
611 (300K)
707 (300K)
792 (300K)
977 (300K)
1026 (300K)
1178 (300K)
1413 (300K)
1653 (300K)
1919 (300K)		 1731 (237258)
2096 (212554)
596 (170089)
1343 (68846)
2319 (65272)
291 (46965)
1523 (43086)
2216 (40961)
123 (36488)
2304 (22243)		 k = 1764 proven composite by partial algebraic factors.
353 58 3, 59   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)		 none - proven 52 (129583)
26 (1614)
20 (754)
54 (471)
22 (319)
4 (259)
38 (142)
46 (105)
36 (29)
44 (12)		  
354 141 5, 71 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*354^q - 1) *
     (m*354^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 353 (353) 71 (600K) 19 (55480)
6 (25565)
22 (11351)
66 (9943)
116 (1543)
136 (1031)
62 (606)
65 (429)
48 (405)
124 (378)		 k = 4, 9, 49, and 64 proven composite by partial algebraic factors.
355 46190 7, 13, 89, 103 All k where k = m^2
and m = = 34 or 55 mod 89:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*355^q - 1) *
     (m*355^q + 1)
   odd n:
     factor of 89		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 59 (59)		 56 k's remaining at n=100K.

See k's at Riesel Base 355 remain.		 19848 (95459)
26790 (93371)
33840 (92385)
38768 (89019)
33368 (81218)
24170 (80670)
32652 (79817)
7958 (78596)
44522 (73239)
10734 (71316)		 k = 20736 proven composite by partial algebraic factors.
356 8 3, 7   k = = 1 mod 5 (5)
k = = 1 mod 71 (71)		 none - proven 5 (432)
7 (5)
2 (4)
3 (2)
4 (1)		  
357 584078 5, 179, 2549   k = = 1 mod 2 (2)
k = = 1 mod 89 (89)		 2773 k's remaining at n=10K.

See k's at Riesel Base 357 remain.		 501834 (9996)
351506 (9991)
447868 (9984)
247914 (9984)
324668 (9980)
238680 (9977)
34610 (9963)
320328 (9959)
329584 (9956)
8054 (9956)		  
358 27606383 5, 359, 25633   k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 17 (17)		 265552 k's remaining at n=2.5K. To be shown later. 26409332 (2500)
26222298 (2500)
26117538 (2500)
25909799 (2500)
25557755 (2500)
24778049 (2500)
24658319 (2500)
23983167 (2500)
23799614 (2500)
23417915 (2500)		  
359 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 179 (179)		 none - proven 2 (10)  
360 3782 19, 29, 109   k = = 1 mod 359 (359) 36 k's remaining at n=100K.

See k's at Riesel Base 360 remain.		 2260 (92070)
3704 (78440)
1616 (69323)
1082 (62970)
2471 (55895)
412 (51664)
248 (46819)
40 (45644)
1250 (42348)
3511 (38065)		  
361 8870 7, 13, 127, 181 All k = m^2 for all n; factors to:
(m*19^n - 1) *
(m*19^n + 1)		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 1772 (300K)
4832 (300K)
6954 (300K)
7422 (300K)		 438 (273787)
3522 (110239)
3224 (108879)
1640 (88683)
3314 (60756)
4740 (45551)
6990 (42853)
2258 (41883)
1842 (38353)
2520 (36912)		 k = 144, 324, 900, 1764, 2304, 3600, 5184, 6084, and 8100 proven composite by full algebraic factors.
362 10 3, 11   k = = 1 mod 19 (19) none - proven 7 (146341)
8 (28)
6 (26)
3 (15)
2 (4)
5 (2)
9 (1)
4 (1)		  
363 64 7, 13   k = = 1 mod 2 (2)
k = = 1 mod 181 (181)		 none - proven 34 (103588)
38 (228)
20 (214)
60 (28)
36 (21)
58 (17)
24 (5)
62 (4)
42 (4)
18 (4)		  
364 74 5, 73 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*364^q - 1) *
     (m*364^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 11 (11)		 none - proven 20 (79)
30 (73)
32 (67)
8 (59)
53 (28)
51 (17)
65 (16)
63 (16)
71 (15)
5 (8)		 k = 9 proven composite by partial algebraic factors.
365 62 3, 61   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 13 (13)		 none - proven 46 (18381)
28 (337)
38 (70)
56 (18)
44 (12)
20 (10)
6 (6)
10 (3)
60 (2)
32 (2)		  
366 2109 7, 31, 619   k = = 1 mod 5 (5)
k = = 1 mod 73 (73)		 1747 (2M) 2038 (1028507)
1983 (271591)
729 (183817)
1110 (154149)
907 (124278)
93 (60429)
2039 (45784)
767 (23501)
1059 (22401)
1563 (20157)		  
367 620 7, 13, 23, 619   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 61 (61)		 none - proven 456 (90682)
114 (68120)
530 (55209)
344 (35288)
302 (14890)
252 (4744)
74 (3471)
234 (2704)
120 (1299)
206 (974)		  
368 40 3, 41   k = = 1 mod 367 (367) 36 (600K) 32 (15514)
11 (10866)
39 (2404)
23 (2204)
37 (983)
35 (862)
16 (137)
10 (83)
38 (32)
18 (25)		  
369 36 5, 37 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*369^q - 1) *
     (m*369^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 23 (23)		 none - proven 14 (1042)
26 (991)
18 (66)
20 (35)
34 (4)
8 (4)
12 (3)
2 (3)
10 (2)
32 (1)		 k = 4 proven composite by partial algebraic factors.
370 531 7, 53   k = = 1 mod 3 (3)
k = = 1 mod 41 (41)		 188 (300K)
225 (300K)
405 (300K)		 237 (65280)
132 (32206)
476 (9618)
209 (6400)
317 (4666)
344 (2391)
492 (2352)
107 (2137)
324 (1763)
302 (1545)		  
371 32 3, 31   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 37 (37)		 none - proven 28 (111)
20 (44)
30 (24)
2 (8)
18 (3)
24 (2)
14 (2)
8 (2)
22 (1)
12 (1)		  
372 4477 5, 13, 373   k = = 1 mod 7 (7)
k = = 1 mod 53 (53)		 419 (400K)
944 (400K)
961 (400K)
1493 (400K)
1747 (400K)
1854 (400K)
2718 (400K)
2985 (400K)
3058 (400K)
3301 (400K)
3418 (400K)
4064 (400K)
4447 (400K)		 4431 (327835)
2642 (302825)
229 (217261)
2025 (179001)
1682 (177234)
3271 (119926)
2996 (94515)
3563 (76554)
577 (68130)
4423 (63494)		  
373 74 7, 13, 73   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 31 (31)		 18 (600K) 66 (31)
30 (15)
68 (14)
60 (11)
50 (10)
14 (8)
36 (5)
54 (4)
8 (4)
72 (3)		  
374 4 3, 5   k = = 1 mod 373 (373) none - proven 3 (3)
2 (2)		  
375 836460 7, 47, 139, 1009   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)
k = = 1 mod 17 (17)		 2476 k's remaining at n=10K.

See k's at Riesel Base 375 remain.		 369140 (9995)
225928 (9988)
209568 (9983)
399228 (9982)
686860 (9975)
462830 (9972)
270988 (9955)
312820 (9949)
736192 (9948)
295394 (9946)		  
376 144 13, 29   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 none - proven 32 (1254)
59 (449)
90 (210)
38 (98)
8 (70)
80 (30)
132 (24)
129 (22)
123 (20)
105 (19)		  
377 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 47 (47)		 none - proven 6 (6)
2 (4)
4 (3)		  
378 1517 5, 17, 379   k = = 1 mod 13 (13)
k = = 1 mod 29 (29)		 9 (300K)
112 (300K)
317 (300K)
617 (300K)
919 (300K)
1087 (300K)		 214 (219424)
1427 (58523)
91 (27170)
949 (19413)
361 (11129)
1036 (8723)
137 (8654)
1203 (7918)
1435 (7522)
1438 (5825)		  
379 56 5, 19   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 none - proven 18 (76)
54 (6)
24 (6)
26 (5)
20 (5)
44 (4)
32 (4)
42 (2)
14 (2)
48 (1)		  
380 128 3, 127   k = = 1 mod 379 (379) 38 (300K)
50 (300K)
79 (300K)		 63 (145268)
125 (6358)
22 (4223)
122 (3792)
2 (3786)
44 (3430)
4 (2039)
113 (1874)
95 (834)
20 (710)		  
381 168652 7, 13, 43, 191   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 19 (19)		 182 k's remaining at n=100K.

See k's at Riesel Base 381 remain.		 67460 (96777)
33198 (95351)
22182 (93944)
160082 (91046)
75544 (90950)
108668 (89348)
140180 (84616)
149288 (83806)
94312 (82097)
89800 (82065)		  
382 13404 5, 13, 383   k = = 1 mod 3 (3)
k = = 1 mod 127 (127)		 132 k's remaining at n=100K.

See k's at Riesel Base 382 remain.		 1994 (97236)
422 (94640)
10158 (93824)
11664 (92511)
11223 (92408)
477 (92228)
4440 (87002)
2183 (80971)
4221 (79917)
2528 (78364)		  
383 208 3, 5, 41, 113   k = = 1 mod 2 (2)
k = = 1 mod 191 (191)		 116 (694K)
134 (694K)
136 (694K)
148 (694K)
170 (694K)
178 (694K)		 70 (147947)
44 (143148)
82 (47643)
2 (20956)
202 (6467)
194 (2504)
14 (2084)
152 (1872)
16 (1567)
58 (1005)		  
384 6 5, 7 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*384^q - 1) *
     (m*384^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 383 (383) none - proven 5 (2)
2 (2)
3 (1)		 k = 4 proven composite by partial algebraic factors.
385 3449490 13, 193, 5701 All k where k = m^2
and m = = 81 or 112 mod 193:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*385^q - 1) *
     (m*385^q + 1)
   odd n:
     factor of 193		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 3683 k's remaining at n=10K.

See k's at Riesel Base 385 remain.		 2899992 (9994)
2274698 (9985)
2561040 (9982)
3098220 (9981)
2698610 (9980)
996074 (9977)
3310922 (9971)
2158934 (9971)
1667814 (9966)
104480 (9965)		 k = 248004, 435600, 2742336, and 3305124 proven composite by partial algebraic factors.
386 44 3, 43   k = = 1 mod 5 (5)
k = = 1 mod 7 (7)
k = = 1 mod 11 (11)		 none - proven 38 (15162)
35 (418)
9 (93)
32 (32)
10 (31)
28 (15)
5 (12)
3 (9)
24 (3)
13 (3)		  
387 98 5, 17, 97   k = = 1 mod 2 (2)
k = = 1 mod 193 (193)		 none - proven 96 (6658)
18 (3767)
58 (3346)
24 (735)
38 (662)
74 (423)
4 (171)
10 (60)
82 (40)
30 (21)		  
388 205391 5, 7, 13, 19, 389 All k where k = m^2
and m = = 115 or 274 mod 389:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*388^q - 1) *
     (m*388^q + 1)
   odd n:
     factor of 389		 k = = 1 mod 3 (3)
k = = 1 mod 43 (43)		 2747 k's remaining at n=10K.

See k's at Riesel Base 388 remain.		 131121 (9999)
87666 (9995)
83312 (9984)
202500 (9981)
191759 (9973)
94592 (9968)
192419 (9967)
77615 (9961)
36917 (9946)
116526 (9937)		 No k's proven composite by algebraic factors.
389 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 97 (97)		 none - proven 2 (20)  
390 137 17, 23 All k where k = m^2
and m = = 4 or 13 mod 17:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*390^q - 1) *
     (m*390^q + 1)
   odd n:
     factor of 17		 k = = 1 mod 389 (389) none - proven 45 (12968)
59 (218)
36 (85)
111 (36)
86 (33)
131 (30)
69 (29)
82 (22)
55 (22)
52 (21)		 k = 16 proven composite by partial algebraic factors.
391 1820454 7, 19, 109, 2689   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 13 (13)		 4989 k's remaining at n=10K.

See k's at Riesel Base 391 remain.		 889770 (9995)
418392 (9995)
1178892 (9989)
803832 (9983)
136424 (9983)
1463790 (9982)
224820 (9979)
951168 (9977)
490512 (9971)
1569240 (9969)		  
392 74 3, 5, 73   k = = 1 mod 17 (17)
k = = 1 mod 23 (23)		 7 (600K) 28 (213295)
56 (25238)
72 (2316)
32 (2234)
20 (1690)
41 (974)
19 (449)
43 (291)
59 (176)
36 (57)		  
393 11358 13, 43, 277 All k where k = m^2
and m = = 14 or 183 mod 197:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*393^q - 1) *
     (m*393^q + 1)
   odd n:
     factor of 197		 k = = 1 mod 2 (2)
k = = 1 mod 7 (7)		 35 k's remaining at n=100K.

See k's at Riesel Base 393 remain.		 8238 (87770)
7604 (83811)
5710 (83023)
1444 (78835)
7406 (66842)
8472 (65939)
7784 (63112)
1634 (62613)
1766 (51066)
7112 (42184)		 k = 196 proven composite by partial algebraic factors.
394 159 5, 79 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*394^q - 1) *
     (m*394^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 131 (131)		 none - proven 80 (298731)
86 (220461)
81 (118571)
89 (87976)
78 (31874)
146 (25129)
141 (5107)
14 (1106)
41 (919)
57 (652)		 k = 9 and 144 proven composite by partial algebraic factors.
395 10 3, 11   k = = 1 mod 2 (2)
k = = 1 mod 197 (197)		 none - proven 2 (396)
6 (14)
8 (2)
4 (1)		  
396 41672 7, 37, 607 All k where k = m^2
and m = = 63 or 334 mod 397:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*396^q - 1) *
     (m*396^q + 1)
   odd n:
     factor of 397		 k = = 1 mod 5 (5)
k = = 1 mod 79 (79)		 111 k's remaining at n=100K.

See k's at Riesel Base 396 remain.		 33903 (96776)
30144 (93291)
8337 (87166)
6108 (81370)
12408 (80013)
12965 (79069)
22345 (75832)
6624 (75251)
21543 (75000)
31319 (68627)		 k = 3969 proven composite by partial algebraic factors.
397 172134 5, 7, 13, 37, 199   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 11 (11)		 688 k's remaining at n=25K.

See k's at Riesel Base 397 remain.		 170442 (24877)
19722 (24658)
32364 (24428)
80594 (24420)
130170 (24337)
56238 (24203)
33956 (24082)
23022 (24052)
36354 (24009)
163764 (23988)		  
398 8 3, 7   k = = 1 mod 397 (397) 7 (600K) 2 (32)
5 (22)
4 (3)
6 (2)
3 (1)		  
400 20080878 13, 127, 401, 421 All k = m^2 for all n; factors to:
(m*20^n - 1) *
(m*20^n + 1)		 k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 19 (19)		 111272 k's remaining at n=2.5K. To be shown later. 19346231 (2500)
18818888 (2500)
18788313 (2500)
18515286 (2500)
18399765 (2500)
18193146 (2500)
16561097 (2500)
16183715 (2500)
16126127 (2500)
15983174 (2500)		 k = 3^2, 9^2, 12^2, 18^2, 21^2, 24^2, 30^2, 33^2, 39^2, 42^2, (etc. pattern repeating every 21m where k not = = 1 mod 19) proven composite by full algebraic factors.
401 68 3, 67   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)		 38 (600K) 8 (140)
2 (112)
10 (77)
30 (61)
64 (23)
28 (21)
58 (15)
20 (10)
62 (8)
52 (7)		  
402 92 13, 31 All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*402^q - 1) *
     (m*402^q + 1)
   odd n:
     factor of 13		 k = = 1 mod 401 (401) 32 (600K) 26 (5981)
61 (2310)
76 (1243)
36 (1069)
22 (542)
44 (339)
77 (286)
37 (234)
75 (93)
60 (78)		 k = 25 and 64 proven composite by partial algebraic factors.
403 24744 5, 101, 109 All k where k = m^2
and m = = 10 or 91 mod 101:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*403^q - 1) *
     (m*403^q + 1)
   odd n:
     factor of 101		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 67 (67)		 60 k's remaining at n=100K.

See k's at Riesel Base 403 remain.		 15954 (97315)
21212 (89160)
1836 (86213)
12006 (81973)
9482 (76336)
10824 (75572)
5526 (73462)
19968 (68388)
7550 (67957)
13248 (66156)		 No k's proven composite by algebraic factors.
404 4 3, 5   k = = 1 mod 13 (13)
k = = 1 mod 31 (31)		 none - proven 3 (12)
2 (4)		  
405 146 7, 29 All k where k = m^2
and m = = 12 or 17 mod 29:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*405^q - 1) *
     (m*405^q + 1)
   odd n:
     factor of 29		 k = = 1 mod 2 (2)
k = = 1 mod 101 (101)		 none - proven 62 (1314)
140 (680)
44 (209)
48 (140)
104 (48)
142 (40)
120 (37)
114 (31)
8 (29)
132 (20)		 k = 144 proven composite by partial algebraic factors.
406 593 11, 37   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 260 (500K)
297 (500K)		 197 (23220)
417 (6574)
485 (3771)
287 (3259)
419 (3109)
527 (1706)
428 (1358)
144 (1253)
120 (582)
438 (494)		  
407 16 3, 17   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 29 (29)		 none - proven 14 (452)
10 (345)
2 (10)
12 (5)
6 (1)
4 (1)		  
408 5316 5, 13, 409   k = = 1 mod 11 (11)
k = = 1 mod 37 (37)		 40 k's remaining at n=100K.

See k's at Riesel Base 408 remain.		 142 (97284)
3784 (89487)
2822 (60110)
2010 (57298)
3132 (55783)
1854 (50388)
1369 (44511)
2797 (43704)
4446 (40190)
3683 (37925)		  
409 534 5, 41 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*409^q - 1) *
     (m*409^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 17 (17)		 284 (500K)
344 (500K)		 230 (20579)
116 (11237)
288 (5771)
264 (1624)
122 (1376)
326 (1097)
96 (773)
128 (575)
242 (220)
254 (194)		 k = 144 proven composite by partial algebraic factors.
410 136 3, 137   k = = 1 mod 409 (409) 47 (300K)
58 (300K)
64 (300K)		 95 (110710)
111 (41397)
39 (27445)
98 (26998)
67 (25659)
100 (8877)
16 (7095)
65 (5868)
106 (1951)
132 (1785)		  
411 60254 13, 89, 103   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 41 (41)		 122 k's remaining at n=100K.

See k's at Riesel Base 411 remain.		 59842 (98748)
16652 (98471)
16778 (95497)
33078 (93803)
23444 (91822)
25254 (83954)
27912 (83570)
29814 (80643)
34028 (78059)
38482 (76578)		  
412 69 5, 7, 17   k = = 1 mod 3 (3)
k = = 1 mod 137 (137)		 6 (600K) 8 (29791)
9 (12153)
57 (1933)
38 (776)
14 (97)
60 (77)
33 (76)
68 (59)
41 (30)
3 (20)		  
413 22 3, 23   k = = 1 mod 2 (2)
k = = 1 mod 103 (103)		 none - proven 4 (23)
14 (20)
2 (6)
20 (4)
8 (4)
12 (2)
18 (1)
16 (1)
10 (1)
6 (1)		  
414 84 5, 83 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*414^q - 1) *
     (m*414^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 46*m^2
and m = = 1 or 4 mod 5:
   even n:
     factor of 5
   for odd n let k = 46*m^2
   and let n=2*q-1; factors to:
     [m*3^n*46^q - 1] *
     [m*3^n*46^q + 1]		 k = = 1 mod 7 (7)
k = = 1 mod 59 (59)		 none - proven 82 (21952)
74 (5106)
25 (379)
75 (89)
66 (61)
69 (54)
16 (45)
59 (30)
40 (20)
51 (17)		 k = 4, 9, and 49 proven composite by condition 1.

k = 46 proven composite by condition 2.
416 140 3, 139   k = = 1 mod 5 (5)
k = = 1 mod 83 (83)		 55 (600K) 53 (6640)
113 (2420)
8 (2224)
58 (1669)
133 (911)
125 (850)
62 (294)
74 (246)
139 (127)
38 (104)		  
417 56 11, 19   k = = 1 mod 2 (2)
k = = 1 mod 13 (13)		 none - proven 18 (45418)
16 (281)
54 (116)
48 (74)
32 (52)
44 (47)
36 (37)
6 (23)
8 (14)
42 (13)		  
418 11733 5, 29, 419   k = = 1 mod 3 (3)
k = = 1 mod 139 (139)		 56 k's remaining at n=100K.

See k's at Riesel Base 418 remain.		 6561 (89543)
9510 (81890)
11702 (65520)
521 (65021)
929 (62613)
7628 (62581)
2637 (61183)
11501 (56039)
1319 (53016)
4829 (43787)		  
419 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)
k = = 1 mod 19 (19)		 none - proven 2 (2)  
420 6548233 13, 151, 421, 1171 (Condition 1):
All k where k = m^2
and m = = 29 or 392 mod 421:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*420^q - 1) *
     (m*420^q + 1)
   odd n:
     factor of 421
(Condition 2):
All k where k = 105*m^2
and m = = 58 or 363 mod 421:
   even n:
     factor of 421
   for odd n let k = 105*m^2
   and let n=2*q-1; factors to:
     [m*2^n*105^q - 1] *
     [m*2^n*105^q + 1]		 k = = 1 mod 419 (419) 63188 k's remaining at n=2.5K. To be shown later. 6229527 (2500)
6128655 (2500)
5441862 (2500)
5288508 (2500)
4310144 (2500)
4112225 (2500)
2509738 (2500)
2263804 (2500)
1986937 (2500)
1927646 (2500)		 k = 841, 153664, 202500, 660969, 758641, 1522756, 1669264, 2739025, 2934369, 4309776, 4553956, 6235009, and 6528025 proven composite by condition 1.

k = 353220 proven composite by condition 2.
421 73640 13, 17, 211   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 7 (7)		 50 k's remaining at n=100K.

See k's at Riesel Base 421 remain.		 5864 (99477)
62054 (98670)
34848 (89339)
21312 (83093)
30408 (82078)
17334 (77784)
8958 (72815)
72788 (71038)
71952 (70703)
7790 (66082)		  
422 46 3, 47   k = = 1 mod 421 (421) 11 (300K)
13 (300K)
14 (300K)
29 (300K)
37 (300K)		 41 (22802)
4 (21737)
23 (5568)
8 (2944)
26 (642)
2 (540)
16 (247)
3 (190)
42 (48)
45 (43)		  
423 1536 5, 29, 53 All k where k = m^2
and m = = 23 or 30 mod 53:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*423^q - 1) *
     (m*423^q + 1)
   odd n:
     factor of 53		 k = = 1 mod 2 (2)
k = = 1 mod 211 (211)		 264 (300K)
372 (300K)
478 (300K)
552 (300K)
998 (300K)
1074 (300K)
1324 (300K)		 302 (295123)
824 (236540)
1112 (173962)
1114 (115395)
1052 (58212)
1106 (50490)
370 (38928)
1522 (27770)
1490 (27060)
474 (25859)		 k = 900 proven composite by partial algebraic factors.
424 69 5, 17 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*424^q - 1) *
     (m*424^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 47 (47)		 18 (300K)
21 (300K)
44 (300K)		 59 (38)
26 (31)
50 (16)
54 (12)
51 (11)
24 (10)
5 (10)
53 (9)
30 (8)
35 (7)		 k = 9 proven composite by partial algebraic factors.
425 70 3, 71   k = = 1 mod 2 (2)
k = = 1 mod 53 (53)		 none - proven 64 (467857)
50 (5842)
46 (3819)
40 (2047)
10 (917)
16 (255)
14 (202)
38 (100)
52 (87)
56 (24)		  
426 62 7, 61   k = = 1 mod 5 (5)
k = = 1 mod 17 (17)		 none - proven 55 (162)
7 (60)
29 (49)
12 (29)
40 (19)
53 (15)
45 (13)
25 (13)
60 (8)
34 (6)		  
427 2080614 5, 17, 107, 3889   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 71 (71)		 16442 k's remaining at n=2.5K. To be shown later. 1929920 (2500)
296772 (2500)
174282 (2500)
99374 (2500)
1430588 (2499)
162258 (2499)
1933382 (2498)
1905956 (2498)
1771808 (2498)
1150196 (2498)		  
428 10 3, 11   k = = 1 mod 7 (7)
k = = 1 mod 61 (61)		 none - proven 4 (55)
2 (4)
7 (3)
6 (2)
5 (2)
9 (1)
3 (1)		  
429 44 5, 43 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*429^q - 1) *
     (m*429^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 107 (107)		 none - proven 26 (14823)
8 (452)
34 (24)
24 (12)
6 (9)
20 (7)
30 (4)
32 (3)
42 (2)
18 (2)		 k = 4 proven composite by partial algebraic factors.
430 45152 7, 19, 163, 379   k = = 1 mod 3 (3)
k = = 1 mod 11 (11)
k = = 1 mod 13 (13)		 432 (500K)
1688 (500K)
9954 (500K)
10433 (500K)
10614 (500K)
14465 (500K)
22412 (500K)
26244 (500K)
30971 (500K)
38246 (500K)
40319 (500K)
44394 (500K)
44510 (500K)		 39653 (460397)
33300 (417849)
14844 (350980)
34910 (221380)
1383 (188603)
33570 (166163)
31235 (162872)
24153 (160500)
34301 (145309)
13254 (117326)		  
431 15380 3, 7, 67, 163   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 43 (43)		 228 k's remaining at n=100K.

See k's at Riesel Base 431 remain.		 13588 (99779)
950 (99260)
1024 (97241)
13878 (96732)
6178 (90609)
7088 (88242)
11060 (87982)
5252 (86678)
15284 (86650)
9250 (80813)		  
432 192596 5, 7, 13, 67, 1493 (Condition 1):
All k where k = m^2
and m = = 179 or 254 mod 433:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*432^q - 1) *
     (m*432^q + 1)
   odd n:
     factor of 433
(Condition 2):
All k where k = 3*m^2
and m = = 17 or 416 mod 433:
   even n:
     factor of 433
   for odd n let k = 3*m^2
   and let n=2*q-1; factors to:
     [m*12^n*3^q - 1] *
     [m*12^n*3^q + 1]		 k = = 1 mod 431 (431) 8757 k's remaining at n=2.5K. To be shown later. 3 (16002)
88488 (2500)
18627 (2500)
4164 (2500)
99419 (2499)
86927 (2498)
156877 (2497)
7547 (2497)
98818 (2496)
79953 (2496)		 k = 32041 and 64516 proven composite by condition 1.

k = 867 proven composite by condition 2.
433 92 7, 31   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 none - proven 6 (283918)
14 (6197)
36 (635)
42 (156)
86 (81)
84 (24)
80 (20)
90 (18)
74 (13)
62 (12)		  
434 4 3, 5   k = = 1 mod 433 (433) none - proven 2 (1166)
3 (1)		  
436 645 19, 23   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 29 (29)		 162 (500K)
344 (500K)		 512 (84560)
413 (36050)
75 (33186)
459 (32192)
173 (12829)
345 (10195)
392 (9237)
39 (4659)
113 (3790)
485 (2083)		  
437 14 3, 5, 13   k = = 1 mod 2 (2)
k = = 1 mod 109 (109)		 none - proven 12 (5)
8 (4)
10 (3)
2 (2)
6 (1)
4 (1)		  
438 2194 5, 17, 439   k = = 1 mod 19 (19)
k = = 1 mod 23 (23)		 28 k's remaining at n=100K.

See k's at Riesel Base 438 remain.		 1458 (95702)
2029 (88660)
211 (73142)
2012 (54439)
1647 (44328)
543 (42061)
159 (36140)
823 (35172)
1600 (30469)
1674 (30323)		  
439 144 5, 11   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 73 (73)		 44 (500K)
120 (500K)		 96 (205245)
122 (32573)
12 (18751)
66 (9827)
32 (1598)
104 (522)
26 (361)
62 (266)
14 (86)
84 (26)		  
440 8 3, 7   k = = 1 mod 439 (439) none - proven 6 (2)
5 (2)
2 (2)
7 (1)
4 (1)
3 (1)		  
441 118 13, 17 All k = m^2 for all n; factors to:
(m*21^n - 1) *
(m*21^n + 1)		 k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 11 (11)		 none - proven 92 (2369)
40 (113)
52 (63)
84 (44)
90 (30)
88 (9)
68 (9)
110 (4)
50 (4)
22 (4)		 k = 4 and 64 proven composite by full algebraic factors.
442 54047 5, 41, 443   k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 71 k's remaining at n=100K.

