What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove
or disprove its primality.
Here are some criterions that can be used to recognize these numbers
:
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N
should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3.
N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
7501 | 25592^10119+10119^25592 | 102500 | Hans Havermann | 02/2019 |
7502 | (5*10^102492-23)/9 | 102492 | Serge Batalov | 11/2022 |
7503 | 7^121268+82 | 102484 | Lelio R Paula | 10/2016 |
7504 | (6883*2^340443-1)/162401 | 102483 | Lelio R Paula | 05/2015 |
7505 | 2^340434-5955 | 102481 | Lelio R Paula | 11/2016 |
7506 | (7*10^102480-19)/3 | 102481 | Robert Price | 10/2020 |
7507 | (2^340381+47)/7 | 102465 | Lelio R Paula | 12/2013 |
7508 | 111^50095+110 | 102461 | Norbert Schneider | 04/2017 |
7509 | 180^45427-45427^180 | 102451 | Norman Luhn | 09/2024 |
7510 | 2^340291-20301 | 102438 | Enzo Doria | 06/2013 |
7511 | 12^94915+89 | 102431 | Lelio R Paula | 10/2016 |
7512 | (106*10^102422+17)/3 | 102424 | Robert Price | 04/2021 |
7513 | 24466^15349+15349^24466 | 102417 | Hans Havermann | 03/2019 |
7514 | 2^340212+111546435 | 102415 | Paul Bourdelais | 10/2021 |
7515 | 2^340208-20373 | 102413 | Enzo Doria | 06/2013 |
7516 | 6^131598-17273 | 102404 | Enzo Doria | 02/2013 |
7517 | (2^340132+1182)/2 | 102390 | Stefano Morozzi | 09/2020 |
7518 | (2^340133+1166)/2 | 102390 | Stefano Morozzi | 09/2020 |
7519 | 2^340115-21181 | 102385 | Enzo Doria | 06/2013 |
7520 | (55459*2^340090+1)/1591 | 102379 | Lelio R Paula | 07/2014 |
7521 | (2^340064+3630)/2 | 102370 | Stefano Morozzi | 09/2020 |
7522 | 9348*31^68638+13 | 102369 | Eric Chen | 04/2024 |
7523 | 89^52511-88^52511 | 102365 | Robert Price | 06/2015 |
7524 | 3^214539-112756 | 102362 | Enzo Doria | 07/2014 |
7525 | 23159^23450-23450^23159 | 102353 | Norbert Schneider | 12/2019 |
7526 | 2^340000-19877 | 102351 | Enzo Doria | 06/2013 |
7527 | 2^339990-114845 | 102348 | Enzo Doria | 05/2015 |
7528 | 311^41058-41058^311 | 102348 | Norman Luhn | 09/2024 |
7529 | (3^214516-2)/51383 | 102346 | Lelio R Paula | 12/2013 |
7530 | 20^78661-99 | 102341 | Lelio R Paula | 09/2016 |
7532 | 2^339951-19585 | 102336 | Enzo Doria | 05/2013 |
7531 | (17*10^102335-167)/3 | 102336 | Robert Price | 05/2022 |
7533 | (13*2^339943+1)/45 | 102333 | Lelio R Paula | 12/2013 |
7534 | (236282#+121441)/(121441*25499429) | 102332 | Makoto Morimoto | 08/2020 |
7535 | 5*10^102323-91 | 102324 | Robert Price | 03/2021 |
7537 | 2^339889+29327 | 102317 | Yves Minet | 06/2010 |
7536 | (167*10^102315-17)/3 | 102317 | Robert Price | 03/2020 |
7538 | 26348^7641+7641^26348 | 102314 | Hans Havermann | 03/2019 |
7539 | Phi(239414,10)/6333218543 | 102303 | Makoto Kamada | 08/2019 |
7540 | 2^339834-109493 | 102301 | Enzo Doria | 04/2014 |
7541 | (16*10^102299-19)/3 | 102300 | Robert Price | 02/2019 |
