| 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 factor: 8114899840326779533679915276470289950126585679 |
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 |
| 86243 | no | yes | no factor: 1627710365249 |
| 95369 | no | no factor: 297995890279 |
yes |
| 110503 | no | yes | no factor: 48832113344350037579071829046935480686609 |
| 117239 | no | no no factor < 2^65 (ECM t=35digits) |
yes |
| 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 |
| 15135397 | no | no no factor < 2^70 |
yes (prp) |
| 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 factor: 17973642059656480077259129 |
| 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 |
| M61 | yes (-1) | unknown no factor < 2^119.6 (2*220,000,000,000,000,000*M61) |
no factor: 1328165573307087715777 |
| M127 | yes (-1) | unknown no factor < 2^185 (2*145,000,000,000,000,000*M127) |
no factor: 886407410000361345663448535540258622490179142922169401 |