See k's at Riesel Base 442 remain.		 13706 (94765)
15068 (90122)
42737 (86138)
3944 (85976)
12044 (83104)
40619 (81656)
49508 (79678)
18129 (79635)
9062 (78006)
50484 (73160)		  
443 28 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 13 (13)
k = = 1 mod 17 (17)		 none - proven 8 (416)
16 (165)
2 (12)
22 (7)
20 (6)
12 (3)
10 (3)
4 (3)
26 (2)
24 (1)		  
444 179 5, 89 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*444^q - 1) *
     (m*444^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 111*m^2
and m = = 1 or 4 mod 5:
   even n:
     factor of 5
   for odd n let k = 111*m^2
   and let n=2*q-1; factors to:
     [m*2^n*111^q - 1] *
     [m*2^n*111^q + 1]		 k = = 1 mod 443 (443) 11 (300K)
26 (300K)
74 (300K)
96 (300K)
114 (300K)		 123 (51913)
36 (44313)
56 (15219)
128 (7715)
100 (2407)
39 (1588)
60 (787)
41 (739)
43 (728)
174 (660)		 k = 4, 9, 49, 64, 144, and 169 proven composite by condition 1.

k = 111 proven composite by condition 2.
445 43338 7, 13, 727   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 37 (37)		 91 k's remaining at n=100K.

See k's at Riesel Base 445 remain.		 31890 (95227)
34136 (92574)
33170 (91596)
22226 (91370)
31628 (90875)
39026 (81547)
22080 (79452)
15332 (78822)
27062 (70361)
15590 (62266)		  
446 74 3, 7, 13, 73   k = = 1 mod 5 (5)
k = = 1 mod 89 (89)		 13 (300K)
55 (300K)
64 (300K)		 35 (157542)
10 (152027)
34 (50995)
3 (4850)
44 (988)
43 (409)
59 (330)
20 (330)
23 (276)
65 (210)		  
447 148 5, 7, 13   k = = 1 mod 2 (2)
k = = 1 mod 223 (223)		 78 (500K)
118 (500K)		 146 (187198)
46 (1814)
76 (182)
104 (120)
112 (86)
74 (79)
92 (77)
18 (60)
8 (43)
48 (40)		  
448 131556 5, 293, 449 (Condition 1):
All k where k = m^2
and m = = 67 or 382 mod 449:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*448^q - 1) *
     (m*448^q + 1)
   odd n:
     factor of 449
(Condition 2):
All k where k = 7*m^2
and m = = 87 or 362 mod 449:
   even n:
     factor of 449
   for odd n let k = 7*m^2
   and let n=2*q-1; factors to:
     [m*8^n*7^q - 1] *
     [m*8^n*7^q + 1]		 k = = 1 mod 3 (3)
k = = 1 mod 149 (149)		 786 k's remaining at n=25K.

See k's at Riesel Base 448 remain.		 50349 (24884)
87563 (24882)
34127 (24855)
64562 (24795)
124368 (24710)
25983 (24701)
48372 (24700)
81222 (24615)
37301 (24606)
128706 (24549)		 No k's proven composite by condition 1.

k = 52983 proven composite by condition 2.
449 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)		 none - proven 2 (174)  
450 122 11, 41 All k where k = m^2
and m = = 9 or 32 mod 41:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*450^q - 1) *
     (m*450^q + 1)
   odd n:
     factor of 41		 k = = 1 mod 449 (449) none - proven 57 (36788)
25 (2205)
23 (1929)
21 (920)
109 (386)
112 (353)
16 (295)
65 (258)
60 (221)
43 (208)		 k = 81 proven composite by partial algebraic factors.
451 89610 7, 13, 79, 113 All k where k = m^2
and m = = 15 or 98 mod 113:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*451^q - 1) *
     (m*451^q + 1)
   odd n:
     factor of 113		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 63 k's remaining at n=100K.

See k's at Riesel Base 451 remain.		 76688 (95426)
20348 (92318)
81440 (90845)
10604 (86683)
33710 (74990)
58698 (72399)
27582 (67383)
53498 (65927)
86348 (63406)
34688 (62474)		 No k's proven composite by algebraic factors.
452 59 3, 5, 29   k = = 1 mod 11 (11)
k = = 1 mod 41 (41)		 11 (300K)
43 (300K)
52 (300K)		 46 (153285)
47 (7406)
32 (534)
29 (412)
3 (334)
8 (266)
28 (91)
22 (85)
16 (75)
37 (41)		  
453 4658266 5, 227, 20521   k = = 1 mod 2 (2)
k = = 1 mod 113 (113)		 96179 k's remaining at n=2.5K. To be shown later. 4524442 (2500)
4455792 (2500)
4418728 (2500)
4384274 (2500)
3950578 (2500)
3135162 (2500)
3095682 (2500)
3036792 (2500)
2737248 (2500)
2686804 (2500)		  
454 6 5, 7   k = = 1 mod 3 (3)
k = = 1 mod 151 (151)		 none - proven 5 (1)
3 (1)
2 (1)		  
455 20 3, 19   k = = 1 mod 2 (2)
k = = 1 mod 227 (227)		 none - proven 18 (198)
14 (20)
12 (8)
16 (5)
4 (3)
8 (2)
2 (2)
10 (1)
6 (1)		  
457 747684 5, 229, 4177 All k where k = m^2
and m = = 107 or 122 mod 229:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*457^q - 1) *
     (m*457^q + 1)
   odd n:
     factor of 229		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 19 (19)		 5773 k's remaining at n=10K.

See k's at Riesel Base 457 remain.		 639984 (9999)
449234 (9999)
652394 (9988)
125432 (9984)
252722 (9980)
723228 (9975)
68136 (9974)
562038 (9971)
729414 (9968)
247322 (9968)		 k = 112896 proven composite by partial algebraic factors.
458 16 3, 17   k = = 1 mod 457 (457) 11 (700K) 10 (126261)
7 (9823)
9 (83)
12 (15)
6 (11)
5 (6)
14 (4)
8 (2)
2 (2)
15 (1)		  
459 24 5, 23 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*459^q - 1) *
     (m*459^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 229 (229)		 none - proven 14 (136)
22 (16)
20 (6)
16 (5)
18 (4)
10 (2)
2 (2)
12 (1)
8 (1)
6 (1)		 k = 4 proven composite by partial algebraic factors.
460 56243 13, 41, 461 All k where k = m^2
and m = = 48 or 413 mod 461:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*460^q - 1) *
     (m*460^q + 1)
   odd n:
     factor of 461		 k = = 1 mod 3 (3)
k = = 1 mod 17 (17)		 101 k's remaining at n=100K.

See k's at Riesel Base 460 remain.		 28671 (97345)
21365 (89615)
47705 (89060)
125 (86680)
46661 (85446)
30116 (85332)
15800 (84494)
24948 (83174)
39287 (83169)
14067 (83097)		 k = 2304 proven composite by partial algebraic factors.
461 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 23 (23)		 none - proven 4 (3071)
2 (6)		  
462 2924772 5, 13, 73, 463, 571   k = = 1 mod 461 (461) 50851 k's remaining at n=2.5K. To be shown later. 2720794 (2500)
2583247 (2500)
2551403 (2500)
2530092 (2500)
2256624 (2500)
2254087 (2500)
2234893 (2500)
2203589 (2500)
1898964 (2500)
1837558 (2500)		  
463 668 5, 13, 29   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 11 (11)		 216 (500K)
356 (500K)		 642 (6066)
170 (1114)
242 (474)
278 (464)
402 (431)
192 (328)
438 (302)
432 (250)
404 (227)
248 (182)		  
464 4 3, 5   k = = 1 mod 463 (463) none - proven 3 (218)
2 (18)		  
465 706690 7, 13, 233, 337 All k where k = m^2
and m = = 89 or 144 mod 233:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*465^q - 1) *
     (m*465^q + 1)
   odd n:
     factor of 233		 k = = 1 mod 2 (2)
k = = 1 mod 29 (29)		 2896 k's remaining at n=10K.

See k's at Riesel Base 465 remain.		 319908 (9974)
322208 (9965)
213824 (9961)
563428 (9947)
428936 (9940)
297036 (9936)
298818 (9923)
622136 (9921)
6434 (9919)
233158 (9888)		 k = 103684 and 620944 proven composite by partial algebraic factors.
466 21450 7, 43, 241   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 31 (31)		 54 k's remaining at n=100K.

See k's at Riesel Base 466 remain.		 14220 (94517)
21438 (79909)
17835 (78877)
16175 (76897)
10364 (76642)
17669 (70400)
14585 (66967)
15425 (63394)
12608 (62926)
5384 (58375)		  
467 14 3, 13   k = = 1 mod 2 (2)
k = = 1 mod 233 (233)		 none - proven 2 (36)
8 (20)
10 (15)
12 (2)
6 (1)
4 (1)		  
468 202 7, 67   k = = 1 mod 467 (467) 56 (300K)
69 (300K)
104 (300K)
162 (300K)		 141 (89405)
20 (6790)
146 (4814)
102 (2812)
134 (1777)
200 (1210)
169 (559)
92 (487)
174 (440)
97 (340)		  
469 516 5, 47 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*469^q - 1) *
     (m*469^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 13 (13)		 422 (600K) 336 (113211)
474 (76836)
236 (1323)
174 (1168)
96 (967)
288 (362)
194 (314)
122 (258)
6 (255)
314 (136)		 k = 324 proven composite by partial algebraic factors.
470 158 3, 157   k = = 1 mod 7 (7)
k = = 1 mod 67 (67)		 137 (600K) 83 (61902)
88 (3215)
149 (2942)
41 (2694)
5 (630)
157 (559)
91 (301)
147 (285)
25 (251)
76 (231)		  
471 750 7, 13, 31, 37   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 47 (47)		 302 (500K)
408 (500K)		 144 (218627)
464 (22140)
508 (10310)
648 (1590)
190 (1414)
568 (1229)
200 (996)
400 (785)
412 (744)
32 (561)		  
472 87 11, 43   k = = 1 mod 3 (3)
k = = 1 mod 157 (157)		 none - proven 69 (5695)
12 (1529)
78 (1467)
23 (1203)
9 (327)
72 (164)
48 (151)
21 (98)
53 (63)
63 (48)		  
473 14 3, 5, 13   k = = 1 mod 2 (2)
k = = 1 mod 59 (59)		 none - proven 2 (660)
8 (200)
12 (48)
4 (13)
10 (1)
6 (1)		  
474 39 5, 19 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*474^q - 1) *
     (m*474^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 11 (11)
k = = 1 mod 43 (43)		 none - proven 21 (769)
29 (350)
36 (101)
25 (95)
10 (44)
17 (16)
27 (8)
35 (7)
30 (7)
11 (7)		 k = 4 and 9 proven composite by partial algebraic factors.
475 50 7, 17   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 79 (79)		 none - proven 18 (65)
6 (42)
8 (19)
14 (3)
48 (2)
26 (2)
20 (2)
12 (2)
2 (2)
44 (1)		  
476 52 3, 53   k = = 1 mod 5 (5)
k = = 1 mod 19 (19)		 none - proven 49 (72833)
43 (713)
27 (110)
38 (60)
40 (27)
2 (26)
5 (10)
37 (9)
4 (9)
30 (6)		  
477 14102 5, 61, 239   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 17 (17)		 740 (100K)
1036 (100K)
1578 (100K)
1678 (100K)
2624 (100K)
3552 (100K)
3642 (100K)
4148 (100K)
4338 (100K)
4954 (100K)
5294 (100K)
6282 (100K)
6898 (100K)
7528 (100K)
7886 (100K)
9746 (100K)
10234 (100K)
10682 (100K)
11114 (100K)
12124 (100K)
12262 (100K)
12668 (100K)
13326 (100K)
13666 (100K)
13828 (100K)		 7248 (99452)
7198 (82440)
9694 (75892)
5502 (70937)
2114 (70833)
6236 (68802)
3948 (68190)
11834 (60299)
5534 (55864)
490 (55305)		  
478 370268 5, 17, 41, 479   k = = 1 mod 3 (3)
k = = 1 mod 53 (53)		 12041 k's remaining at n=2.5K. To be shown later. 12 (2902)
152634 (2499)
128919 (2497)
108957 (2496)
41778 (2496)
21912 (2496)
19442 (2496)
319635 (2495)
152057 (2495)
64817 (2495)		  
479 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 239 (239)		 none - proven 2 (6)  
480 38 13, 37 (Condition 1):
All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*480^q - 1) *
     (m*480^q + 1)
   odd n:
     factor of 13
(Condition 2):
All k where k = m^2
and m = = 6 or 31 mod 37:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*480^q - 1) *
     (m*480^q + 1)
   odd n:
     factor of 37		 k = = 1 mod 479 (479) none - proven 4 (93609)
30 (12864)
2 (144)
20 (101)
35 (13)
9 (11)
18 (7)
8 (7)
33 (5)
29 (5)		 k = 25 proven composite by condition 1.

k = 36 proven composite by condition 2.
482 8 3, 7   k = = 1 mod 13 (13)
k = = 1 mod 37 (37)		 none - proven 4 (135)
6 (6)
3 (3)
5 (2)
2 (2)
7 (1)		  
483 2584 5, 11, 41   k = = 1 mod 2 (2)
k = = 1 mod 241 (241)		 252 (300K)
298 (300K)
474 (300K)
494 (300K)
1286 (300K)
1442 (300K)
1616 (300K)
1852 (300K)
1948 (300K)
2056 (300K)
2102 (300K)
2168 (300K)
2434 (300K)		 1662 (292719)
2166 (274670)
1398 (183653)
2074 (104445)
1528 (43858)
2562 (21014)
1812 (16939)
782 (15523)
274 (15316)
1550 (12702)		  
484 96 5, 97 All k = m^2 for all n; factors to:
(m*22^n - 1) *
(m*22^n + 1)		 k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 23 (23)		 none - proven 53 (656)
74 (206)
60 (190)
84 (56)
38 (39)
89 (32)
59 (18)
65 (11)
14 (10)
66 (7)		 k = 9 and 81 proven composite by full algebraic factors.
485 6952 3, 7, 13, 223   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)		 91 k's remaining at n=100K.

See k's at Riesel Base 485 remain.		 202 (99889)
6464 (96452)
88 (96195)
1830 (89178)
5108 (88830)
2132 (88716)
800 (83916)
134 (83218)
3986 (79612)
1864 (78181)		  
486 1525283 7, 19, 151, 487   k = = 1 mod 5 (5)
k = = 1 mod 97 (97)		 27683 k's remaining at n=2.5K. To be shown later. 12 (3341)
1077398 (2500)
787860 (2500)
731704 (2500)
313997 (2500)
200679 (2500)
1429288 (2499)
1410550 (2499)
1369142 (2499)
1062639 (2499)		  
487 2256 5, 37, 61 All k where k = m^2
and m = = 11 or 50 mod 61:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*487^q - 1) *
     (m*487^q + 1)
   odd n:
     factor of 61		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 758 (300K)
914 (300K)
1110 (300K)
1128 (300K)
1646 (300K)
1688 (300K)
1728 (300K)
1968 (300K)
2234 (300K)		 900 (146907)
1908 (112659)
1046 (98506)
72 (87924)
1892 (33189)
1710 (32973)
1148 (29427)
396 (25167)
236 (23534)
2130 (22194)		 No k's proven composite by algebraic factors.
488 164 3, 163   k = = 1 mod 487 (487) 28 (300K)
29 (300K)
31 (300K)
58 (300K)
74 (300K)
97 (300K)
116 (300K)
137 (300K)		 133 (279973)
86 (197778)
118 (193957)
87 (193624)
95 (84834)
37 (60063)
7 (33163)
22 (22047)
136 (12213)
11 (10230)		  
489 6 5, 7 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*489^q - 1) *
     (m*489^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 61 (61)		 none - proven 2 (1) k = 4 proven composite by partial algebraic factors.
490 48051 13, 31, 199   k = = 1 mod 3 (3)
k = = 1 mod 163 (163)		 87 k's remaining at n=100K.

See k's at Riesel Base 490 remain.		 15722 (97577)
45737 (95777)
12743 (92886)
13796 (90077)
16659 (86798)
18798 (84166)
26022 (83302)
37059 (83199)
30467 (82377)
39747 (76389)		  
491 40 3, 41   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 7 (7)		 none - proven 4 (1683)
14 (658)
20 (174)
30 (104)
2 (26)
28 (5)
38 (4)
32 (4)
12 (2)
34 (1)		  
492 86 17, 29 All k where k = m^2
and m = = 4 or 13 mod 17:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*492^q - 1) *
     (m*492^q + 1)
   odd n:
     factor of 17		 k = = 1 mod 491 (491) none - proven 81 (399095)
23 (48063)
57 (394)
37 (369)
63 (214)
50 (190)
43 (50)
33 (36)
65 (24)
28 (20)		 k = 16 proven composite by partial algebraic factors.
493 170 13, 19   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 41 (41)		 92 (600K) 74 (373)
38 (48)
114 (39)
96 (39)
116 (34)
146 (26)
152 (22)
104 (13)
102 (11)
14 (11)		  
494 4 3, 5   k = = 1 mod 17 (17)
k = = 1 mod 29 (29)		 none - proven 2 (6)
3 (1)		  
495 117150 7, 31, 37, 101, 193   k = = 1 mod 2 (2)
k = = 1 mod 13 (13)
k = = 1 mod 19 (19)		 112 k's remaining at n=100K.

See k's at Riesel Base 495 remain.		 102878 (98410)
47338 (97189)
35248 (96993)
85096 (96307)
64262 (92752)
64140 (90007)
71808 (88723)
45414 (86196)
2386 (82554)
113366 (78590)		  
496 638 7, 71   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 11 (11)		 57 (600K) 354 (52620)
533 (51483)
633 (13827)
425 (744)
405 (606)
615 (506)
153 (274)
72 (237)
15 (171)
608 (166)		  
497 82 3, 83   k = = 1 mod 2 (2)
k = = 1 mod 31 (31)		 14 (500K)
56 (500K)		 64 (215875)
62 (145374)
28 (61627)
38 (4930)
52 (881)
26 (766)
22 (497)
20 (402)
68 (148)
34 (105)		  
498 96306 5, 193, 499 k = 93025:
   for even n let n=2*q; factors to:
     (305*498^q - 1) *
     (305*498^q + 1)
   odd n:
     covering set 13, 67, 241		 k = = 1 mod 7 (7)
k = = 1 mod 71 (71)		 835 k's remaining at n=25K.

See k's at Riesel Base 498 remain.		 29861 (24970)
21037 (24966)
48970 (24644)
1236 (24530)
66069 (24528)
74864 (24456)
82294 (24417)
59359 (24392)
75131 (24358)
71124 (24296)		  
499 2354 5, 13, 157 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*499^q - 1) *
     (m*499^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 83 (83)		 36 (300K)
356 (300K)
372 (300K)
476 (300K)
674 (300K)
714 (300K)
774 (300K)
1026 (300K)
1194 (300K)
1236 (300K)
1256 (300K)
1554 (300K)
1866 (300K)
1884 (300K)
1934 (300K)
2046 (300K)
2118 (300K)		 218 (159964)
1364 (149080)
842 (118587)
2220 (97105)
1296 (93839)
1754 (81660)
1446 (65259)
1646 (58811)
1698 (45090)
486 (43957)		 k = 144, 324, 1764, and 2304 proven composite by partial algebraic factors.
500 166 3, 167   k = = 1 mod 499 (499) 38 (300K)
53 (300K)
82 (300K)		 74 (218184)
107 (30954)
124 (11795)
143 (11244)
128 (10200)
61 (7535)
22 (6137)
122 (2858)
134 (2746)
58 (1959)		  
501 862 7, 19, 31   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)		 30 (500K)
142 (500K)
324 (500K)
330 (500K)		 242 (279492)
552 (73886)
814 (36926)
752 (16358)
614 (6512)
400 (3031)
842 (2946)
844 (2884)
382 (2316)
524 (2300)		  
502 7136 5, 7, 13, 31, 61   k = = 1 mod 3 (3)
k = = 1 mod 167 (167)		 70 k's remaining at n=100K.

See k's at Riesel Base 502 remain.		 1968 (94066)
4149 (92685)
1256 (87830)
1376 (59978)
5247 (59605)
6014 (54748)
4572 (54710)
6338 (52146)
1653 (48428)
2300 (44713)		  
503 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 251 (251)		 none - proven 2 (860)
6 (22)
4 (1)		  
504 201 5, 101 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*504^q - 1) *
     (m*504^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = m^2
and m = = 10 or 91 mod 101:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*504^q - 1) *
     (m*504^q + 1)
   odd n:
     factor of 101
(Condition 3):
All k where k = 14*m^2
and m = = 2 or 3 mod 5:
   even n:
     factor of 5
   for odd n let k = 14*m^2
   and let n=2*q-1; factors to:
     [m*6^n*14^q - 1] *
     [m*6^n*14^q + 1]		 k = = 1 mod 503 (503) 94 (600K) 116 (36571)
135 (11925)
157 (11720)
129 (8020)
86 (6427)
193 (5317)
69 (3420)
119 (1718)
131 (1343)
179 (1328)		 k = 4, 9, 49, 64, 144, and 169 proven composite by condition 1.

k = 100 proven composite by condition 2.

k = 56 and 126 proven composite by condition 3.
505 714 11, 23   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 68 (600K) 318 (66148)
390 (1540)
296 (900)
452 (219)
656 (203)
32 (176)
410 (156)
552 (119)
90 (116)
324 (91)		  
506 14 3, 13   k = = 1 mod 5 (5)
k = = 1 mod 101 (101)		 none - proven 8 (146)
2 (16)
4 (11)
9 (3)
12 (2)
5 (2)
3 (2)
13 (1)
10 (1)
7 (1)		  
507 11812 5, 97, 127   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)
k = = 1 mod 23 (23)		 618 (100K)
3936 (100K)
4096 (100K)
4244 (100K)
4740 (100K)
4996 (100K)
5462 (100K)
6402 (100K)
6476 (100K)
6908 (100K)
6962 (100K)
6984 (100K)
7262 (100K)
7270 (100K)
7746 (100K)
7796 (100K)
7944 (100K)
8510 (100K)
9064 (100K)
9334 (100K)
9528 (100K)
10546 (100K)
10648 (100K)
10736 (100K)
11138 (100K)		 4124 (98983)
9276 (95530)
4634 (80663)
2808 (71920)
5884 (64759)
7904 (51308)
10386 (50385)
5276 (46031)
2918 (45439)
10016 (44737)		  
508 1225673 5, 7, 37, 73, 509 All k where k = m^2
and m = = 208 or 301 mod 509:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*508^q - 1) *
     (m*508^q + 1)
   odd n:
     factor of 509		 k = = 1 mod 3 (3)
k = = 1 mod 13 (13)		 31004 k's remaining at n=2.5K. To be shown later. 893054 (2500)
752879 (2500)
612018 (2500)
554072 (2500)
459689 (2500)
282762 (2500)
1034679 (2499)
976682 (2499)
945632 (2499)
819629 (2499)		 k = 514089 and 656100 proven composite by partial algebraic factors.
509 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 127 (127)		 none - proven 2 (46)  
510 218 7, 73   k = = 1 mod 509 (509) 160 (500K)
202 (500K)		 48 (77480)
204 (5163)
80 (3552)
120 (1953)
22 (1835)
6 (1638)
146 (1530)
196 (1439)
9 (1115)
113 (1089)		  
513 221706 7, 139, 271 (Condition 1):
All k where k = m^2
and m = = 16 or 241 mod 257:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*513^q - 1) *
     (m*513^q + 1)
   odd n:
     factor of 257
(Condition 2):
All k where k = 513*m^2
and m = = 16 or 241 mod 257:
   [Reverse condition 1]		 k = = 1 mod 2 (2) 2095 k's remaining at n=25K.

See k's at Riesel Base 513 remain.		 4 (38031)
135412 (24963)
48724 (24951)
80072 (24874)
167890 (24870)
25602 (24850)
69976 (24726)
67484 (24663)
111738 (24624)
43012 (24566)		 k = 256 proven composite by condition 1.

k = 131328 proven composite by condition 2.
514 104 5, 103 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*514^q - 1) *
     (m*514^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 19 (19)		 none - proven 30 (424652)
21 (5833)
41 (5747)
75 (3707)
90 (3611)
26 (1545)
44 (368)
45 (224)
14 (126)
29 (80)		 k = 9 proven composite by partial algebraic factors.
515 44 3, 43   k = = 1 mod 2 (2)
k = = 1 mod 257 (257)		 none - proven 2 (58466)
38 (4800)
12 (2029)
4 (1579)
42 (228)
8 (70)
30 (20)
32 (16)
14 (14)
24 (10)		  
516 142 11, 47   k = = 1 mod 5 (5)
k = = 1 mod 103 (103)		 87 (600K) 78 (130647)
133 (21183)
129 (5636)
122 (857)
140 (504)
107 (191)
73 (136)
43 (100)
120 (62)
34 (37)		  
517 36 7, 37   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 43 (43)		 none - proven 30 (47)
20 (22)
8 (11)
6 (6)
24 (5)
18 (3)
32 (2)
26 (1)
14 (1)
12 (1)		  
518 172 3, 173   k = = 1 mod 11 (11)
k = = 1 mod 47 (47)		 7 (300K)
58 (300K)
74 (300K)
113 (300K)
139 (300K)		 94 (138071)
136 (59529)
97 (45151)
118 (33501)
71 (7430)
62 (4782)
44 (4268)
152 (3482)
115 (3369)
38 (2044)		  
519 14 5, 13 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*519^q - 1) *
     (m*519^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 37 (37)		 none - proven 6 (29)
12 (4)
2 (2)
10 (1)		 k = 4 proven composite by partial algebraic factors.
520 1128 7, 19, 97   k = = 1 mod 3 (3)
k = = 1 mod 173 (173)		 324 (300K)
576 (300K)
1094 (300K)		 638 (243506)
216 (131563)
330 (58090)
179 (26432)
233 (18595)
312 (14483)
26 (13420)
960 (8588)
533 (7843)
1122 (4660)		  
521 28 3, 29   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 13 (13)		 none - proven 20 (10)
2 (8)
22 (3)
12 (2)
8 (2)
24 (1)
18 (1)
10 (1)
4 (1)		  
522 9797 5, 7, 13, 31, 43   k = = 1 mod 521 (521) 149 k's remaining at n=100K.