7542 | (11^98221-5^98221)/6 | 102286 | Robert Price | 01/2013 |
7543 | 3^214365+1820 | 102279 | Lelio R Paula | 10/2016 |
7544 | 31978^1579+1579^31978 | 102278 | Hans Havermann | 03/2019 |
7545 | (89*10^102262-467)/9 | 102263 | Robert Price | 04/2022 |
7546 | (11*2^339705-1)/183 | 102261 | Lelio R Paula | 03/2014 |
7547 | 2^339694-16995 | 102259 | Lelio R Paula | 09/2016 |
7548 | (56*10^102255+691)/9 | 102256 | Robert Price | 05/2019 |
7549 | 122^49008+121 | 102249 | Norbert Schneider | 10/2018 |
7550 | (2^339652+3178)/2 | 102246 | Stefano Morozzi | 09/2020 |
7551 | 7^120985-38 | 102245 | Lelio R Paula | 10/2016 |
7552 | 10^102244+122961 | 102245 | Patrick De Geest | 12/2016 |
7553 | 10^102244-27 | 102244 | Lelio R Paula | 09/2016 |
7554 | 7^120982-62 | 102242 | Lelio R Paula | 10/2016 |
7555 | (2^339640+2670)/2 | 102242 | Stefano Morozzi | 09/2020 |
7556 | 4*6^131382-5 | 102236 | Lelio R Paula | 11/2014 |
7557 | (2^339607+3290)/2 | 102232 | Stefano Morozzi | 02/2021 |
7558 | 2^339586-1091 | 102226 | Yves Minet | 11/2012 |
7559 | 11^98161-3072000 | 102225 | Enzo Doria | 12/2012 |
7560 | 9*7^120961-4 | 102225 | Lelio R Paula | 11/2014 |
7561 | 5*3^214250+2 | 102224 | Serge Batalov | 10/2010 |
7562 | 12^94713-59 | 102213 | Lelio R Paula | 10/2016 |
7563 | 12^94705+89 | 102204 | Lelio R Paula | 10/2016 |
7564 | 2^339407-177 | 102172 | Lelio R Paula | 08/2011 |
7565 | 4*10^102163-57 | 102164 | Robert Price | 10/2018 |
7566 | 2^339355+65 | 102157 | Lelio R Paula | 07/2011 |
7567 | (28*10^102142-31)/3 | 102143 | Robert Price | 12/2019 |
7568 | (2^339323+47)/880715 | 102141 | Lelio R Paula | 12/2013 |
7569 | (2^339268+1758)/2 | 102130 | Stefano Morozzi | 09/2020 |
7570 | U(610865) | 102130 | Serge Batalov | 07/2024 |
7571 | s(178551) | 102122 | Robert Price | 05/2020 |
7572 | (797*10^102112-23)/9 | 102114 | Robert Price | 01/2022 |
7573 | (5*10^102107+7)/3 | 102108 | Tyler Busby | 02/2023 |
7574 | (2^339175+2790)/2 | 102102 | Stefano Morozzi | 02/2021 |
7576 | 2^339168+21 | 102100 | Lelio R Paula | 07/2011 |
7577 | 2^339167-108807 | 102100 | Enzo Doria | 03/2014 |
7575 | (2^339169+42)/2 | 102100 | Stefano Morozzi | 09/2020 |
7578 | 2^339156+163 | 102097 | Lelio R Paula | 08/2011 |
7579 | (2^339149+746)/2 | 102094 | Stefano Morozzi | 09/2020 |
7580 | (25*10^102076-67)/3 | 102077 | Robert Price | 06/2019 |
7581 | 2^339081-4543 | 102074 | Yves Minet | 03/2019 |
7582 | (3435^28867-1)/3434 | 102069 | Serge Batalov | 06/2022 |
7583 | 2*10^102062+77 | 102063 | Robert Price | 08/2020 |
7585 | 24327^15668+15668^24327 | 102053 | Hans Havermann | 02/2019 |
7584 | 10^102052+66793 | 102053 | Patrick De Geest | 09/2022 |
7586 | 10^102052-7000001 | 102052 | Robert Price | 06/2021 |
7587 | 10^102052-618623 | 102052 | Patrick De Geest | 09/2022 |
7588 | 2^339000-175635 | 102050 | Stefano Morozzi | 12/2021 |
