New Mersenne Conjecture

p p=2^k +/- 1
or
p=4^k +/- 3
2^p - 1 prime (2^p + 1)/3 prime
3 yes (-1) yes yes
5 yes (+1) yes yes
7 yes (-1/+3) yes yes
11 no no
factor: 23
yes
13 yes (-3) yes yes
17 yes (+1) yes yes
19 yes (+3) yes yes
23 no no
factor: 47
yes
31 yes (-1) yes yes
43 no no
factor: 431
yes
61 yes (-3) yes yes
67 yes (+3) no
factor: 193707721
no
factor: 7327657
79 no no
factor: 2687
yes
89 no yes no
factor: 179
101 no no
factor: 7432339208719
yes
107 no yes no
factor: 643
127 yes (-1) yes yes
167 no no
factor: 2349023
yes
191 no no
factor: 383
yes
199 no no
factor: 164504919713
yes
257 yes (+1) no
factor: 535006138814359
no
factor: 37239639534523
313 no no
factor: 10960009
yes
347 no no
factor: 14143189112952632419639
yes
521 no yes no
factor: 501203
607 no yes no
factor: 115331
701 no no
factor: 796337
yes
1021 yes (-3) no
factor: 40841
no
factor: 10211
1279 no yes no
factor: 706009
1709 no no
factor: 379399
yes
2203 no yes no
factor: 13219
2281 no yes no
factor: 22811
2617 no no
factor: 78511
yes
3217 no yes no
factor: 7489177
3539 no no
factor: 7079
yes
4093 yes (-3) no
factor: 2397911088359
no
factor: 3732912210059
4099 yes (+3) no
factor: 73783
no
factor: 2164273
4253 no yes no
factor: 118071787
4423 no yes no
factor: 2827782322058633
5807 no no
factor: 139369
yes
8191 yes (-1) no
factor: 338193759479
no (prp test)
no factor (P-1 B1=10^10 B2=10^12)
9689 no yes no
factor: 19379
9941 no yes no
factor: 11120148512909357034073
10501 no no
factor: 2160708549249199
yes
10691 no no
factor: 21383
yes
11213 no yes no
factor: 181122707148161338644285289935461939
11279 no no
factor: 2198029886879
yes
12391 no no
factor: 198257
yes
14479 no no
factor: 27885728233673
yes
16381 yes (-3) no
no factor < 2^64 (ECM t=45digits)
no
factor: 163811
19937 no yes no (prp test)
no factor < 2^59 (ECM t=50digits)
21701 no yes no
factor: 43403
23209 no yes no
factor: 4688219
42737 no no
factor: 542280975142237477071005102443059419300063
yes
44497 no yes no
factor: 2135857
65537 yes (+1) no
factor: 513668017883326358119
no
factor: 13091975735977
65539 yes (+3) no
factor: 3354489977369
no
factor: 58599599603
83339 no no
factor: 166679
yes (prp)
86243 no yes no
factor: 1627710365249
95369 no no
factor: 297995890279
yes (prp)
110503 no yes no
factor: 48832113344350037579071829046935480686609
117239 no no
no factor < 2^65 (ECM t=35digits)
yes (prp)
127031 no no
factor: 12194977
yes (prp)
131071 yes (-1) no
factor: 231733529
no
factor: 2883563
132049 no yes no
factor: 618913299601153
138937 no no
factor: 100068818503
yes (prp)
141079 no no
factor: 458506751
yes (prp)
216091 no yes no
factor: 10704103333093885136919332089553661899
262147 yes (+3) no
factor: 268179002471
no
factor: 4194353
267017 no no
factor: 1602103
yes (prp)
269987 no no
factor: 1940498230606195707774295455176153
yes (prp)
374321 no no
no factor < 2^65 (ECM t=35digits)
yes (prp)
524287 yes (+1) no
factor: 62914441
no (prp test)
no factor < 2^70
756839 no yes no
factor: 1640826953
859433 no yes no
factor: 1718867
986191 no no
no factor < 2^67 (ECM t=35digits)
yes (prp)
1048573 yes (-3) no
factor: 73400111
no (prp test)
no factor < 2^70
1257787 no yes no
factor: 20124593
1398269 no yes no
factor: 23609117451215727502931
2976221 no yes no
factor: 434313978089
3021377 no yes no
factor: 95264016811
4031399 no no
factor: 8062799
yes (prp)
4194301 yes (-3) no
factor: 2873888432993463577
no
factor: 14294177809
6972593 no yes no
factor: 142921867730820791335455211
13347311 no no
factor: 26694623
yes (prp)
13372531 no no
factor: 451135705817
yes (prp)
13466917 no yes no
factor: 781081187
16777213 yes (-3) no
no factor < 2^75
no
factor: 68470872139190782171
20996011 no yes no
factor: 50965926368055564259063193
24036583 no yes no
factor: 11681779339
25964951 no yes no
factor: 155789707
30402457 no yes no (prp test)
no factor < 2^70 (ECM t=25digits)
32582657 no yes no
factor: 13526662966442476828963
37156667 no yes no
factor: 297253337
42643801 no yes no
factor: 405661842777846034141594389769
43112609 no yes no
factor: 86225219
57885161 no yes no
factor: 7061989643
74207281 no yes no (prp test)
no factor < 2^79 (ECM t=25digits)
77232917 no yes no
factor: 3460697185562027
82589933 no yes no (prp test)
no factor < 2^80
268435459 yes (+3) no (prp test)
no factor < 2^83
no
factor: 414099276471761
1073741827 yes (+3) no
factor: 16084529043983099051873383
unknown
no factor < 2^84
2147483647 yes (-1) no
factor: 295257526626031
unknown
no factor < 2^86






Updated 2019-07-13