See k's at Riesel Base 522 remain.		 8712 (98793)
2076 (98070)
6832 (93418)
2304 (91345)
2107 (87581)
4202 (87012)
6853 (81398)
7756 (79342)
4536 (76334)
5248 (75866)		  
523 132 5, 17, 131   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 29 (29)		 none - proven 126 (222906)
120 (43047)
66 (479)
108 (188)
36 (147)
90 (49)
54 (43)
24 (33)
42 (31)
80 (30)		  
524 4 3, 5   k = = 1 mod 523 (523) none - proven 2 (164)
3 (1)		  
525 8364188 13, 263, 10601   k = = 1 mod 2 (2)
k = = 1 mod 131 (131)		 53207 k's remaining at n=2.5K. To be shown later. 7665514 (2500)
7222756 (2500)
5730668 (2500)
4532150 (2500)
4088832 (2500)
4034342 (2500)
3140266 (2500)
2590606 (2500)
1589634 (2500)
1579648 (2500)		  
526 900 17, 31   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 7 (7)		 125 (300K)
273 (300K)
630 (300K)		 774 (41592)
509 (8078)
870 (4102)
342 (2949)
588 (2430)
278 (2338)
495 (2264)
119 (2036)
804 (1302)
147 (916)		  
527 10 3, 11   k = = 1 mod 2 (2)
k = = 1 mod 263 (263)		 none - proven 4 (46073)
6 (42)
2 (24)
8 (14)		  
528 47 5, 13, 23   k = = 1 mod 17 (17)
k = = 1 mod 31 (31)		 none - proven 34 (3644)
45 (1486)
22 (154)
26 (83)
27 (23)
29 (21)
37 (19)
42 (16)
7 (15)
40 (9)		  
529 54 5, 53 All k = m^2 for all n; factors to:
(m*23^n - 1) *
(m*23^n + 1)		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 11 (11)		 none - proven 30 (500)
6 (141)
26 (107)
24 (72)
14 (26)
2 (3)
44 (2)
42 (2)
20 (2)
50 (1)		 k = 36 proven composite by full algebraic factors.
530 58 3, 59   k = = 1 mod 23 (23) 10 (300K)
32 (300K)
43 (300K)
55 (300K)		 23 (2292)
53 (908)
22 (415)
26 (394)
16 (309)
29 (256)
8 (218)
14 (194)
5 (188)
44 (100)		  
531 20 7, 19   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 53 (53)		 none - proven 18 (6)
8 (5)
4 (5)
12 (2)
14 (1)
10 (1)
2 (1)		  
532 573 13, 41 (Condition 1):
All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*532^q - 1) *
     (m*532^q + 1)
   odd n:
     factor of 13
(Condition 2):
All k where k = m^2
and m = = 9 or 32 mod 41:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*532^q - 1) *
     (m*532^q + 1)
   odd n:
     factor of 41		 k = = 1 mod 3 (3)
k = = 1 mod 59 (59)		 none - proven 156 (534754)
204 (454080)
378 (139463)
452 (115413)
245 (49578)
261 (40095)
38 (39410)
329 (31767)
347 (15956)
129 (8760)		 k = 324 and 441 proven composite by condition 1.

k = 81 proven composite by condition 2.
533 88 3, 89   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 19 (19)		 74 (600K) 56 (898)
38 (356)
54 (121)
82 (91)
10 (27)
86 (22)
52 (19)
26 (14)
12 (8)
60 (7)		  
534 106 5, 107 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*534^q - 1) *
     (m*534^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 13 (13)
k = = 1 mod 41 (41)		 29 (500K)
59 (500K)		 11 (80327)
46 (27767)
25 (297)
74 (218)
69 (136)
44 (108)
20 (95)
19 (78)
32 (47)
81 (35)		 k = 4, 9, 49, and 64 proven composite by partial algebraic factors.
535 746580 7, 13, 61, 67, 73   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 89 (89)		 3106 k's remaining at n=10K.

See k's at Riesel Base 535 remain.		 482264 (9994)
622418 (9991)
222840 (9972)
326328 (9968)
716270 (9949)
473610 (9939)
479354 (9938)
12530 (9919)
118002 (9913)
313632 (9906)		  
536 178 3, 179   k = = 1 mod 5 (5)
k = = 1 mod 107 (107)		 9 (300K)
29 (300K)
32 (300K)
79 (300K)
107 (300K)
144 (300K)
152 (300K)
163 (300K)
170 (300K)		 58 (296735)
53 (20026)
35 (17414)
135 (11070)
173 (5090)
43 (4397)
77 (2500)
8 (2458)
134 (1312)
2 (840)		  
537 113788 5, 7, 13, 109, 269 All k where k = m^2
and m = = 82 or 187 mod 269:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*537^q - 1) *
     (m*537^q + 1)
   odd n:
     factor of 269		 k = = 1 mod 2 (2)
k = = 1 mod 67 (67)		 1041 k's remaining at n=25K.

See k's at Riesel Base 537 remain.		 45392 (24833)
25026 (24826)
76332 (24789)
93158 (24400)
59508 (24340)
49658 (24174)
56562 (24162)
92966 (24150)
91844 (24083)
111510 (24035)		 k = 6724 proven composite by partial algebraic factors.
538 8 5, 7, 13   k = = 1 mod 3 (3)
k = = 1 mod 179 (179)		 none - proven 6 (14)
2 (8)
5 (1)
3 (1)		  
539 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 269 (269)		 none - proven 2 (2)  
540 800138 17, 541, 1009 (Condition 1):
All k where k = m^2
and m = = 52 or 489 mod 541:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*540^q - 1) *
     (m*540^q + 1)
   odd n:
     factor of 541
(Condition 2):
All k where k = 15*m^2
and m = = 229 or 312 mod 541:
   even n:
     factor of 541
   for odd n let k = 15*m^2
   and let n=2*q-1; factors to:
     [m*6^n*15^q - 1] *
     [m*6^n*15^q + 1]
(Condition 3):
k = 61009:
   for even n let n=2*q; factors to:
     (247*540^q - 1) *
     (247*540^q + 1)
   odd n:
     covering set 17, 1009		 k = = 1 mod 7 (7)
k = = 1 mod 11 (11)		 1121 k's remaining at n=25K.

See k's at Riesel Base 540 remain.		 16069 (24978)
635600 (24970)
582248 (24893)
1531 (24786)
190243 (24765)
591035 (24717)
649812 (24708)
501244 (24672)
369596 (24661)
539292 (24643)		 k = 2704 proven composite by condition 1.

k = 786615 proven composite by condition 2.

k = 61009 proven composite by condition 3.
541 15546458 13, 271, 11257   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 121957 k's remaining at n=2.5K. To be shown later. 8552162 (2500)
6828540 (2500)
6726722 (2500)
6723648 (2500)
3111810 (2500)
1656572 (2500)
1612968 (2500)
13643562 (2499)
13637454 (2499)
13567122 (2499)		  
542 182 3, 181   k = = 1 mod 541 (541) 11 (300K)
19 (300K)
37 (300K)
42 (300K)
74 (300K)
80 (300K)
97 (300K)
100 (300K)
131 (300K)
134 (300K)
149 (300K)		 172 (189173)
89 (141296)
71 (134230)
133 (83867)
13 (70447)
28 (66555)
104 (56400)
115 (41905)
127 (33605)
55 (29513)		  
543 2500 7, 13, 17, 19 All k where k = m^2
and m = = 4 or 13 mod 17:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*543^q - 1) *
     (m*543^q + 1)
   odd n:
     factor of 17		 k = = 1 mod 2 (2)
k = = 1 mod 271 (271)		 40 k's remaining at n=100K.

See k's at Riesel Base 543 remain.		 1070 (74900)
2136 (72722)
1108 (56957)
1702 (53548)
1626 (48033)
1616 (46085)
1654 (31247)
466 (23517)
368 (23481)
1582 (23451)		 k = 16, 900, and 1444 proven composite by partial algebraic factors.
544 219 5, 109 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*544^q - 1) *
     (m*544^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 181 (181)		 none - proven 101 (16983)
159 (8446)
39 (4418)
6 (4411)
38 (3437)
74 (1676)
179 (1280)
171 (411)
194 (356)
65 (288)		 k = 9 and 144 proven composite by partial algebraic factors.
545 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 17 (17)		 none - proven 2 (84)
6 (4)
4 (1)		  
546 11732602 17, 89, 241, 547   k = = 1 mod 5 (5)
k = = 1 mod 109 (109)		 75963 k's remaining at n=2.5K. To be shown later. 11296667 (2500)
10896593 (2500)
10627994 (2500)
9713050 (2500)
9503885 (2500)
9474075 (2500)
9202119 (2500)
9120327 (2500)
8585770 (2500)
7309673 (2500)		  
547 1556732 5, 41, 113, 137 All k where k = m^2
and m = = 37 or 100 mod 137:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*547^q - 1) *
     (m*547^q + 1)
   odd n:
     factor of 137		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 13 (13)		 3234 k's remaining at n=25K.

See k's at Riesel Base 547 remain.		 162992 (24978)
241068 (24955)
1455738 (24939)
323022 (24910)
1445486 (24906)
908562 (24905)
649794 (24836)
916388 (24830)
1391922 (24829)
325058 (24814)		 k = 419904 and 992016 proven composite by partial algebraic factors.
548 13 3, 5, 17   k = = 1 mod 547 (547) 7 (600K) 4 (45)
12 (14)
3 (14)
5 (8)
2 (4)
11 (2)
8 (2)
6 (2)
10 (1)
9 (1)		  
549 34 5, 11 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*549^q - 1) *
     (m*549^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 137 (137)		 6 (600K) 12 (369)
24 (78)
28 (15)
26 (15)
14 (14)
22 (5)
32 (4)
18 (4)
30 (2)
10 (2)		 k = 4 proven composite by partial algebraic factors.
550 666 19, 29 All k where k = m^2
and m = = 12 or 17 mod 29:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*550^q - 1) *
     (m*550^q + 1)
   odd n:
     factor of 29		 k = = 1 mod 3 (3)
k = = 1 mod 61 (61)		 57 (300K)
153 (300K)
225 (300K)
324 (300K)
609 (300K)		 581 (270707)
227 (159478)
639 (15821)
30 (10353)
494 (5125)
465 (4865)
189 (3654)
647 (2777)
2 (1380)
51 (1116)		 k = 144 proven composite by partial algebraic factors.
551 22 3, 23   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 11 (11)		 10 (600K) 14 (60134)
2 (2718)
8 (416)
20 (30)
18 (2)
4 (1)		  
552 78 7, 79   k = = 1 mod 19 (19)
k = = 1 mod 29 (29)		 15 (400K)
34 (400K)
43 (400K)
69 (400K)		 55 (227540)
21 (1366)
13 (986)
8 (211)
18 (186)
31 (169)
33 (62)
68 (55)
62 (36)
57 (33)		  
553 31854 5, 53, 277 All k where k = m^2
and m = = 60 or 217 mod 277:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*553^q - 1) *
     (m*553^q + 1)
   odd n:
     factor of 277		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 23 (23)		 50 k's remaining at n=100K.

See k's at Riesel Base 553 remain.		 25356 (96266)
1148 (93737)
12182 (93023)
1512 (91126)
15866 (83923)
20466 (82546)
18126 (78841)
27188 (77884)
7698 (65661)
20640 (65054)		 k = 3600 proven composite by partial algebraic factors.
554 4 3, 5   k = = 1 mod 7 (7)
k = = 1 mod 79 (79)		 none - proven 2 (34)
3 (4)		  
555 58202 7, 13, 3391   k = = 1 mod 2 (2)
k = = 1 mod 277 (277)		 236 k's remaining at n=100K.

See k's at Riesel Base 555 remain.		 42422 (99129)
50716 (98711)
9718 (98236)
46770 (97857)
31604 (96191)
52802 (95176)
31190 (95145)
52534 (93979)
37220 (89573)
10224 (89336)		  
557 32 3, 31   k = = 1 mod 2 (2)
k = = 1 mod 139 (139)		 none - proven 26 (63710)
30 (22290)
28 (3207)
14 (1364)
8 (112)
4 (27)
16 (9)
12 (9)
20 (8)
2 (8)		  
558 259 13, 43 (Condition 1):
All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*558^q - 1) *
     (m*558^q + 1)
   odd n:
     factor of 13
(Condition 2):
All k where k = 62*m^2
and m = = 2 or 11 mod 13:
   even n:
     factor of 13
   for odd n let k = 62*m^2
   and let n=2*q-1; factors to:
     [m*3^n*62^q - 1] *
     [m*3^n*62^q + 1]		 k = = 1 mod 557 (557) 121 (300K)
170 (300K)
173 (300K)
181 (300K)
194 (300K)
246 (300K)
253 (300K)		 216 (195427)
27 (117379)
242 (34134)
155 (26612)
39 (25021)
239 (6323)
231 (4222)
115 (3488)
172 (3014)
78 (2066)		 k = 25 and 64 proven composite by condition 1.

k = 248 proven composite by condition 2.
559 6 5, 7   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 31 (31)		 none - proven 2 (1)  
560 10 3, 11   k = = 1 mod 13 (13)
k = = 1 mod 43 (43)		 none - proven 8 (19904)
2 (36)
3 (6)
5 (2)
9 (1)
7 (1)
6 (1)
4 (1)		  
561 5975464 37, 281, 4253 All k where k = m^2
and m = = 53 or 228 mod 281:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*561^q - 1) *
     (m*561^q + 1)
   odd n:
     factor of 281		 k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 7 (7)		 11851 k's remaining at n=2.5K. To be shown later. 5641692 (2498)
5171792 (2498)
4982798 (2498)
4430792 (2498)
4115548 (2498)
3847648 (2498)
2418994 (2498)
38030 (2498)
3898400 (2496)
2323942 (2496)		 k = 51984, 2125764, and 4080400 proven composite by partial algebraic factors.
562 191 7, 13, 19   k = = 1 mod 3 (3)
k = = 1 mod 11 (11)
k = = 1 mod 17 (17)		 none - proven 159 (2631)
39 (944)
126 (423)
29 (403)
66 (326)
81 (267)
47 (266)
140 (176)
153 (59)
101 (57)		  
563 46 3, 47   k = = 1 mod 2 (2)
k = = 1 mod 281 (281)		 28 (600K) 20 (16012)
26 (1714)
44 (264)
14 (68)
24 (33)
12 (24)
22 (23)
40 (15)
38 (8)
6 (5)		  
564 114 5, 113 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*564^q - 1) *
     (m*564^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 563 (563) 39 (500K)
86 (500K)		 29 (19502)
69 (1576)
94 (772)
62 (628)
96 (401)
26 (243)
81 (193)
12 (84)
72 (47)
74 (30)		 k = 4, 9, 49, and 64 proven composite by partial algebraic factors.
565 20598 37, 43, 67   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 47 (47)		 32 k's remaining at n=200K.

See k's at Riesel Base 565 remain.		 18092 (198465)
3098 (195049)
16260 (167947)
12902 (162944)
12596 (149039)
8742 (135774)
4836 (124142)
7316 (124048)
19394 (118343)
17636 (109660)		  
566 8 3, 7   k = = 1 mod 5 (5)
k = = 1 mod 113 (113)		 none - proven 7 (164827)
4 (23873)
2 (4)
5 (2)
3 (1)		  
567 2202 5, 13, 71   k = = 1 mod 2 (2)
k = = 1 mod 283 (283)		 214 (300K)
296 (300K)
922 (300K)
1366 (300K)
1492 (300K)
1584 (300K)		 694 (276568)
1334 (223344)
78 (107896)
988 (47799)
1568 (33108)
772 (23724)
948 (14179)
1338 (11676)
1268 (11250)
224 (9940)		  
568 19347 5, 89, 569 All k where k = m^2
and m = = 86 or 483 mod 569:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*568^q - 1) *
     (m*568^q + 1)
   odd n:
     factor of 569		 k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 90 k's remaining at n=100K.

See k's at Riesel Base 568 remain.		 17793 (94378)
14637 (90914)
18447 (87927)
6276 (85494)
13251 (84543)
17441 (83999)
9482 (82211)
1944 (80663)
12021 (79209)
6471 (78329)		 No k's proven composite by algebraic factors.
569 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 71 (71)		 none - proven 2 (60)  
570 12511182 7, 13, 17, 61, 193, 571   k = = 1 mod 569 (569) 250358 k's remaining at n=2.5K. To be shown later. 12142168 (2500)
11939442 (2500)
11854251 (2500)
11601775 (2500)
10261900 (2500)
9903484 (2500)
9432967 (2500)
9201245 (2500)
9189526 (2500)
8899258 (2500)		  
571 12 11, 13   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 19 (19)		 none - proven 2 (2)
8 (1)		  
572 190 3, 191   k = = 1 mod 571 (571) 43 (300K)
76 (300K)
88 (300K)
97 (300K)
119 (300K)
134 (300K)
154 (300K)
160 (300K)		 44 (172464)
110 (61926)
82 (44557)
148 (43659)
40 (36489)
26 (31434)
181 (18121)
32 (4914)
52 (4373)
2 (3804)		  
573 204 7, 41   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)
k = = 1 mod 13 (13)		 6 (600K) 128 (67678)
104 (40080)
124 (4365)
42 (3823)
162 (1283)
120 (1269)
20 (456)
186 (323)
148 (201)
28 (152)		  
574 24 5, 23 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*574^q - 1) *
     (m*574^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 191 (191)		 none - proven 21 (4803)
11 (11)
14 (8)
2 (8)
6 (5)
23 (4)
12 (4)
17 (3)
20 (2)
5 (2)		 k = 9 proven composite by partial algebraic factors.
575 77600 13, 73, 349   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 41 (41)		 979 k's remaining at n=25K.

See k's at Riesel Base 575 remain.		 17276 (24944)
39274 (24935)
67142 (24816)
41906 (24762)
18188 (24674)
70240 (24583)
37048 (24487)
57148 (24427)
38026 (24407)
21422 (24404)		  
576 17798 7, 13, 79, 349 All k = m^2 for all n; factors to:
(m*24^n - 1) *
(m*24^n + 1)		 k = = 1 mod 5 (5)
k = = 1 mod 23 (23)		 71 k's remaining at n>=100K.

See k's and test limits at Riesel Base 576 remain.		 8894 (105312)
2844 (101928)
13757 (86784)
12665 (79945)
14877 (79200)
15950 (79124)
12063 (75846)
5555 (74739)
7680 (74612)
1824 (69284)		 k = 2^2, 3^2, 5^2, 7^2, 8^2, 10^2, 12^2, 13^2, 15^2, (etc. pattern repeating every 5m where k not = = 1 mod 23) proven composite by full algebraic factors.
577 18 5, 13, 17   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 none - proven 14 (5775)
12 (17)
8 (2)
6 (1)
2 (1)		  
578 142 3, 5, 109   k = = 1 mod 577 (577) 22 (300K)
43 (300K)
52 (300K)
74 (300K)
101 (300K)
103 (300K)
106 (300K)
110 (300K)
118 (300K)
127 (300K)		 26 (199886)
2 (129468)
75 (111929)
59 (100148)
109 (46807)
137 (34626)
65 (16290)
49 (16111)
29 (11936)
71 (7306)		  
579 204 5, 29 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*579^q - 1) *
     (m*579^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 17 (17)		 none - proven 104 (222402)
114 (162252)
106 (112337)
96 (22899)
66 (19131)
166 (14571)
124 (11848)
94 (7238)
116 (1127)
136 (911)		 k = 4, 64, and 144 proven composite by partial algebraic factors.
580 167 7, 83   k = = 1 mod 3 (3)
k = = 1 mod 193 (193)		 none - proven 48 (174782)
125 (4550)
164 (2437)
90 (1888)
84 (1843)
144 (1367)
20 (616)
162 (223)
86 (209)
57 (175)		  
581 98 3, 97   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 29 (29)		 2 (600K) 58 (16145)
64 (2477)
14 (208)
32 (158)
4 (77)
60 (37)
20 (32)
80 (24)
70 (15)
68 (12)		  
582 54 11, 53   k = = 1 mod 7 (7)
k = = 1 mod 83 (83)		 52 (600K) 4 (5841)
33 (1847)
27 (1088)
3 (444)
10 (360)
53 (290)
34 (221)
44 (208)
17 (204)
23 (199)		  
583 2846 5, 7, 13, 31, 73 All k where k = m^2
and m = = 27 or 46 mod 73:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*583^q - 1) *
     (m*583^q + 1)
   odd n:
     factor of 73		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 97 (97)		 242 (300K)
522 (300K)
536 (300K)
984 (300K)
1128 (300K)
1518 (300K)
2304 (300K)
2664 (300K)
2702 (300K)
2766 (300K)		 354 (172967)
2016 (151394)
578 (98441)
1242 (85103)
462 (77448)
114 (30196)
2118 (23589)
1376 (19397)
158 (16488)
1022 (16242)		 No k's proven composite by algebraic factors.
584 4 3, 5   k = = 1 mod 11 (11)
k = = 1 mod 53 (53)		 none - proven 2 (54)
3 (2)		  
585 14271738 137, 293, 1249 (Condition 1):
All k where k = m^2
and m = = 138 or 155 mod 293:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*585^q - 1) *
     (m*585^q + 1)
   odd n:
     factor of 293
(Condition 2):
All k where k = 65*m^2
and m = = 121 or 172 mod 293:
   even n:
     factor of 293
   for odd n let k = 65*m^2
   and let n=2*q-1; factors to:
     [m*3^n*65^q - 1] *
     [m*3^n*65^q + 1]		 k = = 1 mod 2 (2)
k = = 1 mod 73 (73)		 138122 k's remaining at n=2.5K. To be shown later. 13722440 (2500)
13389106 (2500)
12463252 (2500)
11660608 (2500)
10709728 (2500)
10489466 (2500)
9744710 (2500)
9580442 (2500)
8409034 (2500)
7777260 (2500)		 k = 19044, 200704, 524176, 1069156, 1716100, 2624400, 3594816, 4866436, 6160324, 7795264, 9412624, 11410884, and 13351716 proven composite by condition 1.

k = 1922960 and 11140740 proven composite by condition 2.
586 5906982 17, 37, 89, 587   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 13 (13)		 52466 k's remaining at n=2.5K. To be shown later. 5833784 (2500)
5587728 (2500)
5187363 (2500)
4357008 (2500)
2531072 (2500)
1760528 (2500)
1692105 (2500)
842903 (2500)
5164350 (2499)
3236798 (2499)		  
587 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 293 (293)		 none - proven 2 (26)
6 (2)
4 (1)		  
588 94 19, 31   k = = 1 mod 587 (587) 3 (500K)
16 (500K)		 83 (1629)
22 (915)
58 (557)
77 (263)
32 (231)
24 (227)
30 (150)
62 (104)
48 (104)
55 (90)		  
589 1004 5, 59 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*589^q - 1) *
     (m*589^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 74 (300K)
216 (300K)
648 (300K)
926 (300K)		 174 (180580)
816 (22557)
654 (5638)
744 (4026)
566 (2785)
672 (2533)
506 (2387)
966 (2247)
354 (2172)
854 (1878)		 k = 144 and 324 proven composite by partial algebraic factors.
590 196 3, 197   k = = 1 mod 19 (19)
k = = 1 mod 31 (31)		 98 (300K)
109 (300K)
152 (300K)		 67 (86975)
38 (43480)
2 (15526)
114 (6492)
100 (3615)
56 (2602)
146 (738)
18 (717)
124 (707)
148 (661)		  
591 30820 17, 37, 10273 All k where k = m^2
and m = = 6 or 31 mod 37:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*591^q - 1) *
     (m*591^q + 1)
   odd n:
     factor of 37		 k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 59 (59)		 55 k's remaining at n=100K.

See k's at Riesel Base 591 remain.		 21794 (98943)
28760 (98412)
27332 (95597)
19044 (92315)
2948 (90512)
19988 (89773)
16494 (85147)
28460 (82666)
24294 (82653)
17970 (75095)		 k = 4624, 6400, and 20164 proven composite by partial algebraic factors.
592 17196 5, 29, 593 All k where k = m^2
and m = = 77 or 516 mod 593:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*592^q - 1) *
     (m*592^q + 1)
   odd n:
     factor of 593		 k = = 1 mod 3 (3)
k = = 1 mod 197 (197)		 158 k's remaining at n=100K.

See k's at Riesel Base 592 remain.		 5927 (96521)
4976 (95447)
12653 (91839)
10950 (88614)
3194 (85899)
12704 (85808)
11076 (84359)
8792 (82638)
7209 (82292)
10046 (81614)		 No k's proven composite by algebraic factors.
593 10 3, 11   k = = 1 mod 2 (2)
k = = 1 mod 37 (37)		 none - proven 2 (4)
8 (2)
6 (1)
4 (1)		  
594 6 5, 7 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*594^q - 1) *
     (m*594^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 593 (593) none - proven 3 (2)
5 (1)
2 (1)		 k = 4 proven composite by partial algebraic factors.
595 291890 13, 31, 43, 149 All k where k = m^2
and m = = 44 or 105 mod 149:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*595^q - 1) *
     (m*595^q + 1)
   odd n:
     factor of 149		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 11 (11)		 91 k's remaining at n=100K.

See k's at Riesel Base 595 remain.		 212922 (97899)
274260 (97374)
287334 (97200)
189380 (95821)
10442 (95182)
89306 (94257)
61182 (92718)
48854 (91733)
239786 (87878)
258782 (86872)		 No k's proven composite by algebraic factors.
596 200 3, 199   k = = 1 mod 5 (5)
k = = 1 mod 7 (7)
k = = 1 mod 17 (17)		 none - proven 40 (3327)
104 (1950)
74 (1100)
83 (588)
7 (489)
160 (465)
153 (271)
34 (225)
39 (190)
145 (171)		  
597 116 13, 23 All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*597^q - 1) *
     (m*597^q + 1)
   odd n:
     factor of 13		 k = = 1 mod 2 (2)
k = = 1 mod 149 (149)		 none - proven 70 (44147)
58 (3655)
32 (1454)
78 (1259)
68 (730)
8 (592)
114 (232)
92 (85)
98 (51)
96 (23)		 k = 64 proven composite by partial algebraic factors.
598 43728 5, 37, 599   k = = 1 mod 3 (3)
k = = 1 mod 199 (199)		 231 k's remaining at n=100K.

See k's at Riesel Base 598 remain.		 26954 (99892)
30342 (97891)
15687 (97099)
30017 (96255)
36048 (95422)
6092 (94998)
591 (94437)
12077 (94203)
11976 (93995)
26864 (89991)		  
599 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 13 (13)
k = = 1 mod 23 (23)		 none - proven 2 (6)  
600 102772 7, 13, 19, 37, 601 (Condition 1):
All k where k = m^2
and m = = 125 or 476 mod 601:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*600^q - 1) *
     (m*600^q + 1)
   odd n:
     factor of 601
(Condition 2):
All k where k = 6*m^2
and m = = 48 or 553 mod 601:
   even n:
     factor of 601
   for odd n let k = 6*m^2
   and let n=2*q-1; factors to:
     [m*10^n*6^q - 1] *
     [m*10^n*6^q + 1]		 k = = 1 mod 599 (599) 911 k's remaining at n=25K.

See k's at Riesel Base 600 remain.		 49116 (24943)
102685 (24925)
84779 (24856)
55009 (24824)
84757 (24719)
42474 (24710)
65097 (24662)
40864 (24558)
102062 (24487)
83440 (24418)		 k = 15625 proven composite by condition 1.

k = 13824 proven composite by condition 2.
601 818 7, 43   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 300 (300K)
482 (300K)
744 (300K)		 624 (44279)
50 (30735)
120 (4663)
384 (1412)
750 (1133)
42 (990)
722 (825)
204 (429)
258 (356)
734 (302)		  
602 68 3, 67   k = = 1 mod 601 (601) 58 (500K)
66 (500K)		 14 (53392)
67 (41049)
12 (36517)
29 (792)
25 (623)
40 (165)
33 (112)
13 (95)
35 (78)
52 (77)		  
603 11324 5, 13, 151   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 43 (43)		 41 k's remaining at n=100K.

See k's at Riesel Base 603 remain.		 5036 (85265)
10668 (72980)
168 (48485)
10778 (46302)
9512 (45638)
2498 (41694)
3608 (35838)
8796 (33642)
5822 (33563)
2282 (31784)		  
604 21 5, 11 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*604^q - 1) *
     (m*604^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 67 (67)		 none - proven 18 (66)
20 (7)
2 (4)
11 (3)
14 (2)
17 (1)
15 (1)
12 (1)
8 (1)
6 (1)		 k = 9 proven composite by partial algebraic factors.
605 100 3, 101   k = = 1 mod 2 (2)
k = = 1 mod 151 (151)		 none - proven 52 (13569)
86 (7788)
74 (5268)
44 (3210)
10 (2379)
50 (1910)
38 (1598)
80 (322)
64 (205)
2 (188)		  
606 74660 13, 41, 607   k = = 1 mod 5 (5)
k = = 1 mod 11 (11)		 419 k's remaining at n=25K.

See k's at Riesel Base 606 remain.		 44349 (24621)
30230 (24607)
39574 (24596)
68987 (24582)
53155 (24561)
37398 (24507)
25212 (24486)
13439 (24480)
6674 (24174)
34960 (23853)		  
607 51584 5, 19, 7369   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 101 (101)		 513 k's remaining at n=25K.