7589 | 2^339000-151667 | 102050 | Stefano Morozzi | 12/2021 |
7590 | 2^338999+79289 | 102049 | Stefano Morozzi | 01/2022 |
7591 | 2^338998-63897 | 102049 | Stefano Morozzi | 12/2022 |
7592 | 2^338997+99659 | 102049 | Stefano Morozzi | 02/2023 |
7593 | 2^338994+188757 | 102048 | Stefano Morozzi | 05/2022 |
7594 | 2^338995+70785 | 102048 | Stefano Morozzi | 11/2022 |
7595 | 2^338994-12183 | 102048 | Stefano Morozzi | 12/2022 |
7596 | 2^338992+181591 | 102047 | Stefano Morozzi | 01/2022 |
7597 | 2^338992+136171 | 102047 | Stefano Morozzi | 03/2022 |
7598 | 2^338991-109435 | 102047 | Stefano Morozzi | 04/2022 |
7599 | 2^338991+193611 | 102047 | Stefano Morozzi | 09/2022 |
7600 | 2^338988-134619 | 102046 | Stefano Morozzi | 04/2022 |
7601 | 2^338987-62557 | 102046 | Stefano Morozzi | 12/2022 |
7602 | 2^338986-60141 | 102045 | Stefano Morozzi | 06/2022 |
7603 | 2^338986+98209 | 102045 | Stefano Morozzi | 11/2022 |
7604 | 2^338981+106391 | 102044 | Stefano Morozzi | 01/2022 |
7605 | 2^338982+34069 | 102044 | Stefano Morozzi | 03/2022 |
7606 | 2^338982-58781 | 102044 | Stefano Morozzi | 04/2022 |
7607 | 2^338980+70833 | 102044 | Stefano Morozzi | 11/2022 |
7608 | 2^338982-92111 | 102044 | Stefano Morozzi | 02/2023 |
7609 | 2^338977+83007 | 102043 | Stefano Morozzi | 02/2022 |
7610 | 2^338979-83601 | 102043 | Stefano Morozzi | 04/2022 |
7611 | 2^338975+28355 | 102042 | Stefano Morozzi | 01/2022 |
7612 | 2^338973+134619 | 102042 | Stefano Morozzi | 03/2022 |
7613 | 2^338974+183777 | 102042 | Stefano Morozzi | 03/2022 |
7614 | 2^338975+69293 | 102042 | Stefano Morozzi | 09/2022 |
7622 | 25080^11711+11711^25080 | 102041 | Hans Havermann | 02/2019 |
7615 | 2^338972+152343 | 102041 | Stefano Morozzi | 12/2021 |
7616 | 2^338972-180623 | 102041 | Stefano Morozzi | 02/2022 |
7617 | 2^338972+84441 | 102041 | Stefano Morozzi | 03/2022 |
7618 | 2^338971+64875 | 102041 | Stefano Morozzi | 05/2022 |
7619 | 2^338971+44985 | 102041 | Stefano Morozzi | 11/2022 |
7620 | 2^338971+145065 | 102041 | Stefano Morozzi | 11/2022 |
7621 | 2^338972-16635 | 102041 | Stefano Morozzi | 01/2023 |
7623 | 2^338968+53461 | 102040 | Stefano Morozzi | 01/2022 |
7624 | 2^338969+160175 | 102040 | Stefano Morozzi | 03/2022 |
7625 | 2^338967+13409 | 102040 | Stefano Morozzi | 04/2022 |
7626 | 2^338969+67635 | 102040 | Stefano Morozzi | 09/2022 |
7627 | 2^338969-15913 | 102040 | Stefano Morozzi | 01/2023 |
7628 | 2^338963-127455 | 102039 | Stefano Morozzi | 12/2021 |
7629 | 2^338963+132195 | 102039 | Stefano Morozzi | 02/2022 |
7630 | 2^338966+137919 | 102039 | Stefano Morozzi | 04/2022 |
7631 | 2^338963-87529 | 102039 | Stefano Morozzi | 12/2022 |
7632 | 2^338963-116859 | 102039 | Stefano Morozzi | 02/2023 |
7639 | (2^338982-7)/1754517 | 102038 | Lelio R Paula | 12/2013 |
7633 | 2^338960+53935 | 102038 | Stefano Morozzi | 01/2022 |
