Generalized repunit probable primes
In Chris Caldwell's sense, a legal generalized repunit prime is a prime number of the form Φp(b) = (bp-1)/(b-1) such that 3 ≤ b ≤ 5p, b ≠ 10, p prime.
Andy Steward maintained a list of all known legal generalized repunit primes; unfortunately, the project is now suspended and he is not accepting submissions any more.
Additionally, Henri and Renaud Lifchitz maintain a list of all known probable primes with more than 10,000 digits.
The list below shows all known (to me) probable primes not listed in the above mentioned sites. Feel free to contribute with new probable primes.
Show numbers with [ ≤ 4300 | ≤ 5400 | ≤ 6700 | ≤ 7700 | ≤ 8500 | > 8500 ] digits
| Φp(b) | Digits | Discoverer | Date of discovery | Notes |
| Φ2381(3718) | 8498 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2557(2104) | 8494 | Bernardo Boncompagni | Jan 9, 2010 | |
| Φ2243(6141) | 8494 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2593(1890) | 8493 | Bernardo Boncompagni | Jan 9, 2010 | |
| Φ2111(10358) | 8473 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2411(3272) | 8471 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2129(9486) | 8464 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2383(3567) | 8462 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ3331(347) | 8460 | Bernardo Boncompagni | Jan 24, 2010 | |
| Φ2203(6934) | 8458 | Bernardo Boncompagni | Jan 5, 2010 | |
| Φ3719(188) | 8456 | Bernardo Boncompagni | Feb 11, 2010 | |
| Φ2377(3612) | 8454 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2269(5311) | 8449 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2411(3197) | 8447 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2729(1247) | 8446 | Bernardo Boncompagni | Jan 13, 2010 | |
| Φ2161(8126) | 8446 | Bernardo Boncompagni | Jan 5, 2010 | |
| Φ2113(9888) | 8438 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2179(7484) | 8438 | Bernardo Boncompagni | Jan 5, 2010 | |
| Φ2309(4523) | 8437 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2131(9140) | 8437 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2153(8308) | 8435 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2251(5607) | 8435 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2267(5271) | 8434 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2131(9086) | 8432 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2111(9906) | 8432 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ3469(270) | 8432 | Bernardo Boncompagni | Jan 28, 2010 | |
| Φ2153(8271) | 8431 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2557(1982) | 8428 | Bernardo Boncompagni | Jan 9, 2010 | |
| Φ2351(3840) | 8424 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2699(1313) | 8414 | Bernardo Boncompagni | Jan 12, 2010 | |
| Φ2129(8980) | 8413 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2131(8879) | 8411 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ3373(312) | 8411 | Bernardo Boncompagni | Jan 26, 2010 | |
| Φ2099(10167) | 8408 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2153(8062) | 8407 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2153(8055) | 8406 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2593(1746) | 8404 | Bernardo Boncompagni | Jan 9, 2010 | |
| Φ3469(265) | 8404 | Bernardo Boncompagni | Jan 28, 2010 | |
| Φ2251(5414) | 8401 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ3463(267) | 8401 | Bernardo Boncompagni | Jan 27, 2010 | |
| Φ2111(9563) | 8400 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2579(1810) | 8399 | Bernardo Boncompagni | Jan 9, 2010 | |
| Φ2417(2987) | 8397 | Bernardo Boncompagni | Jan 8, 2010 | |
| Φ2239(5616) | 8392 | Bernardo Boncompagni | Jan 5, 2010 | |
| Φ2269(4988) | 8387 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2311(4261) | 8385 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2333(3918) | 8380 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2309(4265) | 8378 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ3109(495) | 8375 | Bernardo Boncompagni | Jan 19, 2010 | |
| Φ3449(268) | 8373 | Bernardo Boncompagni | Jan 27, 2010 | |
| Φ2087(10298) | 8371 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2347(3691) | 8369 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2381(3267) | 8364 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2087(10170) | 8360 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2251(5173) | 8356 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2371(3338) | 8351 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2087(10045) | 8349 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2131(8274) | 8345 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2311(4064) | 8337 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2467(2400) | 8336 | Bernardo Boncompagni | Jan 8, 2010 | |
| Φ2309(4088) | 8336 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2113(8807) | 8332 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2087(9861) | 8332 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2777(999) | 8327 | Bernardo Boncompagni | Jan 14, 2010 | |
| Φ2161(7120) | 8322 | Bernardo Boncompagni | Jan 5, 2010 | |
| Φ3467(251) | 8318 | Bernardo Boncompagni | Jan 27, 2010 | |
| Φ2309(4002) | 8315 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2311(3974) | 8315 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2591(1614) | 8309 | Bernardo Boncompagni | Jan 9, 2010 | |