See k's at Riesel Base 607 remain.		 25164 (24835)
7094 (24777)
13584 (24668)
12134 (24497)
14958 (24379)
14106 (24355)
25082 (24296)
50298 (24136)
47366 (24002)
2148 (23651)		  
608 8 3, 7   k = = 1 mod 607 (607) none - proven 7 (87435)
4 (83)
5 (26)
6 (6)
2 (2)
3 (1)		  
609 184 5, 61 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*609^q - 1) *
     (m*609^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 19 (19)		 none - proven 76 (1491)
114 (1252)
136 (333)
116 (123)
108 (104)
70 (73)
72 (41)
56 (37)
44 (20)
138 (17)		 k = 4, 64, and 144 proven composite by partial algebraic factors.
610 753 13, 47 All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*610^q - 1) *
     (m*610^q + 1)
   odd n:
     factor of 13		 k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 29 (29)		 234 (600K) 350 (16580)
32 (3841)
560 (3733)
66 (2921)
530 (2069)
131 (1925)
558 (1404)
375 (1318)
389 (1206)
377 (849)		 k = 324 and 441 proven composite by partial algebraic factors.
611 118 3, 17   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 61 (61)		 10 (600K) 94 (12973)
104 (292)
4 (177)
32 (152)
2 (120)
44 (72)
38 (70)
68 (40)
70 (25)
90 (20)		  
612 105437 5, 173, 613 All k where k = m^2
and m = = 35 or 578 mod 613:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*612^q - 1) *
     (m*612^q + 1)
   odd n:
     factor of 613		 k = = 1 mod 13 (13)
k = = 1 mod 47 (47)		 969 k's remaining at n=25K.

See k's at Riesel Base 612 remain.		 20676 (24951)
12737 (24924)
97979 (24872)
28437 (24790)
21107 (24769)
77899 (24715)
105191 (24709)
46413 (24572)
88961 (24561)
73299 (24480)		 k = 1225 proven composite by partial algebraic factors.
613 34692 5, 53, 307   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 17 (17)		 129 k's remaining at n=100K.

See k's at Riesel Base 613 remain.		 1584 (94460)
4050 (93732)
26552 (90776)
10152 (86820)
33884 (86811)
15066 (86153)
1604 (85447)
28032 (85384)
5378 (84473)
16514 (84199)		  
614 4 3, 5   k = = 1 mod 613 (613) none - proven 2 (312)
3 (3)		  
615 34 7, 11   k = = 1 mod 2 (2)
k = = 1 mod 307 (307)		 12 (600K) 22 (203539)
32 (4)
26 (3)
30 (2)
28 (2)
20 (2)
10 (2)
6 (2)
24 (1)
18 (1)		  
616 23447 13, 17, 617 All k where k = m^2
and m = = 194 or 423 mod 617:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*616^q - 1) *
     (m*616^q + 1)
   odd n:
     factor of 617		 k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 41 (41)		 26 k's remaining at n=100K.

See k's at Riesel Base 616 remain.		 15459 (99075)
21045 (96296)
6965 (58914)
7220 (58110)
22295 (54955)
14958 (52474)
18585 (47642)
7593 (42266)
23135 (40694)
16827 (40289)		 No k's proven composite by algebraic factors.
617 104 3, 103   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 11 (11)		 none - proven 44 (34964)
14 (25724)
38 (2110)
80 (1902)
58 (87)
96 (83)
88 (23)
74 (16)
72 (14)
24 (9)		  
618 2517 7, 37, 211   k = = 1 mod 617 (617) 43 k's remaining at n=100K.

See k's at Riesel Base 618 remain.		 436 (93186)
1546 (83570)
2426 (66885)
1858 (57817)
95 (56517)
282 (54172)
2216 (51494)
1159 (43397)
2424 (41400)
1731 (36706)		  
619 216 5, 31 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*619^q - 1) *
     (m*619^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 103 (103)		 6 (600K) 138 (95328)
206 (33625)
68 (10566)
92 (5818)
26 (2867)
114 (1302)
96 (947)
24 (134)
56 (73)
126 (61)		 k = 144 proven composite by partial algebraic factors.
620 22 3, 23   k = = 1 mod 619 (619) none - proven 20 (120136)
4 (1773)
11 (1434)
15 (562)
21 (39)
16 (11)
8 (10)
9 (9)
12 (6)
5 (4)		  
621 190642 17, 109, 311, 313   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 31 (31)		 516 k's remaining at n=25K.

See k's at Riesel Base 621 remain.		 12134 (24989)
187468 (24926)
115548 (24814)
92658 (24775)
166568 (24742)
168398 (24695)
5052 (24682)
83658 (24676)
51200 (24544)
156222 (24513)		  
622 90 7, 89   k = = 1 mod 3 (3)
k = = 1 mod 23 (23)		 none - proven 78 (402915)
8 (9455)
39 (5160)
62 (104)
32 (38)
41 (26)
50 (25)
60 (18)
87 (17)
26 (15)		  
623 14 3, 13   k = = 1 mod 2 (2)
k = = 1 mod 311 (311)		 none - proven 6 (4110)
8 (50)
4 (3)
12 (2)
2 (2)
10 (1)		  
624 569819 5, 41, 9497 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*624^q - 1) *
     (m*624^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 39*m^2
and m = = 2 or 3 mod 5:
   even n:
     factor of 5
   for odd n let k = 39*m^2
   and let n=2*q-1; factors to:
     [m*4^n*39^q - 1] *
     [m*4^n*39^q + 1]		 k = = 1 mod 7 (7)
k = = 1 mod 89 (89)		 13722 k's remaining at n=6.5K. To be shown later. 87609 (6500)
358944 (6498)
537870 (6496)
5029 (6496)
100261 (6493)
402799 (6492)
264826 (6491)
535001 (6489)
213146 (6489)
162783 (6488)		 k = 2^2, 3^2, 7^2, 12^2, 17^2, 18^2, 23^2, 28^2, 32^2, 33^2, 37^2, 38^2, 42^2, 47^2, 52^2, 53^2, 58^2, 63^2, 67^2, 68^2, (etc. pattern repeating every 35m where k not = = 1 mod 89) proven composite by condition 1.

k = 39*2^2, 39*7^2, 39*8^2, 39*12^2, 39*13^2, 39*22^2, 39*23^2, 39*27^2, 39*28^2, 39*33^2, 39*37^2, 39*42^2, 39*43^2, 39*47^2, 39*48^2, 39*57^2, 39*58^2, 39*62^2, 39*63^2, 39*68^2, (etc. pattern repeating every 35m where k not = = 1 mod 89) proven composite by condition 2.
625 26468 7, 31, 601 All k = m^2 for all n; factors to:
(m*25^n - 1) *
(m*25^n + 1)		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 13 (13)		 59 k's remaining at n>=130K.

See k's and test limits at Riesel Base 625 remain.		 6980 (286678)
6350 (227876)
12440 (169942)
3938 (139508)
22848 (129686)
24432 (125053)
7890 (118501)
20430 (96560)
13214 (95471)
25958 (90420)		 k = 6^2, 18^2, 24^2, 30^2, 36^2, 42^2, 48^2, 54^2, 60^2, 72^2, 78^2, 84^2, 96^2, 102^2, 108^2, 114^2, 120^2, 126^2, 132^2, 138^2, 150^2, 156^2, and 162^2 proven composite by full algebraic factors.

Some k's are being worked on by PrimeGrid's Sierpinski/Riesel Base 5 project.
626 10 3, 11   k = = 1 mod 5 (5) none - proven 5 (110)
8 (20)
7 (9)
2 (8)
9 (5)
4 (1)
3 (1)		  
627 129182 7, 13, 4327 All k where k = m^2
and m = = 28 or 129 mod 157:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*627^q - 1) *
     (m*627^q + 1)
   odd n:
     factor of 157		 k = = 1 mod 2 (2)
k = = 1 mod 313 (313)		 1222 k's remaining at n=25K.

See k's at Riesel Base 627 remain.		 13770 (24982)
2328 (24946)
28982 (24749)
50248 (24696)
11998 (24686)
55974 (24684)
48626 (24622)
120922 (24522)
164 (24425)
68636 (24347)		 k = 784, 81796, and 116964 proven composite by partial algebraic factors.
628 186 17, 37 All k where k = m^2
and m = = 6 or 31 mod 37:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*628^q - 1) *
     (m*628^q + 1)
   odd n:
     factor of 37		 k = = 1 mod 3 (3)
k = = 1 mod 11 (11)
k = = 1 mod 19 (19)		 none - proven 149 (80423)
18 (7889)
120 (6927)
110 (5954)
107 (690)
101 (658)
50 (202)
183 (196)
137 (167)
171 (159)		 k = 36 proven composite by partial algebraic factors.
629 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 157 (157)		 none - proven 2 (186)  
632 14 3, 5, 13   k = = 1 mod 631 (631) none - proven 9 (19)
13 (15)
11 (14)
2 (6)
10 (5)
4 (5)
8 (4)
3 (4)
6 (2)
5 (2)		  
633 1004 5, 7, 13, 17, 67   k = = 1 mod 2 (2)
k = = 1 mod 79 (79)		 64 (300K)
172 (300K)
326 (300K)
708 (300K)
952 (300K)		 152 (19312)
402 (17432)
746 (14574)
752 (6136)
950 (6070)
692 (5190)
192 (3747)
442 (3003)
112 (2879)
92 (2270)		  
634 126 5, 127 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*634^q - 1) *
     (m*634^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 211 (211)		 29 (600K) 20 (476756)
96 (20665)
59 (8118)
114 (3402)
36 (3271)
84 (1994)
41 (603)
69 (268)
26 (237)
93 (215)		 k = 9 proven composite by partial algebraic factors.
635 52 3, 53   k = = 1 mod 2 (2)
k = = 1 mod 317 (317)		 none - proven 6 (36162)
38 (35438)
28 (333)
40 (133)
2 (42)
10 (39)
44 (28)
22 (23)
50 (22)
8 (22)		  
636 27 7, 13 All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*636^q - 1) *
     (m*636^q + 1)
   odd n:
     factor of 13		 k = = 1 mod 5 (5)
k = = 1 mod 127 (127)		 9 (1M) 14 (2231)
22 (23)
12 (14)
17 (3)
5 (3)
20 (2)
19 (2)
13 (2)
2 (2)
24 (1)		 k = 25 proven composite by partial algebraic factors.
637 144 11, 29   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 53 (53)		 none - proven 32 (18096)
8 (722)
36 (279)
48 (55)
140 (28)
128 (15)
66 (14)
120 (12)
104 (11)
62 (9)		  
638 70 3, 71   k = = 1 mod 7 (7)
k = = 1 mod 13 (13)		 7 (300K)
11 (300K)
49 (300K)
59 (300K)		 25 (20295)
26 (2826)
34 (237)
23 (230)
2 (90)
24 (59)
62 (52)
67 (43)
68 (22)
35 (22)		  
639 2136 5, 7, 19, 499 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*639^q - 1) *
     (m*639^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 71*m^2
and m = = 1 or 4 mod 5:
   even n:
     factor of 5
   for odd n let k = 71*m^2
   and let n=2*q-1; factors to:
     [m*3^n*71^q - 1] *
     [m*3^n*71^q + 1]		 k = = 1 mod 2 (2)
k = = 1 mod 11 (11)
k = = 1 mod 29 (29)		 176 (300K)
464 (300K)
566 (300K)
604 (300K)
626 (300K)
816 (300K)
1124 (300K)
1194 (300K)
1576 (300K)
1626 (300K)
1646 (300K)
1954 (300K)
1964 (300K)		 400 (265307)
1756 (187277)
926 (180181)
1836 (120909)
1334 (86774)
382 (59408)
1196 (54973)
1866 (54741)
996 (47739)
564 (46820)		 k = 4, 64, 324, 484, 1444, and 1764 proven composite by condition 1.

k = 1136 proven composite by condition 2.
640 10349 7, 13, 37, 157   k = = 1 mod 3 (3)
k = = 1 mod 71 (71)		 35 k's remaining at n=100K.

See k's at Riesel Base 640 remain.		 2565 (98637)
3446 (98234)
4091 (96387)
7290 (81358)
875 (80166)
2642 (80145)
8891 (77217)
2876 (71982)
2219 (68460)
7326 (64822)		  
641 298 3, 7, 13, 67   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)		 44 (300K)
88 (300K)
108 (300K)
134 (300K)
158 (300K)
170 (300K)
218 (300K)
268 (300K)		 38 (158070)
214 (42969)
148 (10451)
184 (7817)
224 (6450)
142 (6323)
238 (5919)
114 (2714)
200 (1264)
194 (1170)		  
642 3214 5, 17, 643   k = = 1 mod 641 (641) 57 k's remaining at n=100K.

See k's at Riesel Base 642 remain.		 72 (96360)
733 (90458)
2237 (77737)
124 (77733)
2842 (77396)
480 (76579)
2174 (69252)
2401 (65723)
1223 (64099)
2367 (62258)		  
643 300 7, 23   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 107 (107)		 114 (300K)
206 (300K)		 174 (192540)
162 (29547)
216 (16186)
102 (7971)
8 (5573)
104 (1732)
146 (554)
296 (287)
2 (202)
50 (159)		  
644 4 3, 5   k = = 1 mod 643 (643) none - proven 2 (8)
3 (1)		  
645 18 17, 19 All k where k = m^2
and m = = 4 or 13 mod 17:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*645^q - 1) *
     (m*645^q + 1)
   odd n:
     factor of 17		 k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 23 (23)		 none - proven 6 (8)
12 (4)
14 (1)
10 (1)
4 (1)
2 (1)		 k = 16 proven composite by partial algebraic factors.
646 30410 7, 13, 31, 647   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 43 (43)		 85 k's remaining at n=100K.

See k's at Riesel Base 646 remain.		 25827 (96252)
26352 (89063)
2109 (87855)
22163 (87050)
14795 (82703)
19167 (78254)
4533 (77865)
14855 (69214)
22967 (67014)
29474 (65760)		  
647 688 3, 5, 41   k = = 1 mod 2 (2)
k = = 1 mod 17 (17)
k = = 1 mod 19 (19)		 4 (100K)
50 (100K)
74 (100K)
82 (100K)
116 (100K)
128 (100K)
196 (100K)
212 (100K)
228 (100K)
254 (100K)
298 (100K)
314 (100K)
328 (100K)
344 (100K)
394 (100K)
412 (100K)
452 (100K)
472 (100K)
478 (100K)
538 (100K)
542 (100K)
622 (100K)
624 (100K)
634 (100K)
658 (100K)		 418 (65555)
178 (58827)
380 (48780)
94 (35643)
598 (33951)
416 (33330)
620 (22404)
2 (21576)
288 (9675)
284 (9216)		  
648 237 5, 59, 137   k = = 1 mod 647 (647) 21 (500K)
186 (500K)
188 (500K)		 43 (146608)
94 (111133)
71 (74273)
120 (60652)
82 (32667)
100 (25665)
235 (12076)
131 (9334)
206 (4574)
113 (3010)		  
649 14 5, 13   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 none - proven 12 (792)
6 (11)
8 (4)
2 (1)		  
650 8 3, 7   k = = 1 mod 11 (11)
k = = 1 mod 59 (59)		 none - proven 4 (498101)
6 (6)
5 (2)
2 (2)
7 (1)
3 (1)		  
651 4965144 163, 313, 677   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 13 (13)		 14902 k's remaining at n=2.5K. To be shown later. 4531954 (2500)
3469074 (2500)
2851508 (2500)
1651034 (2500)
1434562 (2500)
4949072 (2499)
4255380 (2499)
3588660 (2499)
2298838 (2499)
754018 (2499)		  
652 600759 5, 13, 43, 139, 653 All k where k = m^2
and m = = 149 or 504 mod 653:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*652^q - 1) *
     (m*652^q + 1)
   odd n:
     factor of 653		 k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 31 (31)		 4946 k's remaining at n=10K.

See k's at Riesel Base 652 remain.		 434234 (9984)
135884 (9984)
103442 (9969)
362451 (9962)
95723 (9959)
595523 (9948)
183393 (9948)
118139 (9943)
50612 (9933)
340686 (9923)		 k = 254016 proven composite by partial algebraic factors.
653 110 3, 109   k = = 1 mod 2 (2)
k = = 1 mod 163 (163)		 4 (300K)
32 (300K)
58 (300K)
64 (300K)
82 (300K)
88 (300K)		 70 (10163)
102 (612)
78 (449)
30 (381)
36 (227)
16 (189)
104 (140)
8 (80)
20 (68)
86 (54)		  
654 261 5, 131 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*654^q - 1) *
     (m*654^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 653 (653) 30 (300K)
53 (300K)
56 (300K)
79 (300K)
100 (300K)
204 (300K)
219 (300K)
236 (300K)
239 (300K)		 44 (132422)
132 (73231)
136 (67671)
124 (62210)
114 (37634)
176 (2167)
3 (920)
238 (732)
174 (480)
196 (453)		 k = 4, 9, 49, 64, 144, and 169 proven composite by partial algebraic factors.
655 3294 7, 37, 79 All k where k = m^2
and m = = 9 or 32 mod 41:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*655^q - 1) *
     (m*655^q + 1)
   odd n:
     factor of 41		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 109 (109)		 128 (300K)
204 (300K)
302 (300K)
1926 (300K)
1988 (300K)
2010 (300K)
2418 (300K)
2480 (300K)
2796 (300K)
2912 (300K)		 1682 (218457)
800 (143586)
3266 (95571)
3060 (83770)
1344 (78757)
8 (53008)
1136 (50961)
2276 (45506)
1574 (40078)
288 (32675)		 No k's proven composite by algebraic factors.
656 74 3, 73   k = = 1 mod 5 (5)
k = = 1 mod 131 (131)		 none - proven 20 (878)
50 (734)
40 (393)
17 (198)
29 (140)
65 (124)
5 (90)
55 (61)
47 (54)
72 (48)		  
657 22 5, 7, 97   k = = 1 mod 2 (2)
k = = 1 mod 41 (41)		 none - proven 4 (121)
16 (83)
8 (23)
14 (21)
2 (10)
18 (4)
20 (2)
6 (2)
12 (1)
10 (1)		  
658 22407 5, 13, 659   k = = 1 mod 3 (3)
k = = 1 mod 73 (73)		 98 k's remaining at n=100K.

See k's at Riesel Base 658 remain.		 5897 (92752)
9716 (83511)
11262 (81960)
16938 (80656)
5769 (79672)
38 (79568)
7827 (75162)
16271 (71253)
11556 (70065)
11657 (69443)		  
659 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 47 (47)		 none - proven 2 (2)  
660 322567 37, 61, 661 All k where k = m^2
and m = = 106 or 555 mod 661:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*660^q - 1) *
     (m*660^q + 1)
   odd n:
     factor of 661		 k = = 1 mod 659 (659) 3922 k's remaining at n=10K.

See k's at Riesel Base 660 remain.		 245890 (10000)
313244 (9992)
232318 (9991)
157819 (9989)
213203 (9981)
321904 (9976)
110380 (9968)
246359 (9965)
273534 (9963)
78733 (9962)		 k = 11236 and 308025 proven composite by partial algebraic factors.
662 14 3, 13   k = = 1 mod 661 (661) 7 (600K) 2 (16590)
11 (13306)
13 (1783)
5 (142)
12 (14)
8 (4)
3 (4)
9 (3)
6 (3)
10 (1)		  
663 1244 5, 83, 113   k = = 1 mod 2 (2)
k = = 1 mod 331 (331)		 408 (300K)
414 (300K)
452 (300K)
900 (300K)		 456 (66051)
848 (57568)
662 (47556)
642 (44098)
1126 (33742)
114 (28673)
24 (27791)
366 (25498)
1226 (16973)
1052 (13804)		  
664 6 5, 7   k = = 1 mod 3 (3)
k = = 1 mod 13 (13)
k = = 1 mod 17 (17)		 none - proven 3 (17)
5 (1)
2 (1)		  
665 38 3, 37 All k where k = m^2
and m = = 6 or 31 mod 37:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*665^q - 1) *
     (m*665^q + 1)
   odd n:
     factor of 37
 k = = 1 mod 2 (2)
k = = 1 mod 83 (83)		 8 (400K) 14 (1702)
34 (59)
26 (16)
2 (12)
10 (7)
28 (3)
12 (3)
32 (2)
20 (2)
30 (1)		 k = 36 proven composite by partial algebraic factors.
666 898 23, 29 All k where k = m^2
and m = = 12 or 17 mod 29:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*666^q - 1) *
     (m*666^q + 1)
   odd n:
     factor of 29		 k = = 1 mod 5 (5)
k = = 1 mod 7 (7)
k = = 1 mod 19 (19)		 none - proven 139 (178851)
74 (60158)
753 (5768)
620 (4286)
417 (2321)
219 (2189)
672 (1199)
408 (724)
283 (635)
597 (634)		 k = 144 and 289 proven composite by partial algebraic factors.
667 834 5, 17, 167   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 37 (37)		 288 (300K)
344 (300K)		 258 (37866)
632 (28650)
458 (25155)
500 (12724)
396 (10731)
696 (8087)
776 (5807)
168 (5611)
812 (5024)
692 (3330)		  
668 14 3, 5, 13   k = = 1 mod 23 (23)
k = = 1 mod 29 (29)		 11 (400K) 2 (486)
5 (330)
7 (67)
12 (59)
13 (41)
8 (4)
10 (1)
9 (1)
6 (1)
4 (1)		  
669 66 5, 67 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*669^q - 1) *
     (m*669^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 167 (167)		 none - proven 44 (3132)
2 (2787)
30 (78)
50 (43)
54 (28)
14 (26)
58 (15)
38 (14)
60 (7)
52 (3)		 k = 4 and 64 proven composite by partial algebraic factors.
670 243 11, 61   k = = 1 mod 3 (3)
k = = 1 mod 223 (223)		 none - proven 32 (79644)
210 (4277)
45 (1053)
65 (658)
44 (436)
42 (283)
36 (251)
56 (183)
191 (173)
75 (151)		  
671 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 67 (67)		 none - proven 2 (2)
4 (1)		  
672 41440 13, 19, 1831 All k where k = m^2
and m = = 58 or 615 mod 673:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*672^q - 1) *
     (m*672^q + 1)
   odd n:
     factor of 673		 k = = 1 mod 11 (11)
k = = 1 mod 61 (61)		 407 k's remaining at n=25K.

See k's at Riesel Base 672 remain.		 35917 (24981)
20944 (24536)
14023 (24418)
23139 (24384)
17761 (24315)
3802 (24252)
6578 (24250)
26679 (23669)
36343 (23407)
8524 (23125)		 k = 3364 proven composite by partial algebraic factors.
673 1617938 5, 13, 19, 97, 337 All k where k = m^2
and m = = 148 or 189 mod 337:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*673^q - 1) *
     (m*673^q + 1)
   odd n:
     factor of 337		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 14781 k's remaining at n=2.5K. To be shown later. 1350324 (2500)
630998 (2500)
1581906 (2499)
776024 (2499)
1616052 (2498)
1334732 (2498)
757736 (2498)
356876 (2498)
939546 (2497)
916844 (2497)		 k = 675684 and 1440000 proven composite by partial algebraic factors.
674 4 3, 5   k = = 1 mod 673 (673) none - proven 3 (38)
2 (12)		  
675 37816 7, 13, 631, 2521 (Condition 1):
All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*675^q - 1) *
     (m*675^q + 1)
   odd n:
     factor of 13
(Condition 2):
All k where k = 3*m^2
and m = = 3 or 10 mod 13:
   even n:
     factor of 13
   for odd n let k = 3*m^2
   and let n=2*q-1; factors to:
     [m*15^n*3^q - 1] *
     [m*15^n*3^q + 1]		 k = = 1 mod 2 (2)
k = = 1 mod 337 (337)		 185 k's remaining at n=100K.

See k's at Riesel Base 675 remain.		 22938 (95472)
3678 (94862)
19616 (92808)
32280 (92767)
870 (88674)
30726 (84414)
37350 (83865)
29132 (77276)
34722 (75936)
14494 (75636)		 k = 64, 324, 1156, 1936, 3600, 4900, 7396, 9216, 12544, 14884, 19044, 21904, 26896, 30276, and 36100 proven composite by condition 1.

k = 300, 768, 3888, 5292, 11532, 13872, 23232, and 26508 proven composite by condition 2.
676 149 7, 31, 37 All k = m^2 for all n; factors to:
(m*26^n - 1) *
(m*26^n + 1)		 k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 none - proven 32 (4906)
80 (191)
128 (150)
114 (71)
65 (50)
30 (36)
90 (23)
72 (23)
23 (14)
102 (12)		 k = 9 and 144 proven composite by full algebraic factors.
677 112 3, 113   k = = 1 mod 2 (2)
k = = 1 mod 13 (13)		 60 (300K)
74 (300K)
86 (300K)
94 (300K)		 104 (89520)
38 (40390)
84 (36944)
58 (3959)
56 (3078)
78 (1694)
10 (1361)
44 (540)
82 (325)
32 (278)		  
678 195 7, 97   k = = 1 mod 677 (677) 41 (300K)
55 (300K)
57 (300K)
118 (300K)
139 (300K)		 50 (140989)
127 (130375)
161 (92085)
49 (86691)
25 (85037)
6 (40858)
19 (30245)
85 (16215)
24 (3985)
162 (2399)		  
679 186 5, 17 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*679^q - 1) *
     (m*679^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 113 (113)		 174 (400K) 24 (14350)
66 (6943)
116 (1063)
104 (258)
14 (176)
84 (86)
120 (51)
126 (33)
158 (29)
54 (28)		 k = 144 proven composite by partial algebraic factors.
680 226 3, 227   k = = 1 mod 7 (7)
k = = 1 mod 97 (97)		 none - proven 116 (58870)
59 (27590)
101 (16836)
223 (16443)
16 (10115)
175 (8427)
74 (6678)
47 (1074)
181 (775)
94 (739)		  
681 32 11, 31   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 17 (17)		 none - proven 30 (246)
4 (219)
22 (34)
28 (8)
8 (7)
10 (4)
24 (2)
20 (1)
14 (1)
12 (1)		  
682 40979 5, 7, 13, 683, 1543   k = = 1 mod 3 (3)
k = = 1 mod 227 (227)		 209 k's remaining at n=100K.

See k's at Riesel Base 682 remain.		 4983 (97720)
23774 (97496)
11418 (96340)
14208 (95472)
40718 (95444)
10127 (94050)
39512 (93549)
5684 (93061)
28794 (93008)
36162 (92404)		  
683 20 3, 19   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)
k = = 1 mod 31 (31)		 none - proven 14 (1124)
2 (540)
18 (36)
8 (8)
16 (3)
6 (2)
10 (1)
4 (1)		  
684 46 5, 29, 73 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*684^q - 1) *
     (m*684^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 683 (683) 39 (400K) 38 (1065)
31 (579)
41 (95)
45 (75)
14 (58)
44 (54)
42 (38)
6 (19)
34 (18)
30 (11)		 k = 4 and 9 proven composite by partial algebraic factors.
685 518792 7, 13, 61, 12049   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 19 (19)		 3654 k's remaining at n=10K.

See k's at Riesel Base 685 remain.		 153546 (9993)
156906 (9985)
373668 (9961)
150440 (9940)
26564 (9938)
180942 (9930)
393072 (9927)
94856 (9922)
378758 (9896)
41082 (9864)		  
686 230 3, 229   k = = 1 mod 5 (5)
k = = 1 mod 137 (137)		 32 (300K)
92 (300K)		 199 (215171)
44 (66942)
104 (29844)
4 (16583)
225 (2699)
224 (1966)
160 (815)
40 (711)
147 (610)
17 (402)		  
687 4686 5, 43, 109   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)		 418 (300K)
816 (300K)
924 (300K)
1418 (300K)
1524 (300K)
1644 (300K)
2256 (300K)
3598 (300K)
4000 (300K)
4084 (300K)
4170 (300K)
4368 (300K)		 676 (282491)
2154 (263317)
4508 (204090)
1958 (198762)
4356 (142063)
656 (89119)
2008 (75320)
3756 (72985)
3012 (67569)
1504 (64896)		  
688 105 13, 53   k = = 1 mod 3 (3)
k = = 1 mod 229 (229)		 9 (400K) 27 (8779)
102 (2934)
62 (2250)
92 (2107)
81 (431)
12 (396)
56 (393)
60 (350)
101 (202)
15 (94)		  
689 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 43 (43)		 none - proven 2 (2)  
691 4306490 7, 13, 19, 173, 193 All k where k = m^2
and m = = 80 or 93 mod 173:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*691^q - 1) *
     (m*691^q + 1)
   odd n:
     factor of 173		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 23 (23)		 27776 k's remaining at n=2.5K. To be shown later. 3224714 (2500)
3151548 (2500)
2824604 (2500)
2391132 (2500)
945024 (2500)
308472 (2500)
2966118 (2499)
2709702 (2499)
4123182 (2498)
2440848 (2498)		 k = 374544 and 2722500 proven composite by partial algebraic factors.
692 8 3, 7   k = = 1 mod 691 (691) none - proven 6 (45446)
7 (1041)
2 (8)
3 (6)
5 (2)
4 (1)		  
693 14922 5, 17, 347   k = = 1 mod 2 (2)
k = = 1 mod 173 (173)		 47 k's remaining at n=100K.