7634 | 2^338962+83157 | 102038 | Stefano Morozzi | 02/2022 |
7635 | 2^338961+12341 | 102038 | Stefano Morozzi | 04/2022 |
7636 | 2^338960+63933 | 102038 | Stefano Morozzi | 05/2022 |
7637 | 2^338960+170791 | 102038 | Stefano Morozzi | 11/2022 |
7638 | 2^338962+21679 | 102038 | Stefano Morozzi | 11/2022 |
7640 | 2^338959-30919 | 102037 | Stefano Morozzi | 02/2022 |
7641 | 2^338959+164769 | 102037 | Stefano Morozzi | 05/2022 |
7642 | 2^338958-43161 | 102037 | Stefano Morozzi | 02/2023 |
7643 | 2^338954-177003 | 102036 | Stefano Morozzi | 12/2021 |
7644 | 2^338954+154207 | 102036 | Stefano Morozzi | 01/2022 |
7645 | 2^338956+182493 | 102036 | Stefano Morozzi | 02/2022 |
7646 | 2^338954+162715 | 102036 | Stefano Morozzi | 04/2022 |
7647 | 2^338955-158241 | 102036 | Stefano Morozzi | 04/2022 |
7648 | 2^338956-33395 | 102036 | Stefano Morozzi | 04/2022 |
7649 | 2^338954+190915 | 102036 | Stefano Morozzi | 06/2022 |
7650 | 2^338955+41643 | 102036 | Stefano Morozzi | 09/2022 |
7651 | 2^338954+194427 | 102036 | Stefano Morozzi | 09/2022 |
7652 | 2^338956+117967 | 102036 | Stefano Morozzi | 09/2022 |
7653 | 2^338956+195495 | 102036 | Stefano Morozzi | 11/2022 |
7654 | 2^338954-186371 | 102036 | Stefano Morozzi | 12/2022 |
7655 | 2^338950+175077 | 102035 | Stefano Morozzi | 12/2021 |
7656 | 2^338951-51687 | 102035 | Stefano Morozzi | 12/2021 |
7657 | 2^338951+66123 | 102035 | Stefano Morozzi | 06/2022 |
7658 | 2^338950+19317 | 102035 | Stefano Morozzi | 09/2022 |
7659 | 2^338951-161479 | 102035 | Stefano Morozzi | 12/2022 |
7660 | 2^338950-66335 | 102035 | Stefano Morozzi | 01/2023 |
7661 | 2^338951-41611 | 102035 | Stefano Morozzi | 02/2023 |
7662 | 2^338952-142887 | 102035 | Stefano Morozzi | 02/2023 |
7663 | 2^338949+85449 | 102034 | Stefano Morozzi | 03/2022 |
7664 | 2^338949-184585 | 102034 | Stefano Morozzi | 04/2022 |
7665 | 2^338949-88555 | 102034 | Stefano Morozzi | 12/2022 |
7666 | 2^338948+49393 | 102034 | Stefano Morozzi | 02/2023 |
7667 | 2^338949-17601 | 102034 | Stefano Morozzi | 02/2023 |
7668 | 2^338943+127103 | 102033 | Stefano Morozzi | 12/2021 |
7669 | 2^338944-84003 | 102033 | Stefano Morozzi | 04/2022 |
7670 | 2^338945+138605 | 102033 | Stefano Morozzi | 05/2022 |
7671 | 2^338943+95133 | 102033 | Stefano Morozzi | 11/2022 |
7672 | 2^338943+147435 | 102033 | Stefano Morozzi | 11/2022 |
7673 | 2^338943-116067 | 102033 | Stefano Morozzi | 01/2023 |
7674 | 2^338940+78607 | 102032 | Stefano Morozzi | 01/2022 |
7675 | 2^338942-86687 | 102032 | Stefano Morozzi | 12/2022 |
7676 | 2^338939+151569 | 102031 | Stefano Morozzi | 12/2021 |
7677 | 2^338938+183975 | 102031 | Stefano Morozzi | 03/2022 |
7678 | 2^338937-33429 | 102031 | Stefano Morozzi | 04/2022 |
7679 | 2^338939-183259 | 102031 | Stefano Morozzi | 04/2022 |
7680 | 2^338937-139951 | 102031 | Stefano Morozzi | 01/2023 |