| Φ2083(9740) | 8305 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2287(4272) | 8300 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2081(9748) | 8297 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2617(1482) | 8295 | Bernardo Boncompagni | Jan 10, 2010 | |
| Φ2081(9699) | 8293 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2833(840) | 8282 | Bernardo Boncompagni | Jan 14, 2010 | |
| Φ2207(5608) | 8270 | Bernardo Boncompagni | Jan 5, 2010 | |
| Φ2141(7274) | 8265 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2293(4028) | 8263 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2089(9026) | 8260 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2143(7168) | 8259 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2423(2557) | 8254 | Bernardo Boncompagni | Jan 8, 2010 | |
| Φ2389(2844) | 8248 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2063(9953) | 8244 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2333(3412) | 8239 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2539(1756) | 8235 | Bernardo Boncompagni | Jan 8, 2010 | |
| Φ2659(1250) | 8232 | Bernardo Boncompagni | Jan 10, 2010 | |
| Φ2131(7285) | 8227 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2311(3636) | 8226 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2531(1772) | 8219 | Bernardo Boncompagni | Jan 8, 2010 | |
| Φ2137(6913) | 8202 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2267(4139) | 8196 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2437(2306) | 8192 | Bernardo Boncompagni | Jan 8, 2010 | |
| Φ2137(6841) | 8192 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ3821(139) | 8187 | Bernardo Boncompagni | Feb 14, 2010 | |
| Φ2441(2259) | 8184 | Bernardo Boncompagni | Jan 8, 2010 | |
| Φ2141(6639) | 8180 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2243(4429) | 8176 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2273(3905) | 8161 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2161(5992) | 8160 | Bernardo Boncompagni | Jan 5, 2010 | |
| Φ3517(208) | 8151 | Bernardo Boncompagni | Jan 29, 2010 | |
| Φ2347(2964) | 8146 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2087(8004) | 8143 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2287(3612) | 8134 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2089(7824) | 8130 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2141(6286) | 8129 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2089(7809) | 8128 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2113(7018) | 8124 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ3217(335) | 8121 | Bernardo Boncompagni | Jan 21, 2010 | |
| Φ2179(5307) | 8113 | Bernardo Boncompagni | Jan 5, 2010 | |
| Φ2111(6979) | 8111 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2297(3398) | 8108 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2281(3594) | 8107 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2243(4105) | 8102 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2087(7588) | 8094 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2221(4425) | 8094 | Bernardo Boncompagni | Jan 5, 2010 | |
| Φ2063(8374) | 8090 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2909(600) | 8079 | Bernardo Boncompagni | Jan 15, 2010 | |
| Φ2027(9691) | 8077 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2029(9602) | 8077 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2129(6198) | 8070 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2039(9047) | 8064 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ3049(440) | 8058 | Bernardo Boncompagni | Jan 18, 2010 | |
| Φ2137(5921) | 8058 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2111(6584) | 8058 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2083(7412) | 8058 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2281(3411) | 8055 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2111(6548) | 8052 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2243(3900) | 8052 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2593(1275) | 8050 | Bernardo Boncompagni | Jan 9, 2010 | |
| Φ2473(1792) | 8043 | Bernardo Boncompagni | Jan 8, 2010 | |
| Φ2179(4927) | 8043 | Bernardo Boncompagni | Jan 5, 2010 | |
| Φ2389(2331) | 8042 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2377(2389) | 8027 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2087(7013) | 8023 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2381(2346) | 8022 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2357(2538) | 8021 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2267(3462) | 8021 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2027(9004) | 8012 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ3433(215) | 8005 | Bernardo Boncompagni | Jan 26, 2010 | |
| Φ2017(9337) | 8004 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2371(2380) | 8003 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2011(9573) | 8002 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2203(4303) | 8002 | Bernardo Boncompagni | Jan 5, 2010 | |
| Φ2029(8799) | 8000 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2137(5544) | 7997 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2153(5173) | 7992 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2113(6073) | 7991 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2347(2535) | 7986 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2027(8708) | 7983 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2141(5355) | 7980 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2371(2318) | 7976 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2137(5410) | 7975 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2081(6804) | 7973 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ1997(9830) | 7970 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2269(3257) | 7968 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ1993(9956) | 7965 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2113(5897) | 7964 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2671(957) | 7960 | Bernardo Boncompagni | Jan 12, 2010 | |