See k's at Riesel Base 693 remain.		 1244 (92821)
3884 (89024)
4220 (80535)
1342 (70479)
8212 (67930)
9368 (63446)
1024 (56043)
10622 (55822)
11806 (55141)
3722 (54052)		  
694 279 5, 139 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*694^q - 1) *
     (m*694^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 11 (11)		 96 (500K)
264 (500K)		 72 (12120)
194 (6180)
249 (3724)
219 (3038)
41 (1803)
101 (1615)
128 (870)
266 (389)
27 (314)
66 (233)		 k = 9 proven composite by partial algebraic factors.
695 28 3, 29   k = = 1 mod 2 (2)
k = = 1 mod 347 (347)		 26 (400K) 14 (9970)
6 (384)
4 (149)
2 (10)
20 (8)
12 (7)
8 (4)
24 (2)
18 (2)
22 (1)		  
696 288 17, 41 All k where k = m^2
and m = = 4 or 13 mod 17:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*696^q - 1) *
     (m*696^q + 1)
   odd n:
     factor of 17		 k = = 1 mod 5 (5)
k = = 1 mod 139 (139)		 152 (500K)
225 (500K)		 165 (14317)
119 (4557)
203 (2224)
239 (1873)
188 (1381)
145 (786)
100 (473)
125 (469)
4 (425)
118 (394)		 k = 169 proven composite by partial algebraic factors.
697 4536 5, 13, 349   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 29 (29)		 8 (300K)
554 (300K)
746 (300K)
1178 (300K)
1604 (300K)
1682 (300K)
1782 (300K)
2592 (300K)
2616 (300K)
2634 (300K)
2744 (300K)
3840 (300K)
4106 (300K)
4188 (300K)
4298 (300K)
4386 (300K)
4524 (300K)		 3066 (242498)
2588 (211483)
2172 (210354)
4302 (97021)
2858 (58334)
1028 (48747)
924 (48689)
734 (23653)
1992 (20194)
2574 (18825)		  
698 232 3, 233   k = = 1 mod 17 (17)
k = = 1 mod 41 (41)		 13 (300K)
29 (300K)
55 (300K)
62 (300K)
97 (300K)
119 (300K)
133 (300K)
146 (300K)
158 (300K)
164 (300K)
170 (300K)
178 (300K)
187 (300K)
191 (300K)
202 (300K)
209 (300K)
221 (300K)		 20 (236810)
2 (127558)
196 (54737)
26 (53474)
94 (47531)
71 (44086)
177 (40043)
134 (37348)
64 (29339)
95 (26270)		  
699 6 5, 7 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*699^q - 1) *
     (m*699^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 349 (349)		 none - proven 2 (3) k = 4 proven composite by partial algebraic factors.
701 14 3, 13   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 7 (7)		 none - proven 10 (31)
12 (2)
2 (2)
4 (1)		  
702 75 19, 37 All k where k = m^2
and m = = 6 or 31 mod 37:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*702^q - 1) *
     (m*702^q + 1)
   odd n:
     factor of 37		 k = = 1 mod 701 (701) 32 (400K) 23 (1978)
4 (615)
20 (575)
38 (167)
39 (77)
24 (68)
37 (66)
67 (57)
44 (33)
71 (29)		 k = 36 proven composite by partial algebraic factors.
703 4454 5, 11, 73   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 13 (13)		 384 (300K)
494 (300K)
518 (300K)
714 (300K)
758 (300K)
1044 (300K)
1902 (300K)
1992 (300K)
2144 (300K)
2652 (300K)
2762 (300K)
2892 (300K)
3422 (300K)
3488 (300K)		 4056 (167545)
3596 (94090)
4368 (62145)
3266 (55570)
2292 (33682)
2694 (31112)
3024 (30984)
120 (28666)
1506 (26182)
4310 (20265)		  
704 4 3, 5   k = = 1 mod 19 (19)
k = = 1 mod 37 (37)		 none - proven 2 (62034)
3 (1)		  
705 1881842 7, 13, 353, 1447 (Condition 1):
All k where k = m^2
and m = = 42 or 311 mod 353:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*705^q - 1) *
     (m*705^q + 1)
   odd n:
     factor of 353
(Condition 2):
All k where k = 705*m^2
and m = = 42 or 311 mod 353:
   [Reverse condition 1]		 k = = 1 mod 2 (2)
k = = 1 mod 11 (11)		 16419 k's remaining at n=2.5K. To be shown later. 1248882 (2500)
1120068 (2500)
1071348 (2500)
1815740 (2499)
1718602 (2499)
1593894 (2499)
646402 (2499)
519704 (2499)
813562 (2498)
1266656 (2497)		 k = 1764, 440896, 559504. and 1876900 proven composite by condition 1.

k = 1243620 proven composite by condition 2.
706 302 7, 101   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 47 (47)		 none - proven 83 (126486)
155 (38075)
174 (18016)
27 (8450)
29 (8181)
12 (3271)
129 (2160)
282 (1338)
69 (1226)
239 (563)		  
707 14 3, 5, 13   k = = 1 mod 2 (2)
k = = 1 mod 353 (353)		 none - proven 12 (10572)
2 (350)
8 (4)
4 (3)
10 (1)
6 (1)		  
708 41121 5, 29, 709 All k where k = m^2
and m = = 96 or 613 mod 709:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*708^q - 1) *
     (m*708^q + 1)
   odd n:
     factor of 709		 k = = 1 mod 7 (7)
k = = 1 mod 101 (101)		 236 k's remaining at n=100K.

See k's at Riesel Base 708 remain.		 10379 (99336)
10080 (99306)
22503 (98384)
30875 (98156)
27979 (96123)
4889 (95564)
16988 (93630)
33712 (90648)
15761 (90165)
19803 (89010)		 k = 9216 proven composite by partial algebraic factors.
709 924 5, 71 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*709^q - 1) *
     (m*709^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 59 (59)		 174 (300K)
234 (300K)
354 (300K)
746 (300K)
774 (300K)
776 (300K)		 834 (227380)
170 (183988)
606 (137687)
408 (75507)
218 (47512)
18 (12638)
864 (9624)
300 (7511)
216 (5227)
344 (5224)		 k = 144 and 324 proven composite by partial algebraic factors.
710 80 3, 79   k = = 1 mod 709 (709) 8 (300K)
14 (300K)
47 (300K)
49 (300K)		 35 (137282)
77 (23672)
59 (10818)
34 (1009)
60 (768)
13 (293)
55 (287)
38 (256)
5 (108)
70 (71)		  
711 4540 7, 13, 19, 89 All k where k = m^2
and m = = 34 or 55 mod 89:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*88^q - 1) *
     (m*88^q + 1)
   odd n:
     factor of 89		 k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 71 (71)		 90 (300K)
120 (300K)
588 (300K)
1010 (300K)
1082 (300K)
1262 (300K)
1418 (300K)
1654 (300K)
1920 (300K)
1964 (300K)
2178 (300K)
2648 (300K)
2830 (300K)
3084 (300K)
4104 (300K)		 1660 (130087)
2752 (97111)
3784 (95479)
2402 (86242)
2712 (75859)
2580 (74296)
4390 (69109)
1352 (65558)
2482 (55587)
1490 (41276)		 No k's proven composite by algebraic factors.
712 185 23, 31   k = = 1 mod 3 (3)
k = = 1 mod 79 (79)		 47 (1M) 51 (202369)
114 (127240)
183 (91958)
93 (29415)
164 (24132)
59 (22200)
158 (11611)
78 (2635)
83 (1364)
33 (1350)		  
713 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 89 (89)		 none - proven 6 (2)
2 (2)
4 (1)		  
714 12 11, 13 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*714^q - 1) *
     (m*714^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 23 (23)
k = = 1 mod 31 (31)		 none - proven 7 (6)
10 (2)
5 (2)
11 (1)
8 (1)
6 (1)
3 (1)
2 (1)		 k = 4 and 9 proven composite by partial algebraic factors.
715 9745298 19, 97, 179, 277   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 17 (17)		 14622 k's remaining at n=2.5K. To be shown later. 9020346 (2500)
5024796 (2500)
4040046 (2500)
2312904 (2500)
5700606 (2499)
5512604 (2499)
7869428 (2498)
8360036 (2497)
7342190 (2497)
670616 (2497)		  
716 238 3, 239   k = = 1 mod 5 (5)
k = = 1 mod 11 (11)
k = = 1 mod 13 (13)		 38 (300K)
95 (300K)
190 (300K)
200 (300K)		 134 (105548)
107 (17014)
123 (11523)
194 (6010)
2 (4870)
109 (4559)
29 (4054)
117 (3831)
179 (2898)
233 (1972)		  
717 30514 5, 7, 13, 37, 359   k = = 1 mod 2 (2)
k = = 1 mod 179 (179)		 203 k's remaining at n=100K.

See k's at Riesel Base 717 remain.		 23918 (97172)
19972 (96525)
27578 (94571)
19156 (93329)
23616 (93182)
8988 (92464)
19574 (91105)
10388 (91002)
544 (88719)
4762 (87269)		  
718 1023 7, 13, 61   k = = 1 mod 3 (3)
k = = 1 mod 239 (239)		 9 (100K)
62 (100K)
74 (100K)
225 (100K)
237 (100K)
302 (100K)
324 (100K)
443 (100K)
477 (100K)
573 (100K)
590 (100K)
653 (100K)
693 (100K)
702 (100K)
732 (100K)
788 (100K)
809 (100K)
867 (100K)
872 (100K)
893 (100K)
1016 (100K)
1017 (100K)		 648 (93334)
645 (70853)
596 (59239)
120 (58837)
789 (51476)
491 (45713)
119 (37456)
239 (31831)
273 (30086)
851 (24334)		  
719 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 359 (359)		 none - proven 2 (84)  
720 104 7, 103   k = = 1 mod 719 (719) 20 (300K)
27 (300K)
83 (300K)		 99 (71291)
102 (58992)
78 (6149)
63 (4782)
8 (1675)
86 (114)
62 (82)
23 (77)
5 (76)
31 (62)		  
721 3966270 19, 61, 4261   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 21072 k's remaining at n=2.5K. To be shown later. 3727742 (2500)
3192302 (2500)
2945300 (2500)
2778234 (2500)
2755664 (2500)
1375052 (2499)
1246838 (2499)
356418 (2499)
209372 (2499)
2942852 (2498)		  
722 242 3, 241   k = = 1 mod 7 (7)
k = = 1 mod 103 (103)		 41 (300K)
56 (300K)
73 (300K)
86 (300K)
97 (300K)
158 (300K)
194 (300K)
206 (300K)		 220 (149255)
221 (136558)
19 (65865)
100 (20591)
217 (16893)
191 (16022)
205 (10521)
89 (9068)
26 (5302)
149 (4092)		  
723 12852 5, 13, 181 All k where k = m^2
and m = = 19 or 162 mod 181:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*723^q - 1) *
     (m*723^q + 1)
   odd n:
     factor of 181		 k = = 1 mod 2 (2)
k = = 1 mod 19 (19)		 85 k's remaining at n=100K.

See k's at Riesel Base 723 remain.		 11732 (97020)
9802 (96424)
11098 (91890)
2592 (91434)
9374 (90745)
5868 (89106)
9024 (88081)
3626 (84563)
8592 (73872)
492 (73624)		 No k's proven composite by algebraic factors.
724 59 5, 29 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*724^q - 1) *
     (m*724^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 241 (241)		 none - proven 48 (106132)
44 (15530)
57 (2956)
17 (1082)
39 (448)
27 (292)
6 (263)
24 (232)
26 (89)
21 (19)		 k = 9 proven composite by partial algebraic factors.
725 10 3, 11   k = = 1 mod 2 (2)
k = = 1 mod 181 (181)		 none - proven 2 (102)
4 (3)
8 (2)
6 (1)		  
726 12751579 7, 13, 37, 727, 877   k = = 1 mod 5 (5)
k = = 1 mod 29 (29)		 140272 k's remaining at n=2.5K. To be shown later. 12740674 (2500)
11219549 (2500)
10870937 (2500)
10028574 (2500)
9903640 (2500)
9794419 (2500)
9612582 (2500)
9127358 (2500)
8966609 (2500)
8905805 (2500)		  
727 246 7, 13   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 11 (11)		 8 (400K) 48 (76490)
194 (76084)
156 (43262)
222 (8041)
114 (263)
174 (200)
98 (136)
30 (136)
242 (82)
140 (63)		  
728 212722 3, 5, 105997   k = = 1 mod 727 (727) 24784 k's remaining at n=2.5K. To be shown later. 4 (4527)
76982 (2500)
147987 (2499)
185837 (2498)
118466 (2498)
60927 (2498)
206389 (2497)
195406 (2497)
175648 (2497)
188918 (2496)		  
729 74 5, 73 All k = m^2 for all n; factors to:
(m*27^n - 1) *
(m*27^n + 1)
-or-
All k = m^3 for all n; factors to:
(m*9^n - 1) *
(m^2*81^n + m*9^n + 1)		 k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 13 (13)		 none - proven 24 (149450)
26 (367)
42 (31)
44 (18)
72 (8)
30 (8)
10 (5)
54 (4)
34 (4)
20 (4)		 k = 4 and 16 proven composite by full algebraic factors.
730 171 17, 43   k = = 1 mod 3 (3) 170 (400K) 36 (22937)
81 (9813)
152 (836)
33 (614)
60 (515)
11 (399)
113 (44)
65 (39)
126 (36)
86 (31)		  
731 62 3, 61   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 73 (73)		 34 (400K) 28 (1959)
14 (1142)
32 (1038)
54 (404)
22 (185)
50 (20)
8 (20)
48 (11)
60 (10)
12 (8)		  
732 211836 5, 7, 13, 37, 733 (Condition 1):
All k where k = m^2
and m = = 353 or 380 mod 733:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*732^q - 1) *
     (m*732^q + 1)
   odd n:
     factor of 733
(Condition 2):
All k where k = 183*m^2
and m = = 27 or 706 mod 733:
   even n:
     factor of 733
   for odd n let k = 183*m^2
   and let n=2*q-1; factors to:
     [m*2^n*183^q - 1] *
     [m*2^n*183^q + 1]		 k = = 1 mod 17 (17)
k = = 1 mod 43 (43)		 8311 k's remaining at n=2.5K. To be shown later. 170920 (2500)
96828 (2500)
179349 (2499)
109008 (2499)
12168 (2499)
196202 (2498)
94943 (2498)
6192 (2497)
156968 (2495)
99954 (2495)		 k = 124609 and 144400 proven composite by condition 1.

k = 133407 proven composite by condition 2.
733 4038 5, 13, 367   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 61 (61)		 366 (100K)
372 (100K)
482 (100K)
704 (100K)
824 (100K)
1046 (100K)
1388 (100K)
1454 (100K)
1676 (100K)
1704 (100K)
1976 (100K)
2058 (100K)
2072 (100K)
2088 (100K)
2150 (100K)
2306 (100K)
2462 (100K)
3348 (100K)
3678 (100K)
3782 (100K)
3818 (100K)
3860 (100K)
3978 (100K)		 2186 (89077)
1730 (85198)
398 (74646)
3336 (70075)
2154 (44037)
3320 (39897)
642 (29896)
2304 (27007)
1350 (26017)
4016 (22701)		  
734 4 3, 5   k = = 1 mod 733 (733) none - proven 2 (1082)
3 (23)		  
735 3536594 13, 17, 23, 79, 157   k = = 1 mod 2 (2)
k = = 1 mod 367 (367)		 38151 k's remaining at n=2.5K. To be shown later. 3526814 (2500)
2472522 (2500)
1474642 (2500)
1415552 (2500)
1269086 (2500)
1136210 (2500)
958952 (2500)
596424 (2500)
235692 (2500)
3506562 (2499)		  
736 870 11, 67   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 7 (7)		 560 (400K) 285 (31508)
749 (28425)
32 (19508)
177 (3997)
819 (1263)
590 (1158)
230 (1148)
89 (615)
527 (602)
780 (598)		  
737 40 3, 41   k = = 1 mod 2 (2)
k = = 1 mod 23 (23)		 14 (300K)
22 (300K)		 26 (62278)
16 (28623)
28 (20591)
2 (352)
4 (153)
32 (128)
12 (32)
36 (17)
18 (15)
38 (8)		  
738 13738 7, 13, 31, 241   k = = 1 mod 11 (11)
k = = 1 mod 67 (67)		 123 k's remaining at n=100K.

See k's at Riesel Base 738 remain.		 12587 (97651)
13214 (95620)
6019 (91331)
9412 (88636)
5984 (87644)
2052 (85975)
11867 (84402)
9642 (81883)
1432 (81035)
3384 (79496)		  
739 36 5, 37   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 41 (41)		 none - proven 14 (286)
32 (202)
18 (102)
6 (5)
24 (4)
30 (2)
8 (2)
2 (2)
26 (1)
20 (1)		  
740 14 3, 13   k = = 1 mod 739 (739) none - proven 5 (1594)
10 (93)
8 (14)
6 (5)
2 (4)
4 (3)
3 (3)
12 (2)
11 (2)
13 (1)		  
741 160 7, 53   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 37 (37)		 none - proven 64 (111625)
158 (23778)
90 (2468)
78 (353)
48 (260)
148 (39)
80 (29)
132 (28)
104 (26)
72 (7)		  
742 21546 5, 29, 743   k = = 1 mod 3 (3)
k = = 1 mod 13 (13)
k = = 1 mod 19 (19)		 43 k's remaining at n=100K.

See k's at Riesel Base 742 remain.		 11897 (92329)
7503 (89324)
9485 (80404)
2709 (73727)
15503 (66930)
2232 (63636)
8528 (61079)
7982 (58568)
14073 (58498)
14901 (58378)		  
743 32 3, 31   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 53 (53)		 14 (400K) 28 (437)
18 (53)
12 (23)
20 (20)
24 (16)
26 (10)
10 (9)
30 (2)
2 (2)
16 (1)		  
744 299 5, 149 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*744^q - 1) *
     (m*744^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 186*m^2
and m = = 1 or 4 mod 5:
   even n:
     factor of 5
   for odd n let k = 186*m^2
   and let n=2*q-1; factors to:
     [m*2^n*186^q - 1] *
     [m*2^n*186^q + 1]		 k = = 1 mod 743 (743) 53 (300K)
116 (300K)
120 (300K)
172 (300K)
191 (300K)
221 (300K)
269 (300K)		 44 (297912)
211 (277219)
236 (60517)
242 (35144)
81 (15009)
84 (14068)
47 (8920)
106 (7691)
229 (7084)
204 (6698)		 k = 4, 9, 49, 64, 144, 169, and 289 proven composite by condition 1.

k = 186 proven composite by condition 2.
745 31706 7, 13, 61, 373 All k where k = m^2
and m = = 104 or 269 mod 373:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*745^q - 1) *
     (m*745^q + 1)
   odd n:
     factor of 373		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 31 (31)		 1160 (350K)
1416 (350K)
3662 (350K)
6894 (350K)
9162 (350K)
9650 (350K)
11964 (350K)
15864 (350K)
18300 (350K)
19770 (350K)
20136 (350K)
22034 (350K)
22500 (350K)
24950 (350K)
25736 (350K)
28080 (350K)
29586 (350K)		 6366 (348190)
22598 (338354)
11138 (297992)
26036 (279261)
21290 (203998)
24510 (177846)
16778 (168179)
20588 (158967)
19338 (141683)
17772 (115942)		 No k's proven composite by algebraic factors.
746 34 3, 13, 89   k = = 1 mod 5 (5)
k = = 1 mod 149 (149)		 14 (300K)
25 (300K)		 20 (38608)
30 (444)
18 (405)
29 (284)
4 (81)
2 (62)
15 (40)
33 (10)
32 (6)
7 (5)		  
747 120 11, 17 All k where k = m^2
and m = = 4 or 13 mod 17:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*747^q - 1) *
     (m*747^q + 1)
   odd n:
     factor of 17		 k = = 1 mod 2 (2)
k = = 1 mod 373 (373)		 18 (300K)
32 (300K)
76 (300K)
84 (300K)		 54 (3108)
34 (1805)
4 (525)
56 (125)
44 (124)
74 (113)
108 (71)
58 (70)
24 (63)
42 (42)		 k = 16 proven composite by partial algebraic factors.
748 855 7, 107   k = = 1 mod 3 (3)
k = = 1 mod 83 (83)		 174 (300K)
251 (300K)
314 (300K)
384 (300K)
512 (300K)
636 (300K)
809 (300K)		 645 (106115)
477 (92179)
407 (54675)
705 (45651)
372 (30803)
848 (24437)
134 (21791)
102 (13978)
638 (13857)
50 (9405)		  
749 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)
k = = 1 mod 17 (17)		 none - proven 2 (2)  
750 27353 13, 37, 1171   k = = 1 mod 7 (7)
k = = 1 mod 107 (107)		 77 k's remaining at n=100K.

See k's at Riesel Base 750 remain.		 19435 (99831)
15692 (97783)
21608 (96803)
13330 (95782)
15111 (95653)
23986 (83905)
10962 (80046)
4293 (77894)
22035 (74831)
8362 (70415)		  
751 85682 7, 13, 37, 47   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 233 k's remaining at n=100K.

See k's at Riesel Base 751 remain.		 21198 (99381)
39714 (98810)
81828 (96521)
38544 (95704)
17762 (93339)
52350 (92834)
33590 (92231)
33108 (91500)
69644 (90905)
30314 (90680)		  
752 101 3, 5, 17   k = = 1 mod 751 (751) 8 (300K)
22 (300K)
58 (300K)
64 (300K)
95 (300K)
97 (300K)		 65 (267180)
11 (112210)
59 (70888)
68 (12000)
29 (9580)
66 (4282)
53 (3958)
85 (2271)
82 (2237)
18 (1618)		  
753 144 13, 29 All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*753^q - 1) *
     (m*753^q + 1)
   odd n:
     factor of 13		 k = = 1 mod 2 (2)
k = = 1 mod 47 (47)		 14 (300K)
30 (300K)
88 (300K)
92 (300K)		 46 (8565)
116 (442)
130 (402)
82 (375)
2 (371)
132 (202)
128 (138)
28 (64)
122 (44)
38 (40)		 k = 64 proven composite by partial algebraic factors
754 1056 5, 151 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*754^q - 1) *
     (m*754^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 251 (251)		 134 (300K)
171 (300K)
206 (300K)
254 (300K)
321 (300K)
341 (300K)
344 (300K)
389 (300K)
411 (300K)
444 (300K)
461 (300K)
510 (300K)
564 (300K)
966 (300K)
999 (300K)		 509 (58046)
1019 (33492)
849 (25660)
941 (17463)
446 (13815)
857 (12708)
879 (12192)
84 (11970)
789 (10752)
761 (9465)		 k = 9, 144, 324, and 729 proven composite by partial algebraic factors.
755 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 13 (13)
k = = 1 mod 29 (29)		 none - proven 2 (62)
6 (18)
4 (1)		  
757 27666 5, 73, 379   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 62 k's remaining at n=100K.

See k's at Riesel Base 757 remain.		 6794 (96233)
13094 (91669)
18192 (90198)
25632 (86417)
14184 (83819)
25436 (78590)
3792 (78005)
20088 (74127)
5606 (73954)
20268 (67304)		  
758 10 3, 11   k = = 1 mod 757 (757) none - proven 4 (15573)
7 (67)
8 (14)
9 (13)
5 (6)
2 (4)
6 (1)
3 (1)		  
759 56 5, 19 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*759^q - 1) *
     (m*759^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 379 (379)		 none - proven 34 (266676)
54 (13722)
18 (2706)
6 (761)
36 (391)
40 (95)
38 (55)
42 (33)
8 (22)
26 (15)		 k = 4 proven composite by partial algebraic factors.
761 128 3, 127   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 19 (19)		 32 (400K) 74 (41682)
14 (34278)
44 (9756)
64 (8845)
94 (8297)
110 (1540)
122 (486)
50 (224)
112 (215)
8 (208)		  
762 8 5, 7, 13   k = = 1 mod 761 (761) none - proven 3 (116)
4 (7)
5 (4)
6 (2)
7 (1)
2 (1)		  
763 925778 5, 17, 191, 193   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 127 (127)		 11168 k's remaining at n=2.5K. To be shown later. 92322 (2500)
593352 (2499)
915410 (2497)
458168 (2497)
461594 (2496)
449442 (2495)
385164 (2495)
285234 (2495)
42224 (2495)
627998 (2494)		  
764 4 3, 5   k = = 1 mod 7 (7)
k = = 1 mod 109 (109)		 none - proven 3 (100)
2 (2)		  
765 2114542 53, 383, 5521   k = = 1 mod 2 (2)
k = = 1 mod 191 (191)		 25003 k's remaining at n=2.5K. To be shown later. 1249880 (2500)
334364 (2500)
159878 (2500)
2050544 (2499)
622794 (2499)
229128 (2499)
2106570 (2498)
2060922 (2498)
1853834 (2498)
1957080 (2497)		  
766 1002 13, 59 All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*766^q - 1) *
     (m*766^q + 1)
   odd n:
     factor of 13		 k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 17 (17)		 158 (300K)
339 (300K)
365 (300K)
573 (300K)
707 (300K)		 815 (129146)
872 (33605)
104 (12983)
945 (12283)
417 (5873)
794 (5191)
638 (5059)
149 (4796)
950 (3303)
144 (2967)		 No k's proven composite by algebraic factors.
767 172 3, 7, 19, 67   k = = 1 mod 2 (2)
k = = 1 mod 383 (383)		 44 (300K)
56 (300K)
58 (300K)
104 (300K)
106 (300K)
144 (300K)		 24 (105791)
38 (21544)
26 (17358)
74 (13980)
100 (1025)
72 (776)
142 (521)
154 (487)
86 (402)
126 (261)		  
768 55367 7, 19, 103, 769 All k where k = m^2
and m = = 62 or 707 mod 769:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*768^q - 1) *
     (m*768^q + 1)
   odd n:
     factor of 769		 k = = 1 mod 13 (13)
k = = 1 mod 59 (59)		 855 k's remaining at n=25K.

See k's at Riesel Base 768 remain.		 6 (70213)
28736 (24770)
19409 (24663)
54353 (24638)
32978 (24548)
11234 (24540)
36006 (24465)
2022 (24442)
11512 (24395)
13501 (24385)		 k = 3844 proven composite by partial algebraic factors.
769 6 5, 7   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 none - proven 2 (5)  
770 256 3, 257   k = = 1 mod 769 (769) 37 (300K)
130 (300K)
178 (300K)
218 (300K)		 107 (240408)
214 (148511)
26 (77040)
125 (54154)
199 (48507)
40 (16313)
32 (10462)
83 (6006)
187 (2627)
179 (1236)		  
771 83954 29, 37, 193 All k where k = m^2
and m = = 81 or 112 mod 193:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*771^q - 1) *
     (m*771^q + 1)
   odd n:
     factor of 193		 k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 7 (7)
k = = 1 mod 11 (11)		 64 k's remaining at n=100K.

See k's at Riesel Base 771 remain.		 21310 (99583)
72188 (97781)
69370 (97564)
38840 (93511)
9140 (89197)
82918 (86394)
228 (75856)
26942 (75343)
53182 (75143)
8250 (70449)		 k = 12544 proven composite by partial algebraic factors.
772 27054 5, 13, 773 All k where k = m^2
and m = = 317 or 456 mod 773:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*772^q - 1) *
     (m*772^q + 1)
   odd n:
     factor of 773		 k = = 1 mod 3 (3)
k = = 1 mod 257 (257)		 587 k's remaining at n=25K.

See k's at Riesel Base 772 remain.		 11147 (24944)
21824 (24625)
4407 (24590)
8604 (24311)
10217 (24180)
23535 (24124)
6966 (23966)
12719 (23897)
20135 (23785)
4749 (23644)		 No k's proven composite by algebraic factors.
773 44 3, 43   k = = 1 mod 2 (2)
k = = 1 mod 193 (193)		 38 (400K) 34 (14471)
12 (424)
24 (172)
26 (110)
2 (96)
10 (85)
16 (29)
32 (16)
20 (12)
14 (8)		  
774 61 5, 31 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*774^q - 1) *
     (m*774^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 773 (773) 25 (300K)
30 (300K)		 24 (17938)
29 (8552)
16 (2637)
15 (1937)
44 (1170)
12 (599)
34 (262)
19 (80)
59 (62)
51 (47)		 k = 4, 9, and 49 proven composite by partial algebraic factors.
775 172368 13, 97, 1777 All k where k = m^2
and m = = 22 or 75 mod 97:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*775^q - 1) *
     (m*775^q + 1)
   odd n:
     factor of 97		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 43 (43)		 537 k's remaining at n=25K.

See k's at Riesel Base 775 remain.		 105374 (24812)
45200 (24788)
101270 (24590)
139470 (24551)
82352 (24344)
31518 (24242)
147464 (23999)
33272 (23811)
85998 (23733)
7544 (23694)		 k = 133956 proven composite by partial algebraic factors.
776 8 3, 7   k = = 1 mod 5 (5)
k = = 1 mod 31 (31)		 none - proven 5 (12)
2 (4)
4 (3)
3 (2)
7 (1)		  
778 696 5, 17, 41 All k where k = m^2
and m = = 9 or 32 mod 41:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*778^q - 1) *
     (m*778^q + 1)
   odd n:
     factor of 41		 k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 37 (37)		 56 (300K)
404 (300K)
590 (300K)
657 (300K)		 21 (67710)
534 (37871)
248 (3913)
341 (3242)
177 (1704)
474 (1688)
609 (981)
42 (911)
170 (700)
458 (565)		 k = 81 proven composite by partial algebraic factors.
779 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 389 (389)		 none - proven 2 (220)  
780 285 11, 71   k = = 1 mod 19 (19)
k = = 1 mod 41 (41)		 109 (300K)
122 (300K)		 221 (258841)
25 (19167)
21 (14828)
197 (12296)
43 (11656)
118 (4368)
32 (3286)
211 (1940)
243 (1529)
263 (1158)		  
781 254 17, 23   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 13 (13)		 none - proven 50 (3112)
162 (367)
200 (295)
128 (170)
84 (46)
192 (39)
72 (30)
252 (26)
122 (12)
30 (12)		  
782 28 3, 29   k = = 1 mod 11 (11)
k = = 1 mod 71 (71)		 14 (400K) 7 (1685)
18 (510)
20 (16)
13 (11)
8 (8)
15 (7)
27 (4)
17 (4)
2 (4)
25 (3)		  
783 302 5, 7, 37   k = = 1 mod 2 (2)
k = = 1 mod 17 (17)
k = = 1 mod 23 (23)		 104 (400K) 258 (118544)
174 (98120)
230 (23156)
74 (18264)
4 (12507)
190 (8687)
6 (5022)
92 (2555)
262 (2250)
250 (1231)		  
784 156 5, 157 All k = m^2 for all n; factors to:
(m*28^n - 1) *
(m*28^n + 1)		 k = = 1 mod 3 (3)
k = = 1 mod 29 (29)		 116 (400K) 69 (155668)
126 (2771)
84 (1550)
152 (792)
104 (380)
131 (363)
149 (286)
14 (176)
122 (137)
74 (120)		 k = 9, 36, 81, and 144 proven composite by full algebraic factors.
785 130 3, 131   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)		 none - proven 28 (51277)
16 (26599)
94 (23033)
2 (9670)
58 (823)
20 (434)
122 (306)
66 (229)
44 (228)
38 (224)		  
786 37209 7, 19, 4651   k = = 1 mod 5 (5)
k = = 1 mod 157 (157)		 472 k's remaining at n=25K.

See k's at Riesel Base 786 remain.		 28505 (24796)
17263 (24758)
22359 (24686)
30027 (24201)
24567 (23993)
35904 (23990)
17554 (23883)
29157 (23865)
19847 (23745)
3854 (23525)		  
787 27332 5, 7, 13, 37, 151 All k where k = m^2
and m = = 14 or 183 mod 197:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*787^q - 1) *
     (m*787^q + 1)
   odd n:
     factor of 197		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 131 (131)		 159 k's remaining at n=100K.

See k's at Riesel Base 787 remain.		 5108 (98388)
7188 (90408)
13626 (89481)
848 (88695)
19958 (86955)
26268 (86464)
24414 (84908)
16158 (84752)
3968 (80954)
14832 (75716)		 No k's proven composite by algebraic factors.
788 14 3, 5, 13   k = = 1 mod 787 (787) none - proven 9 (11325)
7 (1663)
2 (332)
5 (264)
11 (42)
3 (9)
8 (4)
12 (3)
4 (3)
6 (2)		  
789 236 5, 79 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*789^q - 1) *
     (m*789^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 197 (197)		 120 (300K)
126 (300K)		 116 (156635)
146 (151073)
74 (80808)
184 (15372)
54 (3220)
206 (2931)
92 (2288)
234 (1758)
136 (725)
84 (598)		 k = 4, 64, and 144 proven composite by partial algebraic factors.
790 225 7, 113   k = = 1 mod 3 (3)
k = = 1 mod 263 (263)		 48 (400K) 20 (40772)
146 (400)
81 (399)
29 (323)
41 (140)
101 (136)
147 (122)
57 (121)
104 (98)
185 (93)		  
791 10 3, 11   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 79 (79)		 none - proven 8 (4)
2 (4)
4 (1)		  
792 1158 13, 61 (Condition 1):
All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*792^q - 1) *
     (m*792^q + 1)
   odd n:
     factor of 13
(Condition 2):
All k where k = m^2
and m = = 11 or 50 mod 61:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*792^q - 1) *
     (m*792^q + 1)
   odd n:
     factor of 61
(Condition 3):
All k where k = 22*m^2
and m = = 4 or 9 mod 13:
   even n:
     factor of 13
   for odd n let k = 22*m^2
   and let n=2*q-1; factors to:
     [m*6^n*22^q - 1] *
     [m*6^n*22^q + 1]
(Condition 4):
All k where k = 22*m^2
and m = = 5 or 56 mod 61:
   even n:
     factor of 61
   for odd n let k = 22*m^2
   and let n=2*q-1; factors to:
     [m*6^n*22^q - 1] *
     [m*6^n*22^q + 1]		 k = = 1 mod 7 (7)
k = = 1 mod 113 (113)		 245 (300K)
389 (300K)
417 (300K)
677 (300K)
742 (300K)
818 (300K)
1026 (300K)		 1152 (264617)
1067 (207705)
1111 (190801)
963 (143627)
558 (84648)
198 (74478)
672 (48437)
207 (36384)
560 (35721)
383 (20163)		 k = 25, 324, 441, and 961 proven composite by condition 1.

k = 121 proven composite by condition 2.

k = 352 proven composite by condition 3.

k = 550 proven composite by condition 4.
793 1834536 5, 41, 73, 397 All k where k = m^2
and m = = 63 or 334 mod 397:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*793^q - 1) *
     (m*793^q + 1)
   odd n:
     factor of 397		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 11 (11)		 18639 k's remaining at n=2.5K. To be shown later. 469968 (2500)
460572 (2500)
1666676 (2499)
1299960 (2499)
714662 (2499)
1649970 (2498)
1400822 (2498)
612752 (2498)
397778 (2498)
233010 (2498)		 k = 1272384 and 1572516 proven composite by partial algebraic factors.
794 4 3, 5   k = = 1 mod 13 (13)
k = = 1 mod 61 (61)		 none - proven 2 (6)
3 (1)		  
795 5770 29, 199, 641   k = = 1 mod 2 (2)
k = = 1 mod 397 (397)		 256 (100K)
338 (100K)
576 (100K)
1148 (100K)
1208 (100K)
1296 (100K)
1322 (100K)
1688 (100K)
1696 (100K)
1764 (100K)
1896 (100K)
1942 (100K)
1976 (100K)
1982 (100K)
2586 (100K)
3144 (100K)
3270 (100K)
3824 (100K)
4178 (100K)
4314 (100K)
4610 (100K)
4744 (100K)
4756 (100K)		 1248 (94478)
5184 (91435)
1852 (87627)
5058 (78597)
2446 (73020)
1478 (72919)
5016 (72081)
1436 (58378)
3222 (54308)
100 (42137)		  
797 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 199 (199)		 none - proven 6 (2)
2 (2)
4 (1)		  
798 339 5, 13, 17 All k where k = m^2
and m = = 4 or 13 mod 17:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*798^q - 1) *
     (m*798^q + 1)
   odd n:
     factor of 17		 k = = 1 mod 797 (797) 188 (300K)
283 (300K)
307 (300K)		 279 (235749)
322 (104936)
302 (104367)
317 (37478)
186 (10550)
82 (10042)
234 (5052)
271 (4406)
220 (1388)
68 (1374)		 k = 16 and 169 proven composite by partial algebraic factors.
800 88 3, 89   k = = 1 mod 17 (17)
k = = 1 mod 47 (47)		 8 (1M) 25 (124713)
4 (33837)
5 (20508)
23 (20452)
53 (14346)
85 (6307)
77 (3362)
36 (1169)
28 (1089)
73 (937)		  
802 408 5, 11, 197   k = = 1 mod 3 (3)
k = = 1 mod 89 (89)		 81 (300K)
128 (300K)
144 (300K)
156 (300K)
218 (300K)
276 (300K)
309 (300K)
329 (300K)
351 (300K)
366 (300K)		 248 (7802)
191 (5649)
159 (4653)
56 (4403)
359 (4389)
287 (3589)
354 (3456)
281 (1895)
219 (1736)
62 (1444)		  
803 68 3, 67   k = = 1 mod 2 (2)
k = = 1 mod 401 (401)		 14 (300K)
52 (300K)		 64 (98003)
22 (34391)
44 (12372)
38 (328)
34 (119)
4 (89)
32 (56)
30 (48)
2 (48)
16 (31)		  
804 6 5, 7 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*804^q - 1) *
     (m*804^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 11 (11)
k = = 1 mod 73 (73)		 none - proven 5 (1)
3 (1)
2 (1)		 k = 4 proven composite by partial algebraic factors.
805 92 13, 31   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 67 (67)		 none - proven 90 (2212)
30 (48)
74 (35)
14 (23)
86 (19)
78 (8)
20 (8)
56 (6)
12 (6)
72 (4)		  
806 268 3, 269   k = = 1 mod 5 (5)
k = = 1 mod 7 (7)
k = = 1 mod 23 (23)		 125 (400K)
214 (400K)		 152 (229984)
27 (71900)
74 (55078)
140 (21738)
203 (19520)
79 (10799)
97 (6167)
202 (3629)
80 (1948)
65 (1834)		  
807 32824 5, 101, 521 All k where k = m^2
and m = = 10 or 91 mod 101:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*807^q - 1) *
     (m*807^q + 1)
   odd n:
     factor of 101		 k = = 1 mod 2 (2)
k = = 1 mod 13 (13)
k = = 1 mod 31 (31)		 198 k's remaining at n=100K.

See k's at Riesel Base 807 remain.		 20144 (98989)
2468 (98442)
23192 (95126)
26314 (92023)
32684 (91403)
21914 (91323)
5064 (89117)
31210 (88163)
25554 (87657)
21316 (86915)		 k = 100 proven composite by partial algebraic factors.
808 59058 5, 37, 809 All k where k = m^2
and m = = 318 or 491 mod 809:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*808^q - 1) *
     (m*808^q + 1)
   odd n:
     factor of 809		 k = = 1 mod 3 (3)
k = = 1 mod 269 (269)		 947 k's remaining at n=25K.

See k's at Riesel Base 808 remain.		 56106 (24766)
42878 (24633)
44727 (24618)
1367 (24444)
12906 (24417)
4326 (24297)
9497 (24166)
21773 (24160)
24429 (24152)
24594 (24048)		 No k's proven composite by algebraic factors.
809 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 101 (101)		 none - proven 2 (44)  
810 35683 7, 19, 43, 811   k = = 1 mod 809 (809) 223 k's remaining at n=100K.

See k's at Riesel Base 810 remain.		 30226 (98614)
23165 (98273)
31084 (96221)
7120 (96197)
7970 (95811)
5255 (95090)
18952 (94146)
16634 (91126)
10885 (90165)
28690 (90128)		  
811 260 7, 29 All k where k = m^2
and m = = 12 or 17 mod 29:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*811^q - 1) *
     (m*811^q + 1)
   odd n:
     factor of 29		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 none - proven 8 (31783)
258 (28010)
128 (1619)
132 (1618)
210 (1017)
174 (146)
50 (59)
134 (45)
62 (30)
230 (28)		 k = 144 proven composite by partial algebraic factors.
812 13 3, 5, 17   k = = 1 mod 811 (811) 4 (400K) 10 (1575)
5 (50)
2 (10)
8 (8)
3 (3)
11 (2)
12 (1)
9 (1)
7 (1)
6 (1)		  
813 186 11, 37   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 29 (29)		 122 (400K) 34 (189659)
76 (120762)
142 (50872)
118 (27266)
158 (9237)
164 (664)
54 (184)
110 (58)
112 (35)
102 (28)		  
814 164 5, 163 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*814^q - 1) *
     (m*814^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 271 (271)		 44 (300K)
128 (300K)		 14 (197138)
134 (92080)
23 (17640)
8 (17365)
158 (7221)
101 (6241)
83 (1114)
81 (831)
98 (439)
104 (396)		 k = 9 and 144 proven composite by partial algebraic factors.
815 16 3, 17   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)
k = = 1 mod 37 (37)		 8 (400K) 14 (470)
10 (3)
2 (2)
6 (1)
4 (1)		  
816 343 19, 43   k = = 1 mod 5 (5)
k = = 1 mod 163 (163)		 18 (300K)
113 (300K)
204 (300K)		 214 (51534)
277 (14926)
267 (5467)
135 (3003)
207 (2716)
315 (834)
322 (540)
60 (529)
94 (520)
324 (443)		  
817 6189398 5, 41, 409, 1009 All k where k = m^2
and m = = 143 or 266 mod 409:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*817^q - 1) *
     (m*817^q + 1)
   odd n:
     factor of 409		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 17 (17)		 74092 k's remaining at n=2.5K. To be shown later. 6132890 (2500)
5559084 (2500)
5539334 (2500)
5177472 (2500)
4764698 (2500)
4093028 (2500)
3657872 (2500)
3652962 (2500)
2887568 (2500)
1551108 (2500)		 k = 304704 and 3617604 proven composite by partial algebraic factors.
818 8 3, 7   k = = 1 mod 19 (19)
k = = 1 mod 43 (43)		 none - proven 5 (4)
3 (4)
7 (3)
6 (2)
2 (2)
4 (1)		  
819 124 5, 41 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*819^q - 1) *
     (m*819^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 409 (409)		 none - proven 6 (407)
104 (360)
86 (119)
94 (98)
66 (67)
118 (66)
26 (61)
34 (26)
122 (24)
54 (18)		 k = 4 and 64 proven composite by partial algebraic factors.
820 390795 17, 37, 821 All k where k = m^2
and m = = 295 or 526 mod 821:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*820^q - 1) *
     (m*820^q + 1)
   odd n:
     factor of 821		 k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 13 (13)		 527 k's remaining at n=25K.

See k's at Riesel Base 820 remain.		 308468 (24687)
216345 (24669)
240092 (24501)
378368 (24497)
154580 (24380)
214668 (24299)
101159 (24129)
239298 (24114)
330003 (24100)
370179 (24020)		 No k's proven composite by algebraic factors.
821 958 3, 137   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 41 (41)		 58 (300K)
144 (300K)
158 (300K)
188 (300K)
242 (300K)
662 (300K)
680 (300K)
688 (300K)
742 (300K)
814 (300K)
872 (300K)
928 (300K)		 178 (233901)
790 (227461)
380 (119910)
404 (107718)
938 (70510)
674 (48964)
464 (44160)
898 (42303)
500 (35260)
140 (24442)		  
822 156369 5, 337, 823   k = = 1 mod 821 (821) 8895 k's remaining at n=2.5K. To be shown later. 137768 (2500)
109571 (2499)
108763 (2499)
135182 (2498)
113769 (2496)
82939 (2496)
152011 (2495)
132529 (2495)
74393 (2495)
113933 (2494)		  
823 8262 7, 43, 751   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 137 (137)		 68 k's remaining at n=100K.

See k's at Riesel Base 823 remain.		 36 (94169)
3102 (93790)
7448 (91882)
3306 (90326)
4466 (83645)
8222 (81210)
7368 (80817)
3768 (68094)
2306 (67007)
2762 (63684)		  
824 4 3, 5   k = = 1 mod 823 (823) none - proven 2 (102)
3 (3)		  
825 176 7, 59   k = = 1 mod 2 (2)
k = = 1 mod 103 (103)		 none - proven 146 (1954)
174 (328)
48 (294)
160 (126)
26 (113)
134 (75)
106 (65)
76 (34)
70 (21)
50 (21)		  
827 14 3, 5, 13   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 59 (59)		 none - proven 6 (9)
2 (2)
12 (1)
10 (1)
4 (1)		  
828 144 7, 13, 19   k = = 1 mod 827 (827) 64 (300K)
68 (300K)		 74 (76296)
15 (2308)
53 (2120)
55 (1769)
86 (1282)
97 (1124)
41 (1106)
121 (1101)
79 (1012)
139 (579)		  
829 84 5, 83   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 23 (23)		 none - proven 26 (2956)
50 (364)
14 (134)
12 (86)
56 (83)
74 (78)
68 (23)
18 (22)
20 (11)
62 (6)		  
830 278 3, 277   k = = 1 mod 829 (829) 9 (300K)
95 (300K)
107 (300K)
121 (300K)
144 (300K)		 74 (238594)
263 (64410)
218 (54608)
226 (44351)
53 (31194)
269 (30552)
197 (27370)
188 (25418)
224 (23718)
212 (19742)		  
831 1721084 13, 449, 769 (Condition 1):
All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*831^q - 1) *
     (m*831^q + 1)
   odd n:
     factor of 13
(Condition 2):
All k where k = 831*m^2
and m = = 5 or 8 mod 13:
   [Reverse condition 1]		 k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 83 (83)		 25415 k's remaining at n=2.5K. To be shown later. 1632240 (2500)
1085980 (2500)
1055482 (2500)
9558 (2500)
1572728 (2499)
892984 (2499)
281718 (2499)
1713568 (2498)
1380482 (2498)
744958 (2498)		 k = 8^2, 18^2, 60^2, 70^2, 112^2, 122^2, 138^2, 148^2, 190^2, 200^2, 242^2, 252^2, (etc. pattern repeating every 130m where k not = = 1 mod 83) proven composite by condition 1.

k = 53184 and 269244 proven composite by condition 2.
832 50 7, 17   k = = 1 mod 3 (3)
k = = 1 mod 277 (277)		 none - proven 35 (332073)
20 (8944)
36 (183)
8 (127)
26 (22)
3 (19)
41 (18)
18 (15)
42 (13)
48 (12)		  
833 140 3, 139   k = = 1 mod 2 (2)
k = = 1 mod 13 (13)		 104 (400K) 28 (53769)
76 (10911)
74 (996)
122 (348)
20 (256)
134 (92)
50 (50)
80 (48)
78 (44)
42 (39)		  
834 166 5, 167 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*834^q - 1) *
     (m*834^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 7 (7)
k = = 1 mod 17 (17)		 none - proven 130 (8495)
24 (2856)
136 (2249)
126 (973)
76 (567)
34 (346)
54 (286)
119 (242)
150 (191)
47 (131)		 k = 4, 9, 49, and 144 proven composite by partial algebraic factors.
835 56 11, 19   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 139 (139)		 none - proven 12 (7)
54 (6)
30 (4)
50 (2)
48 (2)
32 (2)
26 (2)
24 (2)
18 (2)
44 (1)		  
836 32 3, 31   k = = 1 mod 5 (5)
k = = 1 mod 167 (167)		 8 (400K) 23 (350)
2 (330)
18 (214)
28 (213)
5 (56)
20 (38)
10 (21)
12 (11)
17 (10)
30 (8)		  
837 2094 5, 13, 419   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)
k = = 1 mod 19 (19)		 554 (300K)
578 (300K)
676 (300K)
876 (300K)
1138 (300K)
1296 (300K)		 968 (183539)
1258 (134139)
1000 (122503)
974 (74416)
1416 (68007)
534 (63527)
1752 (62706)
1262 (58622)
662 (32380)
274 (31465)		  
838 180384 5, 7, 13, 97, 839   k = = 1 mod 3 (3)
k = = 1 mod 31 (31)		 3293 k's remaining at n=10K.

See k's at Riesel Base 838 remain.		 162207 (9992)
149496 (9978)
7859 (9972)
112907 (9968)
162903 (9946)
127811 (9943)
58511 (9926)
134247 (9923)
9864 (9909)
135587 (9908)		  
839 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 419 (419)		 none - proven 2 (2)  
840 84608 37, 61, 313 (Condition 1):
All k where k = m^2
and m = = 12 or 17 mod 29:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*840^q - 1) *
     (m*840^q + 1)
   odd n:
     factor of 29
(Condition 2):
All k where k = 210*m^2
and m = = 5 or 24 mod 29:
   even n:
     factor of 29
   for odd n let k = 210*m^2
   and let n=2*q-1; factors to:
     [m*2^n*210^q - 1] *
     [m*2^n*210^q + 1]		 k = = 1 mod 839 (839) 760 k's remaining at n=25K.

See k's at Riesel Base 840 remain.		 48951 (24942)
23083 (24924)
74543 (24911)
27087 (24841)
43586 (24812)
58873 (24331)
28886 (24204)
69215 (24047)
57780 (24045)
11496 (23892)		 k = 144, 289, 1681, 2116, 4900, 5625, 9801, 10816, 16384, 17689, 24649, 26244, 34596, 36481, 46225, 48400, 59536, 62001, 74529, and 77284 proven composite by condition 1.

k = 5250 proven composite by condition 2.
841 24090 13, 67, 271 All k = m^2 for all n; factors to:
(m*29^n - 1) *
(m*29^n + 1)		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 7 (7)		 542 (300K)
1280 (300K)
5474 (300K)
7634 (300K)
10154 (300K)
12494 (300K)
12912 (300K)
13412 (300K)
13898 (300K)
15942 (300K)
16712 (300K)
21422 (300K)		 5732 (194967)
11480 (181102)
19308 (146474)
16604 (125777)
9714 (116064)
4442 (92170)
22218 (61289)
17244 (56627)
8700 (46497)
1644 (44888)		 k = 144, 324, 900, 1764, 3600, 5184, 10404, 11664, 19044, and 22500 proven composite by full algebraic factors.
842 280 3, 281   k = = 1 mod 29 (29) 13 (100K)
25 (100K)
36 (100K)
43 (100K)
68 (100K)
82 (100K)
86 (100K)
89 (100K)
119 (100K)
127 (100K)
133 (100K)
137 (100K)
148 (100K)
172 (100K)
202 (100K)
211 (100K)
226 (100K)
242 (100K)
244 (100K)
249 (100K)
254 (100K)
269 (100K)		 130 (51293)
170 (46660)
17 (35640)
71 (33982)
186 (33489)
38 (18790)
28 (15283)
253 (13291)
251 (12378)
121 (10287)		  
843 8652 5, 13, 19, 37, 211   k = = 1 mod 2 (2)
k = = 1 mod 421 (421)		 67 k's remaining at n=100K.

See k's at Riesel Base 843 remain.		 316 (97299)
3488 (92798)
3402 (92647)
4742 (80636)
8276 (79118)
4544 (77655)
5616 (77642)
526 (76511)
5574 (75387)
7288 (72185)		  
844 14 5, 13 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*844^q - 1) *
     (m*844^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 281 (281)		 none - proven 6 (145)
2 (81)
8 (31)
12 (4)
11 (1)
5 (1)
3 (1)		 k = 9 proven composite by partial algebraic factors.
845 46 3, 47   k = = 1 mod 2 (2)
k = = 1 mod 211 (211)		 none - proven 2 (39406)
22 (593)
38 (138)
24 (84)
26 (74)
28 (33)
44 (28)
14 (20)
6 (19)
36 (15)		  
846 34 7, 11   k = = 1 mod 5 (5)
k = = 1 mod 13 (13)		 none - proven 10 (12780)
4 (3319)
13 (356)
8 (35)
32 (22)
9 (9)
20 (8)
7 (7)
22 (5)
3 (5)		  
847 1357806 5, 41, 53, 401 (Condition 1):
All k where k = m^2
and m = = 23 or 30 mod 53:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*847^q - 1) *
     (m*847^q + 1)
   odd n:
     factor of 53
(Condition 2):
All k where k = 7*m^2
and m = = 12 or 41 mod 53:
   even n:
     factor of 53
   for odd n let k = 7*m^2
   and let n=2*q-1; factors to:
     [m*11^n*7^q - 1] *
     [m*11^n*7^q + 1]		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 47 (47)		 12433 k's remaining at n=2.5K. To be shown later. 894398 (2500)
1056620 (2499)
472572 (2498)
316788 (2498)
885786 (2497)
783906 (2497)
1200222 (2496)
805110 (2496)
1331006 (2495)
398456 (2495)		 k = 900, 82944, 121104, 367236, 443556, 853776, and 968256 proven composite by condition 1.

k = 1008, 655452, and 762300 proven composite by condition 2.
848 284 3, 283   k = = 1 mod 7 (7)
k = = 1 mod 11 (11)		 74 (400K)
172 (400K)
178 (400K)
224 (400K)
266 (400K)		 7 (218439)
117 (82410)
185 (75298)
94 (65401)
194 (36212)
13 (23589)
187 (16055)
140 (10384)
72 (8804)
209 (7232)		  
849 16 5, 17 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*849^q - 1) *
     (m*849^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 53 (53)		 none - proven 14 (4114)
10 (21)
6 (19)
12 (2)
8 (1)
2 (1)		 k = 4 proven composite by partial algebraic factors.
850 369 23, 37 All k where k = m^2
and m = = 6 or 31 mod 37:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*850^q - 1) *
     (m*850^q + 1)
   odd n:
     factor of 37		 k = = 1 mod 3 (3)
k = = 1 mod 283 (283)		 221 (400K) 339 (57302)
275 (6084)
248 (3822)
159 (3088)
281 (2411)
206 (1484)
341 (1022)
252 (830)
108 (632)
312 (600)		 k = 36 proven composite by partial algebraic factors.
851 70 3, 71   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 17 (17)		 none - proven 20 (2040)
64 (1729)
44 (1646)
22 (11)
24 (7)
68 (6)
32 (6)
42 (5)
38 (4)
58 (3)		  
852 8529 5, 41, 853   k = = 1 mod 23 (23)
k = = 1 mod 37 (37)		 81 k's remaining at n=100K.

See k's at Riesel Base 852 remain.		 559 (98945)
1258 (95659)
3002 (93492)
5694 (88979)
7121 (88093)
164 (85037)
5257 (82424)
6320 (81236)
6821 (77634)
8336 (76378)		  
853 62 7, 61   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 71 (71)		 none - proven 12 (244)
6 (234)
42 (94)
48 (68)
60 (26)
44 (19)
56 (6)
26 (6)
18 (6)
2 (4)		  
854 4 3, 5   k = = 1 mod 853 (853) none - proven 3 (5)
2 (2)		  
856 108467 7, 181, 193 All k where k = m^2
and m = = 207 or 650 mod 857:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*856^q - 1) *
     (m*856^q + 1)
   odd n:
     factor of 857		 k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 19 (19)		 527 k's remaining at n=25K.