| Φ2713(857) | 7955 | Bernardo Boncompagni | Jan 12, 2010 | |
| Φ2081(6666) | 7954 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2029(8324) | 7951 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ3319(249) | 7951 | Bernardo Boncompagni | Jan 24, 2010 | |
| Φ3331(244) | 7951 | Bernardo Boncompagni | Jan 24, 2010 | |
| Φ1997(9551) | 7945 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ3221(292) | 7939 | Bernardo Boncompagni | Jan 21, 2010 | |
| Φ2063(7055) | 7936 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ3803(122) | 7933 | Bernardo Boncompagni | Feb 13, 2010 | |
| Φ2081(6511) | 7933 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ3821(119) | 7929 | Bernardo Boncompagni | Feb 14, 2010 | |
| Φ2143(4956) | 7915 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2099(5873) | 7908 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2659(939) | 7902 | Bernardo Boncompagni | Jan 10, 2010 | |
| Φ2309(2653) | 7902 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2591(1121) | 7899 | Bernardo Boncompagni | Jan 9, 2010 | |
| Φ1997(9056) | 7899 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2677(894) | 7898 | Bernardo Boncompagni | Jan 12, 2010 | |
| Φ2207(3803) | 7898 | Bernardo Boncompagni | Jan 5, 2010 | |
| Φ2131(5044) | 7887 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2087(6034) | 7887 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2293(2753) | 7885 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2221(3558) | 7884 | Bernardo Boncompagni | Jan 5, 2010 | |
| Φ2341(2337) | 7883 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ2179(4152) | 7881 | Bernardo Boncompagni | Jan 5, 2010 | |
| Φ2011(8177) | 7865 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ1997(8667) | 7860 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2083(5899) | 7851 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2267(2908) | 7849 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2089(5689) | 7841 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2069(6156) | 7837 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2447(1598) | 7836 | Bernardo Boncompagni | Jan 8, 2010 | |
| Φ2887(517) | 7832 | Bernardo Boncompagni | Jan 15, 2010 | |
| Φ1979(9069) | 7829 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2843(567) | 7826 | Bernardo Boncompagni | Jan 14, 2010 | |
| Φ1997(8318) | 7825 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2243(3087) | 7824 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2017(7591) | 7823 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2687(816) | 7821 | Bernardo Boncompagni | Jan 12, 2010 | |
| Φ2393(1855) | 7818 | Bernardo Boncompagni | Jan 7, 2010 | |
| Φ1999(8178) | 7818 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2281(2682) | 7817 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ2011(7724) | 7815 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2087(5486) | 7801 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ1993(8224) | 7799 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2417(1688) | 7798 | Bernardo Boncompagni | Jan 8, 2010 | |
| Φ2003(7830) | 7796 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2129(4590) | 7793 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ1999(7869) | 7785 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2029(6891) | 7785 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2617(940) | 7778 | Bernardo Boncompagni | Jan 10, 2010 | |
| Φ2731(704) | 7774 | Bernardo Boncompagni | Jan 13, 2010 | |
| Φ1949(9744) | 7771 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ1951(9650) | 7770 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2243(2909) | 7766 | Bernardo Boncompagni | Jan 6, 2010 | |
| Φ1997(7690) | 7757 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2543(1122) | 7754 | Bernardo Boncompagni | Jan 9, 2010 | |
| Φ1951(9453) | 7753 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2153(3991) | 7750 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2069(5581) | 7749 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ3187(270) | 7747 | Bernardo Boncompagni | Jan 20, 2010 | |
| Φ2089(5121) | 7746 | Bernardo Boncompagni | Jan 4, 2010 | |
| Φ2087(5141) | 7742 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2789(596) | 7738 | Bernardo Boncompagni | Jan 14, 2010 | |
| Φ2179(3552) | 7733 | Bernardo Boncompagni | Jan 5, 2010 | |
| Φ1951(9166) | 7727 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2549(1076) | 7726 | Bernardo Boncompagni | Jan 9, 2010 | |
| Φ2003(7162) | 7718 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ1949(9094) | 7712 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ1987(7631) | 7711 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2441(1442) | 7708 | Bernardo Boncompagni | Jan 8, 2010 | |
| Φ2437(1458) | 7707 | Bernardo Boncompagni | Jan 8, 2010 | |
| Φ2053(5694) | 7707 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ2011(6813) | 7706 | Bernardo Boncompagni | Jan 3, 2010 | |
| Φ3191(260) | 7704 | Bernardo Boncompagni | Jan 20, 2010 | |
This page was last updated on October 27, 2011.