See k's at Riesel Base 856 remain.		 83987 (24713)
94517 (24668)
47312 (24579)
53768 (24151)
52025 (23951)
61889 (23916)
3389 (23831)
74610 (23757)
6000 (23729)
27702 (23676)		 k = 42849 proven composite by partial algebraic factors.
857 10 3, 11   k = = 1 mod 2 (2)
k = = 1 mod 107 (107)		 none - proven 6 (23082)
4 (195)
8 (22)
2 (2)		  
858 24053 5, 29, 859   k = = 1 mod 857 (857) 249 k's remaining at n=100K.

See k's at Riesel Base 858 remain.		 12742 (99711)
16657 (98142)
19414 (97412)
10361 (96854)
16934 (95377)
3406 (94666)
21936 (91423)
5813 (90493)
20120 (89828)
17672 (89194)		  
859 44 5, 43   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 11 (11)
k = = 1 mod 13 (13)		 none - proven 26 (90133)
42 (6610)
24 (42)
36 (11)
30 (4)
20 (4)
38 (3)
2 (3)
32 (1)
18 (1)		  
860 8 3, 7   k = = 1 mod 859 (859) none - proven 2 (62)
5 (12)
7 (5)
6 (4)
4 (3)
3 (1)		  
861 323168 13, 37, 1543   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 43 (43)		 703 k's remaining at n=25K.

See k's at Riesel Base 861 remain.		 167540 (24921)
281504 (24776)
280294 (24716)
273588 (24622)
295080 (24614)
152902 (24558)
73342 (24554)
158180 (24509)
257024 (24310)
154004 (24184)		  
862 26417 13, 19, 31, 37   k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 41 (41)		 158 k's remaining at n=100K.

See k's at Riesel Base 862 remain.		 12653 (97184)
22841 (97179)
13269 (96943)
11909 (95309)
18203 (94994)
1010 (92163)
9678 (88891)
10338 (86211)
13083 (85622)
14234 (84425)		  
863 14 3, 5, 13   k = = 1 mod 2 (2)
k = = 1 mod 431 (431)		 none - proven 8 (4492)
4 (2403)
2 (4)
12 (3)
6 (2)
10 (1)		  
864 174 5, 173 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*864^q - 1) *
     (m*864^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 6*m^2
and m = = 1 or 4 mod 5:
   even n:
     factor of 5
   for odd n let k = 6*m^2
   and let n=2*q-1; factors to:
     [m*12^n*6^q - 1] *
     [m*12^n*6^q + 1]		 k = = 1 mod 863 (863) 114 (400K) 134 (319246)
123 (20922)
111 (10033)
151 (5007)
26 (4229)
92 (3160)
94 (2888)
28 (1944)
59 (1394)
36 (1267)		 k = 4, 9, 49, 64, 144, and 169 proven composite by condition 1.

k = 6 and 96 proven composite by condition 2.
866 35 3, 17   k = = 1 mod 5 (5)
k = = 1 mod 173 (173)		 none - proven 8 (108590)
20 (12734)
7 (7227)
10 (2193)
23 (244)
2 (78)
24 (77)
18 (55)
27 (29)
14 (18)		  
867 92 7, 31   k = = 1 mod 2 (2)
k = = 1 mod 433 (433)		 8 (500K) 6 (61410)
84 (5877)
68 (363)
42 (78)
34 (64)
56 (49)
48 (42)
12 (42)
76 (14)
14 (11)		  
868 78 11, 79   k = = 1 mod 3 (3)
k = = 1 mod 17 (17)		 none - proven 54 (35296)
12 (2699)
9 (2403)
62 (56)
2 (30)
63 (18)
48 (14)
45 (13)
77 (12)
44 (12)		  
869 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 31 (31)		 none - proven 2 (2)  
870 66 13, 67 All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*870^q - 1) *
     (m*870^q + 1)
   odd n:
     factor of 13		 k = = 1 mod 11 (11)
k = = 1 mod 79 (79)		 none - proven 65 (3916)
27 (2255)
53 (1485)
14 (1033)
54 (418)
63 (209)
17 (161)
2 (51)
55 (44)
4 (29)		 k = 25 and 64 proven composite by partial algebraic factors.
871 16460 17, 53, 109 All k where k = m^2
and m = = 33 or 76 mod 109:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*871^q - 1) *
     (m*871^q + 1)
   odd n:
     factor of 109		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 29 (29)		 2328 (300K)
2430 (300K)
5262 (300K)
5318 (300K)
5648 (300K)
5664 (300K)
6408 (300K)
7302 (300K)
7772 (300K)
8958 (300K)
10572 (300K)
12032 (300K)
12534 (300K)		 914 (239796)
3084 (237917)
2702 (162988)
9482 (155938)
14280 (139781)
16172 (120722)
1964 (102208)
7430 (99782)
2852 (91588)
9120 (90061)		 No k's proven composite by algebraic factors.
872 98 3, 97   k = = 1 mod 13 (13)
k = = 1 mod 67 (67)		 11 (400K)
16 (400K)
43 (400K)
86 (400K)		 93 (163674)
44 (162680)
95 (76786)
38 (65938)
37 (51045)
91 (26937)
32 (12532)
67 (11949)
2 (6036)
96 (2234)		  
873 208 19, 23   k = = 1 mod 2 (2)
k = = 1 mod 109 (109)		 94 (400K)
114 (400K)		 104 (344135)
70 (39463)
36 (11719)
118 (5478)
180 (1358)
42 (1291)
160 (618)
14 (260)
58 (213)
162 (191)		  
874 6 5, 7   k = = 1 mod 3 (3)
k = = 1 mod 97 (97)		 none - proven 5 (2)
3 (1)
2 (1)		  
875 74 3, 73   k = = 1 mod 2 (2)
k = = 1 mod 19 (19)
k = = 1 mod 23 (23)		 none - proven 38 (256892)
50 (53254)
56 (694)
52 (519)
40 (489)
34 (263)
72 (220)
14 (64)
60 (57)
8 (32)		  
877 50654 7, 37, 991   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 73 (73)		 471 k's remaining at n=25K.

See k's at Riesel Base 877 remain.		 42228 (24959)
10908 (24942)
17658 (24918)
29066 (24810)
8934 (24589)
29576 (24527)
28886 (24483)
18818 (24288)
38222 (24070)
26352 (24066)		  
878 292 3, 293   k = = 1 mod 877 (877) 36 k's remaining at n=100K.

See k's at Riesel Base 878 remain.		 181 (88273)
158 (73524)
157 (69051)
190 (68255)
112 (54035)
284 (46012)
96 (45635)
77 (42180)
91 (27833)
236 (21530)		  
879 34 5, 11 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*879^q - 1) *
     (m*879^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 439 (439)		 24 (400K) 14 (438)
18 (31)
12 (9)
22 (8)
10 (6)
2 (5)
32 (4)
16 (3)
30 (2)
8 (2)		 k = 4 proven composite by partial algebraic factors.
880 48720 13, 103, 193 All k where k = m^2
and m = = 387 or 494 mod 881:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*880^q - 1) *
     (m*880^q + 1)
   odd n:
     factor of 881		 k = = 1 mod 3 (3)
k = = 1 mod 293 (293)		 180 k's remaining at n=100K.

See k's at Riesel Base 880 remain.		 30468 (95118)
6276 (92966)
1763 (90829)
12281 (89586)
28440 (89185)
47426 (88577)
14165 (87347)
25983 (85968)
45012 (84301)
39510 (83021)		 No k's proven composite by algebraic factors.
881 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 11 (11)		 none - proven 2 (132)
4 (3)		  
882 25606 5, 29, 883   k = = 1 mod 881 (881) 253 k's remaining at n=100K.

See k's at Riesel Base 882 remain.		 5056 (98606)
7393 (97499)
11069 (96135)
2312 (93010)
23698 (92126)
21572 (89597)
11492 (88396)
15589 (87597)
1178 (86266)
6543 (85842)		  
883 324 13, 17   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 194 (500K) 188 (88589)
224 (72180)
222 (63471)
306 (13951)
168 (1582)
26 (1234)
192 (1119)
132 (616)
62 (266)
186 (142)		  
884 4 3, 5   k = = 1 mod 883 (883) none - proven 2 (330)
3 (4)		  
885 1041492 7, 19, 73, 443   k = = 1 mod 2 (2)
k = = 1 mod 13 (13)
k = = 1 mod 17 (17)		 3952 k's remaining at n=10K.

See k's at Riesel Base 885 remain.		 983466 (9998)
693632 (9992)
337352 (9980)
114120 (9970)
164300 (9968)
741234 (9964)
387046 (9949)
790282 (9937)
886182 (9918)
143478 (9916)		  
886 1758033 7, 13, 19, 61, 887   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 59 (59)		 29469 k's remaining at n=2.5K. To be shown later. 1677344 (2500)
1511549 (2500)
1447800 (2500)
1417434 (2500)
850167 (2500)
686193 (2500)
567668 (2500)
462893 (2500)
486735 (2499)
1427994 (2498)		  
887 38 3, 37 All k where k = m^2
and m = = 6 or 31 mod 37:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*887^q - 1) *
     (m*887^q + 1)
   odd n:
     factor of 37		 k = = 1 mod 2 (2)
k = = 1 mod 443 (443)		 22 (300K)
26 (300K)		 10 (4107)
34 (263)
24 (141)
28 (115)
2 (40)
14 (28)
16 (27)
20 (8)
32 (6)
30 (3)		 k = 36 proven composite by partial algebraic factors.
888 69 5, 7, 17   k = = 1 mod 887 (887) 64 (400K) 34 (326732)
49 (1931)
41 (454)
20 (364)
27 (310)
51 (229)
67 (204)
17 (202)
4 (201)
57 (187)		  
889 266 5, 89 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*889^q - 1) *
     (m*889^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 37 (37)		 14 (300K)
86 (300K)
194 (300K)
216 (300K)		 234 (5694)
224 (2146)
246 (1351)
258 (1005)
134 (438)
174 (370)
24 (236)
264 (188)
114 (134)
206 (85)		 k = 144 proven composite by partial algebraic factors.
890 10 3, 11   k = = 1 mod 7 (7)
k = = 1 mod 127 (127)		 none - proven 2 (428)
3 (138)
6 (2)
5 (2)
9 (1)
7 (1)
4 (1)		  
892 189 19, 47   k = = 1 mod 3 (3)
k = = 1 mod 11 (11)		 48 (400K)
96 (400K)
170 (400K)		 161 (10534)
174 (2647)
33 (1983)
39 (1245)
36 (1123)
125 (886)
147 (274)
128 (271)
132 (178)
9 (119)		  
893 148 3, 149   k = = 1 mod 2 (2)
k = = 1 mod 223 (223)		 22 (300K)
44 (300K)
94 (300K)		 50 (231310)
134 (67840)
122 (11208)
74 (7812)
146 (4874)
56 (1086)
104 (504)
8 (428)
128 (422)
102 (264)		  
894 284 5, 7, 31, 283 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*894^q - 1) *
     (m*894^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 19 (19)
k = = 1 mod 47 (47)		 6 (300K)
79 (300K)
184 (300K)
216 (300K)
220 (300K)
225 (300K)		 179 (214290)
59 (97604)
276 (55679)
151 (53015)
44 (21516)
209 (4072)
124 (2656)
26 (2427)
181 (1453)
68 (1120)		 k = 4, 9, 49, 64, 144, and 169 proven composite by partial algebraic factors.
895 152774 7, 97, 4129   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 149 (149)		 1042 k's remaining at n=25K.

See k's at Riesel Base 895 remain.		 16080 (24779)
105008 (24745)
6362 (24708)
124130 (24684)
112488 (24645)
2984 (24550)
90132 (24169)
72570 (24023)
71042 (23828)
55356 (23745)		  
896 14 3, 13   k = = 1 mod 5 (5)
k = = 1 mod 179 (179)		 none - proven 12 (1386)
8 (262)
5 (22)
13 (11)
10 (5)
9 (5)
2 (2)
7 (1)
4 (1)
3 (1)		  
897 19308 5, 17, 449 All k where k = m^2
and m = = 67 or 382 mod 449:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*897^q - 1) *
     (m*897^q + 1)
   odd n:
     factor of 449		 k = = 1 mod 2 (2)
k = = 1 mod 7 (7)		 45 k's remaining at n=100K.

See k's at Riesel Base 897 remain.		 9484 (85704)
9334 (79683)
16554 (78440)
18968 (73776)
12196 (71787)
19098 (63246)
11406 (58947)
12296 (57518)
840 (54949)
798 (50260)		 No k's proven composite by algebraic factors.
898 30 29, 31   k = = 1 mod 3 (3)
k = = 1 mod 13 (13)
k = = 1 mod 23 (23)		 none - proven 17 (54)
18 (45)
5 (16)
26 (15)
23 (6)
2 (6)
21 (2)
12 (2)
11 (2)
8 (2)		  
899 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 449 (449)		 none - proven 2 (2)  
900 52 17, 53 All k = m^2 for all n; factors to:
(m*30^n - 1) *
(m*30^n + 1)		 k = = 1 mod 29 (29)
k = = 1 mod 31 (31)		 none - proven 22 (252407)
33 (454)
2 (71)
28 (31)
11 (15)
5 (12)
31 (11)
38 (8)
20 (8)
35 (5)		 k = 4, 9, 16, 25, 36, and 49 proven composite by full algebraic factors.
901 12 7, 11, 13, 19   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 none - proven 8 (1)
2 (1)		  
902 8 3, 7   k = = 1 mod 17 (17)
k = = 1 mod 53 (53)		 none - proven 7 (3005)
5 (4)
2 (4)
3 (3)
6 (2)
4 (1)		  
903 24746 5, 73, 113 All k where k = m^2
and m = = 15 or 98 mod 113:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*903^q - 1) *
     (m*903^q + 1)
   odd n:
     factor of 113		 k = = 1 mod 2 (2)
k = = 1 mod 11 (11)
k = = 1 mod 41 (41)		 39 k's remaining at n=100K.

See k's at Riesel Base 903 remain.		 6972 (99786)
14702 (97862)
18872 (89267)
19166 (87334)
17222 (81175)
20066 (71126)
16554 (64471)
7846 (61171)
23982 (60614)
10966 (60177)		 k = 16384 proven composite by partial algebraic factors.
904 1266 5, 181 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*904^q - 1) *
     (m*904^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 43 (43)		 129 (300K)
159 (300K)
311 (300K)
374 (300K)
444 (300K)
851 (300K)
894 (300K)
900 (300K)
914 (300K)
1031 (300K)
1046 (300K)		 657 (81712)
749 (66948)
180 (36872)
899 (28230)
534 (20854)
723 (19106)
504 (16620)
903 (13429)
419 (10616)
224 (9092)		 k = 9, 144, 324, 729, and 1089 proven composite by partial algebraic factors.
905 152 3, 151   k = = 1 mod 2 (2)
k = = 1 mod 113 (113)		 22 (400K) 70 (189879)
32 (178286)
128 (72312)
4 (4857)
130 (3477)
148 (2455)
92 (1598)
86 (726)
122 (634)
134 (560)		  
907 4050362 5, 7, 13, 227, 661   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 151 (151)		 89943 k's remaining at n=2.5K. To be shown later. 3953730 (2500)
3935754 (2500)
2204238 (2500)
1930562 (2500)
1626980 (2500)
1161264 (2500)
582932 (2500)
355254 (2500)
3084540 (2499)
2875194 (2499)		  
908 29 3, 5, 7, 13, 67   k = = 1 mod 907 (907) none - proven 8 (61796)
13 (3793)
14 (2572)
19 (1305)
26 (354)
16 (63)
22 (39)
2 (30)
23 (28)
21 (18)		  
909 6 5, 7 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*909^q - 1) *
     (m*909^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 227 (227)		 none - proven 2 (14) k = 4 proven composite by partial algebraic factors.
911 20 3, 19   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 7 (7)
k = = 1 mod 13 (13)		 none - proven 2 (14)
18 (2)
12 (2)
10 (1)
4 (1)		  
912 331 11, 83   k = = 1 mod 911 (911) 10 (300K)
12 (300K)
58 (300K)
76 (300K)
78 (300K)
167 (300K)
218 (300K)
263 (300K)
296 (300K)		 228 (236298)
164 (108156)
177 (91873)
93 (14208)
324 (13359)
83 (12002)
298 (9875)
65 (5040)
288 (4039)
285 (2720)		  
913 1368714 5, 7, 13, 109, 457 All k where k = m^2
and m = = 109 or 348 mod 457:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*913^q - 1) *
     (m*913^q + 1)
   odd n:
     factor of 457		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 19 (19)		 16764 k's remaining at n=2.5K. To be shown later. 816492 (2500)
363444 (2500)
352782 (2500)
1202132 (2499)
706290 (2499)
931338 (2498)
741726 (2498)
429738 (2498)
921846 (2497)
824844 (2496)		 k = 121104 proven composite by partial algebraic factors.
914 4 3, 5   k = = 1 mod 11 (11)
k = = 1 mod 83 (83)		 none - proven 2 (438)
3 (1)		  
915 3970630 13, 229, 2477 All k where k = m^2
and m = = 107 or 122 mod 229:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*228^q - 1) *
     (m*228^q + 1)
   odd n:
     factor of 229		 k = = 1 mod 2 (2)
k = = 1 mod 457 (457)		 57194 k's remaining at n=2.5K. To be shown later. 3630140 (2500)
3467372 (2500)
3140422 (2500)
2937940 (2500)
2677020 (2500)
1812632 (2500)
1755598 (2500)
1686736 (2500)
1098600 (2500)
1091940 (2500)		 k = 14884, 112896, 336400, 630436, 1077444, 1567504, 2238016, 2924100, and 3818116 proven composite by partial algebraic factors.
916 132 7, 131   k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 61 (61)		 none - proven 78 (120247)
39 (586)
3 (475)
113 (305)
59 (283)
27 (206)
90 (178)
15 (85)
44 (72)
8 (67)		  
917 16 3, 17   k = = 1 mod 2 (2)
k = = 1 mod 229 (229)		 none - proven 2 (210)
14 (184)
8 (16)
10 (7)
4 (3)
12 (1)
6 (1)		  
918 11946 5, 13, 919   k = = 1 mod 7 (7)
k = = 1 mod 131 (131)		 75 k's remaining at n=100K.

See k's at Riesel Base 918 remain.		 4456 (98561)
11812 (91558)
3768 (87886)
8137 (82711)
10371 (81587)
177 (78784)
1708 (72912)
8606 (71535)
9972 (68594)
8574 (68063)		  
919 24 5, 23   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 17 (17)		 none - proven 6 (11)
2 (4)
14 (2)
20 (1)
12 (1)
8 (1)		  
920 103 3, 7, 13, 19   k = = 1 mod 919 (919) 53 (500K)
61 (500K)
76 (500K)		 29 (367810)
82 (262409)
94 (64819)
86 (45938)
46 (33853)
98 (28244)
102 (11107)
85 (5769)
65 (4998)
81 (4697)		  
922 27 5, 13, 73   k = = 1 mod 3 (3)
k = = 1 mod 307 (307)		 none - proven 18 (582)
2 (342)
23 (12)
21 (10)
3 (8)
24 (4)
5 (4)
17 (2)
12 (2)
8 (2)		  
923 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 461 (461)		 none - proven 6 (114)
2 (2)
4 (1)		  
924 36 5, 37 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*924^q - 1) *
     (m*924^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 13 (13)
k = = 1 mod 71 (71)		 none - proven 6 (329)
20 (127)
34 (38)
30 (27)
29 (18)
5 (12)
35 (11)
23 (5)
17 (5)
8 (5)		 k = 4 and 9 proven composite by partial algebraic factors.
926 104 3, 103   k = = 1 mod 5 (5)
k = = 1 mod 37 (37)		 9 (300K)
22 (300K)
53 (300K)
65 (300K)
85 (300K)
102 (300K)		 70 (131099)
49 (84987)
67 (52457)
95 (6528)
23 (4876)
100 (2631)
73 (1007)
47 (394)
35 (300)
79 (151)		  
927 5886 5, 17, 29, 73 All k where k = m^2
and m = = 12 or 17 mod 29:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*927^q - 1) *
     (m*927^q + 1)
   odd n:
     factor of 29		 k = = 1 mod 2 (2)
k = = 1 mod 463 (463)		 48 k's remaining at n=100K.

See k's at Riesel Base 927 remain.		 3788 (96727)
1846 (96599)
2396 (96325)
3664 (95108)
4146 (84902)
2844 (79788)
3742 (76829)
1028 (74503)
2848 (73382)
5184 (72813)		 k = 144, 2116, and 4900 proven composite by partial algebraic factors.
928 32514 5, 13, 929 All k where k = m^2
and m = = 324 or 605 mod 929:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*928^q - 1) *
     (m*928^q + 1)
   odd n:
     factor of 929		 k = = 1 mod 3 (3)
k = = 1 mod 103 (103)		 629 k's remaining at n=25K.

See k's at Riesel Base 928 remain.		 17703 (24741)
13239 (24540)
8124 (24481)
3713 (24298)
31557 (24271)
18281 (24223)
2283 (24082)
3407 (24015)
22548 (23758)
18957 (23402)		 No k's proven composite by algebraic factors.
929 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 29 (29)		 none - proven 2 (18)  
930 20 7, 19   k = = 1 mod 929 (929) none - proven 13 (354)
8 (101)
10 (13)
15 (11)
18 (4)
14 (2)
11 (2)
7 (2)
6 (2)
2 (2)		  
931 3960 17, 37, 233 All k where k = m^2
and m = = 89 or 144 mod 233:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*931^q - 1) *
     (m*931^q + 1)
   odd n:
     factor of 233		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 31 (31)		 1854 (400K)
3812 (400K)		 3888 (227714)
2498 (51852)
2748 (16634)
242 (5908)
1662 (3762)
3390 (3253)
1728 (3209)
3668 (3164)
698 (2842)
3470 (1507)		 No k's proven composite by algebraic factors.
932 310 3, 311   k = = 1 mod 7 (7)
k = = 1 mod 19 (19)		 142 (300K)
146 (300K)
208 (300K)
221 (300K)
238 (300K)
263 (300K)
277 (300K)
283 (300K)
307 (300K)		 74 (229308)
220 (120737)
250 (29891)
269 (21276)
237 (20750)
181 (14795)
251 (10922)
193 (9183)
293 (8914)
242 (4880)		  
933 389944 5, 7, 13, 37, 467   k = = 1 mod 2 (2)
k = = 1 mod 233 (233)		 12657 k's remaining at n=2.5K. To be shown later. 35038 (2500)
370792 (2499)
174916 (2499)
94586 (2499)
3738 (2498)
182444 (2496)
169348 (2496)
86414 (2496)
50054 (2496)
249474 (2495)		  
934 21 5, 11 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*934^q - 1) *
     (m*934^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 311 (311)		 none - proven 6 (1411)
12 (71)
8 (7)
14 (2)
5 (2)
20 (1)
18 (1)
17 (1)
15 (1)
11 (1)		 k = 9 proven composite by partial algebraic factors.
935 14 3, 13   k = = 1 mod 2 (2)
k = = 1 mod 467 (467)		 none - proven 2 (72)
6 (3)
12 (2)
8 (2)
10 (1)
4 (1)		  
936 100260 7, 31, 37, 937 k=64:
   n = = 0 mod 2:
     let n = 2q; factors to:
     (8*936^q - 1) *
     (8*936^q + 1)
   n = = 0 mod 3:
     let n=3q; factors to:
     (4*936^q - 1) *
     [16*936^(2q) + 4*936^q + 1]
   n = = 1 mod 6:
     factor of 37
   n = = 5 mod 6:
     factor of 109		 k = = 1 mod 5 (5)
k = = 1 mod 11 (11)
k = = 1 mod 17 (17)		 91 k's remaining at n=100K.

See k's at Riesel Base 936 remain.		 74959 (98966)
43250 (98294)
63555 (97705)
55890 (97624)
97510 (95985)
78870 (94573)
78650 (93020)
96659 (91629)
19087 (89737)
52048 (85072)		  
937 1140 7, 67   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 13 (13)		 384 (300K)
428 (300K)
636 (300K)
650 (300K)
848 (300K)
902 (300K)
918 (300K)
932 (300K)
1004 (300K)		 134 (219783)
434 (31271)
68 (10595)
738 (10563)
1086 (7143)
1070 (6014)
948 (5948)
734 (3520)
546 (2037)
678 (1866)		  
938 299 3, 5, 149   k = = 1 mod 937 (937) 14 (100K)
20 (100K)
38 (100K)
47 (100K)
64 (100K)
82 (100K)
97 (100K)
104 (100K)
125 (100K)
152 (100K)
155 (100K)
157 (100K)
163 (100K)
170 (100K)
178 (100K)
179 (100K)
206 (100K)
224 (100K)
236 (100K)
239 (100K)
254 (100K)
269 (100K)
277 (100K)		 247 (90251)
232 (65287)
2 (40422)
216 (29158)
115 (22223)
67 (21067)
251 (13506)
119 (13356)
235 (12565)
258 (10154)		  
939 46 5, 47 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*939^q - 1) *
     (m*939^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 67 (67)		 none - proven 44 (3116)
16 (2115)
38 (1965)
30 (162)
24 (36)
6 (11)
14 (10)
42 (9)
28 (6)
40 (4)		 k = 4 proven composite by partial algebraic factors.
940 36929 7, 73, 577 k = 19044:
   for even n let n=2*q; factors to:
     (138*940^q - 1) *
     (138*940^q + 1)
   odd n:
     covering set 7, 13, 73		 k = = 1 mod 3 (3)
k = = 1 mod 313 (313)		 242 k's remaining at n=100K.

See k's at Riesel Base 940 remain.		 16718 (99412)
15647 (98821)
25967 (98316)
18120 (94182)
15978 (93999)
2480 (92427)
33279 (92131)
7584 (86501)
25770 (86128)
28214 (84792)		  
941 158 3, 157   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 47 (47)		 92 (400K)
112 (400K)		 74 (348034)
122 (137852)
128 (2264)
8 (1684)
90 (860)
132 (414)
44 (278)
50 (244)
110 (160)
154 (157)		  
942 206 23, 41 All k where k = m^2
and m = = 9 or 32 mod 41:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*942^q - 1) *
     (m*942^q + 1)
   odd n:
     factor of 41		 k = = 1 mod 941 (941) 48 (400K)
70 (400K)
114 (400K)
163 (400K)		 85 (27719)
49 (22137)
184 (15716)
102 (9858)
123 (5706)
149 (4575)
183 (4184)
88 (3774)
182 (3166)
44 (3156)		 k = 81 proven composite by partial algebraic factors.
943 18822 5, 7, 13, 19, 59   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 157 (157)		 90 k's remaining at n=100K.

See k's at Riesel Base 943 remain.		 4626 (99554)
11678 (99165)
17792 (97756)
15446 (95909)
14078 (92353)
9470 (86506)
7416 (83054)
9914 (82127)
17216 (80055)
11208 (68770)		  
944 4 3, 5   k = = 1 mod 23 (23)
k = = 1 mod 41 (41)		 none - proven 3 (3)
2 (2)		  
945 386 11, 43   k = = 1 mod 2 (2)
k = = 1 mod 59 (59)		 42 (400K)
302 (400K)		 318 (20872)
208 (12406)
266 (7355)
230 (3954)
342 (2961)
336 (1088)
12 (855)
34 (647)
268 (558)
104 (429)		  
947 80 3, 79   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)
k = = 1 mod 43 (43)		 none - proven 74 (27996)
4 (10055)
16 (8931)
42 (106)
22 (89)
58 (79)
2 (54)
14 (40)
70 (31)
38 (28)		  
948 220 13, 73 All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*948^q - 1) *
     (m*948^q + 1)
   odd n:
     factor of 13		 k = = 1 mod 947 (947) 45 (300K)
53 (300K)
69 (300K)
157 (300K)		 21 (290747)
51 (29018)
62 (14250)
218 (2680)
47 (2218)
209 (1213)
166 (881)
140 (610)
114 (435)
194 (388)		 k = 25 and 64 proven composite by partial algebraic factors.
949 56 5, 19   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 79 (79)		 none - proven 14 (6110)
2 (173)
24 (50)
50 (19)
30 (18)
36 (7)
18 (6)
48 (4)
26 (3)
54 (2)		  
950 316 3, 317   k = = 1 mod 13 (13)
k = = 1 mod 73 (73)		 11 (300K)
28 (300K)
110 (300K)
199 (300K)
227 (300K)
305 (300K)		 116 (258458)
44 (208860)
86 (142078)
25 (120829)
283 (56277)
137 (38862)
125 (31268)
239 (28756)
47 (22724)
121 (13833)		  
951 50 7, 17   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 19 (19)		 none - proven 34 (371834)
10 (21)
48 (6)
42 (4)
30 (3)
24 (3)
44 (1)
40 (1)
38 (1)
32 (1)		  
952 5411 13, 43, 541   k = = 1 mod 3 (3)
k = = 1 mod 317 (317)		 34 k's remaining at n=100K.

See k's at Riesel Base 952 remain.		 1076 (96494)
3576 (88762)
1211 (86277)
4245 (64148)
378 (57814)
2025 (48727)
3089 (47700)
846 (40594)
4689 (38912)
3548 (36718)		  
953 266 3, 53   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 17 (17)		 74 (300K)
104 (300K)
160 (300K)
262 (300K)
264 (300K)		 194 (166836)
118 (29165)
242 (18404)
236 (13330)
44 (6368)
10 (5061)
206 (4506)
168 (2593)
224 (2528)
88 (2369)		  
954 381 5, 191 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*954^q - 1) *
     (m*954^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 106*m^2
and m = = 1 or 4 mod 5:
   even n:
     factor of 5
   for odd n let k = 106*m^2
   and let n=2*q-1; factors to:
     [m*3^n*106^q - 1] *
     [m*3^n*106^q + 1]		 k = = 1 mod 953 (953) 6 (300K)
36 (300K)
81 (300K)
84 (300K)
151 (300K)
158 (300K)
159 (300K)
161 (300K)
176 (300K)
204 (300K)
321 (300K)
326 (300K)
356 (300K)		 346 (159015)
190 (112910)
379 (110860)
254 (103446)
102 (52163)
43 (18511)
109 (10854)
100 (10509)
219 (6376)
214 (6056)		 k = 4, 9, 49, 64, 144, 169, 289, and 324 proven composite by condition 1.

k = 106 proven composite by condition 2.
955 1333860 7, 157, 239, 829   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 53 (53)		 12170 k's remaining at n=2.5K. To be shown later. 521900 (2500)
105780 (2500)
1064364 (2499)
18008 (2499)
1235138 (2498)
960872 (2498)
462962 (2498)
129114 (2498)
989594 (2496)
1196078 (2495)		  
956 10 3, 11   k = = 1 mod 5 (5)
k = = 1 mod 191 (191)		 none - proven 9 (309)
5 (192)
3 (143)
2 (18)
8 (4)
7 (1)
4 (1)		  
957 1438 5, 13, 479 k=64:
   n = = 1 mod 3:
     factor of 73
   n = = 2 mod 3:
     factor of 19
   n = = 0 mod 3:
     let n=3q; factors to:
     (4*957^q - 1) *
     [16*957^(2q) + 4*957^q + 1]		 k = = 1 mod 2 (2)
k = = 1 mod 239 (239)		 8 (300K)
120 (300K)
404 (300K)
1026 (300K)
1046 (300K)
1198 (300K)
1326 (300K)
1432 (300K)		 904 (227111)
452 (55574)
216 (37882)
1294 (27433)
1286 (19831)
648 (12320)
818 (11776)
1168 (10244)
1262 (6421)
998 (5894)		  
958 174 5, 7, 173   k = = 1 mod 3 (3)
k = = 1 mod 11 (11)
k = = 1 mod 29 (29)		 8 (500K) 162 (46431)
83 (41090)
120 (39177)
134 (10565)
156 (6394)
153 (1964)
27 (970)
87 (604)
29 (423)
104 (328)		  
959 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 479 (479)		 none - proven 2 (2)  
961 38 13, 37   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)		 none - proven 14 (187)
12 (36)
30 (24)
2 (3)
32 (2)
18 (2)
24 (1)
20 (1)
8 (1)		  
962 106 3, 107   k = = 1 mod 31 (31) 11 (400K)
13 (400K)
73 (400K)
74 (400K)
89 (400K)
104 (400K)		 44 (47400)
43 (32367)
8 (31840)
26 (13686)
40 (12149)
46 (4989)
51 (4917)
76 (3109)
92 (1636)
58 (911)		  
964 194 5, 193 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*964^q - 1) *
     (m*964^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 107 (107)		 none - proven 129 (112228)
141 (110107)
21 (22931)
179 (19040)
111 (15055)
149 (2136)
72 (1420)
183 (1131)
66 (659)
75 (628)		 k = 9 and 144 proven composite by partial algebraic factors.
965 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 241 (241)		 none - proven 4 (8755)
2 (136)
6 (10)		  
967 408 5, 11, 13   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 23 (23)		 242 (500K) 32 (8416)
320 (3367)
140 (1775)
336 (971)
230 (924)
294 (679)
98 (678)
342 (581)
216 (430)
234 (348)		  
968 16 3, 17   k = = 1 mod 967 (967) 4 (500K) 2 (1750)
7 (39)
9 (13)
14 (8)
12 (2)
11 (2)
8 (2)
5 (2)
15 (1)
13 (1)		  
969 96 5, 97 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*969^q - 1) *
     (m*969^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 11 (11)		 none - proven 2 (24096)
16 (1079)
74 (580)
60 (76)
86 (55)
94 (12)
80 (12)
82 (11)
26 (9)
14 (8)		 k = 4 and 64 proven composite by partial algebraic factors.
970 447630 13, 461, 971   k = = 1 mod 3 (3)
k = = 1 mod 17 (17)
k = = 1 mod 19 (19)		 3431 k's remaining at n=10K.

See k's at Riesel Base 970 remain.		 384434 (9998)
351378 (9993)
205493 (9988)
171711 (9985)
374454 (9978)
269070 (9970)
309072 (9968)
181388 (9963)
296837 (9957)
258644 (9928)		  
971 3578 3, 7, 13, 79   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 97 (97)		 82 k's remaining at n=100K.

See k's at Riesel Base 971 remain.		 1160 (99188)
2444 (78748)
3244 (75063)
794 (71126)
42 (67575)
3340 (66969)
1368 (65297)
2350 (62749)
2900 (58822)
1028 (55708)		  
972 279 7, 139   k = = 1 mod 971 (971) 3 (300K)
8 (300K)
29 (300K)
49 (300K)
69 (300K)
75 (300K)
146 (300K)
174 (300K)		 197 (265841)
166 (141038)
188 (80392)
111 (59402)
260 (41245)
6 (36702)
78 (27907)
36 (24565)
103 (16926)
238 (10322)		  
973 21914 5, 17, 487   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)		 83 k's remaining at n=100K.

See k's at Riesel Base 973 remain.		 3162 (98466)
2964 (89563)
3596 (87761)
15908 (86628)
5376 (84193)
8316 (84014)
16724 (82415)
11064 (74865)
20846 (74089)
18942 (71672)		  
974 4 3, 5   k = = 1 mod 7 (7)
k = = 1 mod 139 (139)		 none - proven 2 (8)
3 (2)		  
975 282032 7, 67, 2029 (Condition 1):
All k where k = m^2
and m = = 11 or 50 mod 61:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*975^q - 1) *
     (m*975^q + 1)
   odd n:
     factor of 61
(Condition 2):
All k where k = 39*m^2
and m = = 6 or 55 mod 61:
   even n:
     factor of 61
   for odd n let k = 39*m^2
   and let n=2*q-1; factors to:
     [m*5^n*39^q - 1] *
     [m*5^n*39^q + 1]		 k = = 1 mod 2 (2)
k = = 1 mod 487 (487)		 2245 k's remaining at n=10K.

See k's at Riesel Base 975 remain.		 89658 (9978)
212902 (9938)
118482 (9923)
5996 (9923)
67152 (9919)
40622 (9917)
171994 (9911)
137722 (9906)
269398 (9878)
116258 (9862)		 k = 2500, 5184, 29584, 37636, 86436, 99856, 173056, and 191844 proven composite by condition 1.

k = 1404 proven composite by condition 2.
976 154367 7, 19, 67, 977 All k where k = m^2
and m = = 252 or 725 mod 977:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*976^q - 1) *
     (m*976^q + 1)
   odd n:
     factor of 977		 k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 13 (13)		 545 k's remaining at n=25K.

See k's at Riesel Base 976 remain.		 38699 (24985)
144333 (24947)
26970 (24629)
122124 (24450)
124878 (24390)
98298 (24390)
128694 (24366)
9797 (24082)
67917 (23966)
11255 (23958)		 k = 63504 proven composite by partial algebraic factors.
977 164 3, 163   k = = 1 mod 2 (2)
k = = 1 mod 61 (61)		 88 (300K)
116 (300K)
136 (300K)
140 (300K)
148 (300K)		 68 (83328)
14 (52076)
16 (21317)
58 (8643)
100 (6407)
128 (5420)
152 (4582)
18 (2155)
74 (1140)
30 (1107)		  
978 177 11, 89   k = = 1 mod 977 (977) 12 (400K)
94 (400K)		 164 (387920)
131 (43291)
137 (16482)
11 (14065)
175 (11722)
160 (10896)
100 (5187)
21 (4326)
33 (4242)
122 (4163)		  
979 6 5, 7   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 163 (163)		 none - proven 2 (2)  
980 110 3, 109   k = = 1 mod 11 (11)
k = = 1 mod 89 (89)		 10 (400K)
31 (400K)		 109 (383669)
7 (50877)
44 (30084)
52 (17045)
107 (13362)
26 (2958)
8 (2656)
19 (2595)
46 (1047)
97 (939)		  
982 4914 5, 17, 983   k = = 1 mod 3 (3)
k = = 1 mod 109 (109)		 71 k's remaining at n=100K.

See k's at Riesel Base 982 remain.		 4845 (98383)
1644 (91540)
4902 (88146)
4848 (87494)
1308 (85760)
2493 (80324)
2321 (77333)
2640 (70708)
2487 (68196)
1002 (65933)		  
983 14 3, 5, 13   k = = 1 mod 2 (2)
k = = 1 mod 491 (491)		 none - proven 2 (200)
12 (12)
8 (2)
10 (1)
6 (1)
4 (1)		  
984 196 5, 197 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*984^q - 1) *
     (m*984^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 983 (983) 99 (300K)
119 (300K)
191 (300K)		 18 (209436)
121 (114465)
120 (97100)
86 (74279)
81 (33591)
11 (4521)
188 (2701)
94 (1628)
164 (1622)
91 (1217)		 k = 4, 9, 49, 64, 144, and 169 proven composite by partial algebraic factors.
985 86 17, 29   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 41 (41)		 none - proven 68 (2248)
50 (1190)
36 (721)
12 (49)
84 (18)
38 (6)
30 (5)
62 (4)
2 (4)
66 (3)		  
986 8 3, 7   k = = 1 mod 5 (5)
k = = 1 mod 197 (197)		 none - proven 7 (12505)
5 (5580)
2 (22)
4 (1)
3 (1)		  
987 170 13, 19 All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*987^q - 1) *
     (m*987^q + 1)
   odd n:
     factor of 13		 k = = 1 mod 2 (2)
k = = 1 mod 17 (17)
k = = 1 mod 29 (29)		 58 (300K)
94 (300K)
118 (300K)		 96 (5035)
158 (1988)
62 (70)
162 (32)
116 (26)
80 (26)
150 (24)
148 (23)
100 (19)
144 (15)		 k = 64 proven composite by partial algebraic factors.
988 300 23, 43   k = = 1 mod 3 (3)
k = = 1 mod 7 (7)
k = = 1 mod 47 (47)		 47 (300K)
93 (300K)		 87 (17243)
186 (7537)
17 (1275)
209 (973)
63 (786)
111 (462)
45 (348)
81 (261)
68 (120)
26 (109)		  
989 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 13 (13)
k = = 1 mod 19 (19)		 none - proven 2 (26868)  
990 1684699 7, 13, 17, 61, 991   k = = 1 mod 23 (23)
k = = 1 mod 43 (43)		 24510 k's remaining at n=2.5K. To be shown later. 9 (23031)
1539090 (2500)
1050731 (2500)
782787 (2500)
1486658 (2499)
1453329 (2499)
1292748 (2499)
1171725 (2499)
1100162 (2499)
1067118 (2499)		  
991 11358 7, 13, 277   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 11 (11)		 1080 (100K)
1518 (100K)
1964 (100K)
2258 (100K)
2382 (100K)
2804 (100K)
2900 (100K)
4124 (100K)
4680 (100K)
5118 (100K)
6540 (100K)
7224 (100K)
7442 (100K)
7842 (100K)
8388 (100K)
9038 (100K)
9270 (100K)
9578 (100K)
9584 (100K)
9608 (100K)
9704 (100K)
10260 (100K)
10362 (100K)
11040 (100K)		 3942 (71722)
32 (52191)
7218 (50722)
5294 (50019)
5240 (48787)
8804 (45118)
9074 (40763)
10050 (38711)
6372 (34388)
3750 (24450)		  
992 172 3, 5, 97   k = = 1 mod 991 (991) 2 (300K)
14 (300K)
22 (300K)
74 (300K)
103 (300K)
116 (300K)
118 (300K)
134 (300K)
146 (300K)		 158 (160514)
123 (33207)
107 (20238)
73 (18311)
160 (14029)
61 (11289)
52 (10701)
8 (10604)
62 (8030)
110 (7798)		  
993 8 5, 7, 13   k = = 1 mod 2 (2)
k = = 1 mod 31 (31)		 none - proven 6 (18)
4 (3)
2 (2)		  
994 399 5, 199 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*994^q - 1) *
     (m*994^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 3 (3)
k = = 1 mod 331 (331)		 26 (300K)
69 (300K)
141 (300K)
201 (300K)		 221 (224221)
209 (154302)
329 (42108)
174 (38976)
86 (33579)
159 (17350)
111 (11617)
224 (9622)
66 (8405)
309 (3164)		 k = 9, 144, and 324 proven composite by partial algebraic factors.
995 82 3, 83   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 71 (71)		 20 (500K) 68 (465908)
38 (9718)
52 (705)
44 (478)
70 (459)
2 (282)
62 (66)
46 (49)
4 (35)
30 (17)		  
996 52840 7, 19, 43, 997 All k where k = m^2
and m = = 161 or 836 mod 997:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*996^q - 1) *
     (m*996^q + 1)
   odd n:
     factor of 997		 k = = 1 mod 5 (5)
k = = 1 mod 199 (199)		 668 k's remaining at n=25K.

See k's at Riesel Base 996 remain.		 47489 (24992)
52742 (24929)
13662 (24929)
14670 (24721)
9767 (24583)
26943 (24483)
11029 (24351)
16503 (23946)
1278 (23568)
50712 (23457)		 No k's proven composite by algebraic factors.
997 101526 7, 13, 31, 1117   k = = 1 mod 2 (2)
k = = 1 mod 499 (499)		 1027 k's remaining at n=25K.

See k's at Riesel Base 997 remain.		 23196 (24870)
56034 (24773)
78212 (24769)
48798 (24700)
38744 (24684)
33954 (24664)
14046 (24593)
43128 (24406)
72048 (24304)
60464 (24299)		  
998 38 3, 37 All k where k = m^2
and m = = 6 or 31 mod 37:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*998^q - 1) *
     (m*998^q + 1)
   odd n:
     factor of 37		 k = = 1 mod 997 (997) 5 (300K)
22 (300K)
29 (300K)
30 (300K)		 14 (16168)
4 (8427)
23 (5298)
25 (2287)
11 (834)
16 (329)
24 (104)
18 (82)
21 (29)
32 (28)		 k = 36 proven composite by partial algebraic factors.
999 3166 5, 17, 197 (Condition 1):
All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*999^q - 1) *
     (m*999^q + 1)
   odd n:
     factor of 5
(Condition 2):
All k where k = 111*m^2
and m = = 1 or 4 mod 5:
   even n:
     factor of 5
   for odd n let k = 111*m^2
   and let n=2*q-1; factors to:
     [m*3^n*111^q - 1] *
     [m*3^n*111^q + 1]		 k = = 1 mod 2 (2)
k = = 1 mod 499 (499)		 56 k's remaining at n=100K.

See k's at Riesel Base 999 remain.		 2110 (99773)
306 (84961)
1566 (80755)
2024 (72422)
940 (67413)
1326 (58041)
2942 (57389)
1014 (52980)
3008 (46983)
1084 (45128)		 k = 4, 64, 144, 324, 484, 784, 1024, 1444, 1764, 2304, and 2704 proven composite by condition 1.

k = 1776 proven composite by condition 2.
1000 12 11, 13 All k = m^3 for all n; factors to:
(m*10^n - 1) *
(m^2*100^n + m*10^n + 1)		 k = = 1 mod 3 (3)
k = = 1 mod 37 (37)		 none - proven 6 (998)
11 (3)
9 (1)
5 (1)
3 (1)
2 (1)		 k = 8 proven composite by full algebraic factors.
1001 1168 3, 167   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)		 70 (300K)
170 (300K)
994 (300K)		 242 (119418)
1024 (110819)
422 (89704)
782 (71888)
478 (30517)
754 (17605)
764 (16782)
280 (14111)
662 (12834)
292 (10169)		  
1002 237 17, 59 All k where k = m^2
and m = = 4 or 13 mod 17:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*1002^q - 1) *
     (m*1002^q + 1)
   odd n:
     factor of 17		 k = = 1 mod 7 (7)
k = = 1 mod 11 (11)
k = = 1 mod 13 (13)		 none - proven 233 (20508)
59 (12045)
208 (652)
58 (526)
186 (314)
135 (188)
25 (139)
76 (126)
139 (123)
39 (95)		 k = 16 proven composite by partial algebraic factors.
1003 396 7, 79, 607   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 167 (167)		 252 (300K)
318 (300K)		 338 (62214)
18 (13746)
128 (3526)
258 (2149)
204 (799)
284 (705)
260 (251)
206 (235)
84 (157)
336 (134)		  
1004 4 3, 5   k = = 1 mod 17 (17)
k = = 1 mod 59 (59)		 none - proven 2 (2)
3 (1)		  
1005 244960 7, 13, 97, 503 k = 17424, 85264, 179776, and 202500:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*1005^q - 1) *
     (m*1005^q + 1)
   odd n:
     covering set 7, 13, 97		 k = = 1 mod 2 (2)
k = = 1 mod 251 (251)		 2554 k's remaining at n=10K.

See k's at Riesel Base 1005 remain.		 9606 (9989)
169454 (9988)
200742 (9979)
27934 (9972)
89140 (9965)
207008 (9945)
229016 (9934)
218908 (9931)
103784 (9921)
61338 (9909)		  
1006 1538 19, 53 All k where k = m^2
and m = = 23 or 30 mod 53:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*1006^q - 1) *
     (m*1006^q + 1)
   odd n:
     factor of 53		 k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 67 (67)		 189 (300K)
417 (300K)
719 (300K)
894 (300K)
944 (300K)
987 (300K)
1158 (300K)
1293 (300K)		 552 (146815)
317 (119362)
1200 (38888)
1104 (32960)
428 (32308)
468 (11862)
584 (10029)
675 (9575)
848 (8594)
1500 (8278)		 k = 900 proven composite by partial algebraic factors.
1007 8 3, 7   k = = 1 mod 2 (2)
k = = 1 mod 503 (503)		 none - proven 2 (8)
6 (2)
4 (1)		  
1008 623563 5, 13, 61, 1009, 1399 All k where k = m^2
and m = = 469 or 540 mod 1009:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*1008^q - 1) *
     (m*1008^q + 1)
   odd n:
     factor of 1009		 k = = 1 mod 19 (19)
k = = 1 mod 53 (53)		 15807 k's remaining at n=2.5K. To be shown later. 545752 (2500)
432793 (2500)
336694 (2500)
196897 (2500)
483014 (2499)
398297 (2499)
373030 (2498)
94548 (2498)
22612 (2498)
7906 (2498)		 k = 219961 and 291600 proven composite by partial algebraic factors.
1009 1314 5, 101 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*1009^q - 1) *
     (m*1009^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 150 (300K)
186 (300K)
434 (300K)
444 (300K)
896 (300K)
924 (300K)		 662 (267747)
1112 (43447)
1292 (28491)
656 (18455)
104 (13718)
534 (12994)
704 (9236)
804 (8664)
584 (7744)
714 (5212)		 k = 144 and 324 proven composite by partial algebraic factors.
1010 338 3, 337   k = = 1 mod 1009 (1009) 9 (300K)
31 (300K)
53 (300K)
74 (300K)
80 (300K)
102 (300K)
125 (300K)
131 (300K)
144 (300K)
185 (300K)
235 (300K)
248 (300K)
256 (300K)
278 (300K)
302 (300K)
317 (300K)		 113 (242194)
137 (190444)
209 (141224)
133 (107841)
146 (75156)
47 (67718)
59 (60250)
266 (27124)
269 (25620)
267 (24439)		  
1011 208 11, 23   k = = 1 mod 2 (2)
k = = 1 mod 5 (5)
k = = 1 mod 101 (101)		 none - proven 22 (28040)
188 (18935)
98 (9020)
68 (1266)
10 (1158)
38 (894)
204 (122)
12 (119)
112 (65)
64 (37)		  
1012 946143 5, 17, 73, 1013 All k where k = m^2
and m = = 45 or 968 mod 1013:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*1012^q - 1) *
     (m*1012^q + 1)
   odd n:
     factor of 1013		 k = = 1 mod 3 (3)
k = = 1 mod 337 (337)		 16390 k's remaining at n=10K.

See k's at Riesel Base 1012 remain.		 528263 (9994)
520382 (9986)
127538 (9982)
869906 (9981)
808274 (9980)
154527 (9980)
902373 (9976)
206081 (9973)
743241 (9971)
224303 (9971)		 k = 2025 proven composite by partial algebraic factors.
1013 14 3, 13   k = = 1 mod 2 (2)
k = = 1 mod 11 (11)
k = = 1 mod 23 (23)		 none - proven 10 (2627)
2 (1116)
8 (872)
6 (2)
4 (1)		  
1014 6 5, 7 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*1014^q - 1) *
     (m*1014^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 1013 (1013) none - proven 5 (2)
3 (1)
2 (1)		 k = 4 proven composite by partial algebraic factors.
1015 11049380 127, 373, 1381   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 13 (13)		 41219 k's remaining at n=2.5K. To be shown later. 9199160 (2500)
9087084 (2500)
7789586 (2500)
6918386 (2500)
6206660 (2500)
5940420 (2500)
5604978 (2500)
5066372 (2500)
4087652 (2500)
3152264 (2500)		  
1016 112 3, 113   k = = 1 mod 5 (5)
k = = 1 mod 7 (7)
k = = 1 mod 29 (29)		 none - proven 7 (23335)
109 (4607)
4 (2715)
53 (934)
14 (392)
95 (232)
19 (159)
97 (131)
52 (105)
32 (92)		  
1017 900 7, 13, 31   k = = 1 mod 2 (2)
k = = 1 mod 127 (127)		 100 (300K)
354 (300K)
396 (300K)
522 (300K)
828 (300K)		 750 (277556)
842 (230634)
508 (199220)
542 (137766)
898 (85783)
840 (80711)
400 (66551)
268 (65254)
22 (47885)
664 (28685)		  
1018 111284 7, 13, 19, 31, 367   k = = 1 mod 3 (3)
k = = 1 mod 113 (113)		 2895 k's remaining at n=10K.

See k's at Riesel Base 1018 remain.		 63527 (9995)
63951 (9979)
60554 (9973)
104261 (9967)
105239 (9955)
87222 (9950)
74400 (9941)
67901 (9917)
73761 (9901)
103314 (9867)		  
1019 4 3, 5   k = = 1 mod 2 (2)
k = = 1 mod 509 (509)		 2 (600K) (none)  
1021 218 7, 73   k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 5 (5)
k = = 1 mod 17 (17)		 none - proven 174 (121880)
92 (487)
48 (142)
132 (64)
32 (56)
90 (48)
72 (46)
30 (22)
44 (19)
104 (18)		  
1022 10 3, 11   k = = 1 mod 1021 (1021) none - proven 4 (469)
3 (126)
9 (13)
8 (8)
5 (6)
7 (5)
2 (4)
6 (1)		  
1023 68394 13, 61, 1321   k = = 1 mod 2 (2)
k = = 1 mod 7 (7)
k = = 1 mod 73 (73)		 142 k's remaining at n=100K.

See k's at Riesel Base 1023 remain.		 48236 (97117)
6124 (92155)
43564 (90968)
61044 (90355)
62206 (83638)
25066 (83565)
25808 (83400)
44502 (79170)
492 (78615)
45958 (78246)		  
1025 20 3, 19   k = = 1 mod 2 (2) 8 (1.075M) 6 (8958)
10 (33)
18 (6)
16 (5)
14 (4)
12 (4)
2 (2)
4 (1)		  
1026 157 13, 79 All k where k = m^2
and m = = 5 or 8 mod 13:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*1026^q - 1) *
     (m*1026^q + 1)
   odd n:
     factor of 13		 k = = 1 mod 5 (5)
k = = 1 mod 41 (41)		 none - proven 113 (9283)
43 (4112)
5 (3391)
155 (1766)
79 (719)
77 (526)
137 (381)
20 (214)
14 (133)
80 (81)		 k = 25 and 64 proven composite by partial algebraic factors.
1027 21332 5, 29, 257 All k where k = m^2
and m = = 16 or 241 mod 257:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*1027^q - 1) *
     (m*1027^q + 1)
   odd n:
     factor of 257		 k = = 1 mod 2 (2)
k = = 1 mod 3 (3)
k = = 1 mod 19 (19)		 32 k's remaining at n=250K.

See k's at Riesel Base 1027 remain.		 12362 (240890)
19062 (206877)
5678 (202018)
17702 (193732)
11726 (185913)
14172 (179381)
15876 (155415)
19512 (150245)
4304 (149224)
9638 (129787)		 No k's proven composite by algebraic factors.
1028 8 3, 7   k = = 1 mod 13 (13)
k = = 1 mod 79 (79)		 none - proven 6 (3294)
5 (6)
7 (3)
2 (2)
4 (1)
3 (1)		  
1029 104 5, 103 All k where k = m^2
and m = = 2 or 3 mod 5:
   for even n let k = m^2
   and let n = 2*q; factors to:
     (m*1029^q - 1) *
     (m*1029^q + 1)
   odd n:
     factor of 5		 k = = 1 mod 2 (2)
k = = 1 mod 257 (257)		 26 (1M) 36 (55979)
98 (859)
80 (816)
92 (810)
56 (363)
32 (172)
44 (150)
90 (68)
34 (52)
96 (49)		 k = 4 and 64 proven composite by partial algebraic factors.
1030 54642 13, 53, 541, 1031   k = = 1 mod 3 (3)
k = = 1 mod 7 (7)		 125 k's remaining at n=100K.

See k's at Riesel Base 1030 remain.		 17391 (99561)
37643 (97976)
39612 (96274)
34178 (91022)
23286 (89794)
43176 (88615)
48390 (85754)
22109 (85734)
16656 (85063)
51758 (81304)		  


Original information obtained from:
Mersenneforum Prime Search Projects Conjectures 'R Us threads:
   Sierpinski/Riesel-Base 22
   Sierpinski/Riesel bases 6 to 18
   Sierpinski base 4
   Sierpinski/Riesel Base 10
   Sierpinski/Riesel-Base 23
   Even k's and the Riesel conjecture
   Even k's and the Sierpinski conjecture
Mersenneforum Prime Search Projects Sierpinski/Riesel Base 5 forum
Riesel Prime database
Riesel Problem project
Seventeen or Bust project
Top 5000 primes


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