7681 | 2^338938-40151 | 102031 | Stefano Morozzi | 01/2023 |
7682 | 2^338938+74449 | 102031 | Stefano Morozzi | 02/2023 |
7683 | 2^338935+179999 | 102030 | Stefano Morozzi | 01/2022 |
7684 | 2^338936+84147 | 102030 | Stefano Morozzi | 03/2022 |
7685 | 2^338935+171261 | 102030 | Stefano Morozzi | 11/2022 |
7686 | 2^338936-41355 | 102030 | Stefano Morozzi | 01/2023 |
7687 | 2^338931+2349 | 102029 | Stefano Morozzi | 12/2021 |
7688 | 2^338933+79935 | 102029 | Stefano Morozzi | 01/2022 |
7689 | 2^338930+33819 | 102029 | Stefano Morozzi | 03/2022 |
7690 | 2^338931-31555 | 102029 | Stefano Morozzi | 03/2022 |
7691 | 2^338933+64169 | 102029 | Stefano Morozzi | 05/2022 |
7692 | 2^338932-184965 | 102029 | Stefano Morozzi | 06/2022 |
7693 | 2^338932+66943 | 102029 | Stefano Morozzi | 09/2022 |
7694 | 2^338932+92995 | 102029 | Stefano Morozzi | 09/2022 |
7695 | 2^338931+97001 | 102029 | Stefano Morozzi | 11/2022 |
7696 | 2^338932-165453 | 102029 | Stefano Morozzi | 01/2023 |
7697 | 2^338933-40899 | 102029 | Stefano Morozzi | 01/2023 |
7698 | 2^338928+2367 | 102028 | Stefano Morozzi | 12/2021 |
7699 | 2^338927+52779 | 102028 | Stefano Morozzi | 01/2022 |
7700 | 2^338927-79539 | 102028 | Stefano Morozzi | 02/2022 |
7701 | 2^338929+60819 | 102028 | Stefano Morozzi | 03/2022 |
7702 | 2^338928-156959 | 102028 | Stefano Morozzi | 03/2022 |
7703 | 2^338927-63919 | 102028 | Stefano Morozzi | 12/2022 |
7704 | 2^338925+106631 | 102027 | Stefano Morozzi | 01/2022 |
7705 | 2^338926+80235 | 102027 | Stefano Morozzi | 01/2022 |
7706 | 2^338926+41607 | 102027 | Stefano Morozzi | 09/2022 |
7707 | 2^338925+195435 | 102027 | Stefano Morozzi | 11/2022 |
7708 | 2^338924-92885 | 102027 | Stefano Morozzi | 02/2023 |
7709 | 2^338922-27291 | 102026 | Stefano Morozzi | 12/2021 |
7710 | 2^338919-103849 | 102025 | Stefano Morozzi | 01/2022 |
7711 | 2^338919+130221 | 102025 | Stefano Morozzi | 01/2022 |
7712 | 2^338918-91967 | 102025 | Stefano Morozzi | 02/2023 |
7713 | 2^338917+561057 | 102025 | Boyan Hu | 03/2024 |
7714 | 2^338914-79121 | 102024 | Stefano Morozzi | 02/2022 |
7715 | 2^338916+134047 | 102024 | Stefano Morozzi | 03/2022 |
7716 | 2^338914-11315 | 102024 | Stefano Morozzi | 12/2022 |
7717 | 2^338910+81027 | 102023 | Stefano Morozzi | 01/2022 |
7718 | 2^338912+179821 | 102023 | Stefano Morozzi | 01/2022 |
7719 | 2^338909+100769 | 102022 | Stefano Morozzi | 11/2021 |
7720 | 2^338908-100839 | 102022 | Stefano Morozzi | 12/2021 |
7721 | 2^338909-25951 | 102022 | Stefano Morozzi | 12/2021 |
7722 | 2^338909+66845 | 102022 | Stefano Morozzi | 09/2022 |
7723 | 2^338907+73509 | 102022 | Stefano Morozzi | 11/2022 |
7724 | 2^338906-25823 | 102021 | Stefano Morozzi | 12/2021 |
7725 | 2^338904+75951 | 102021 | Stefano Morozzi | 12/2021 |
7726 | 2^338906+6685 | 102021 | Stefano Morozzi | 01/2022 |
7727 | 2^338905+160365 | 102021 | Stefano Morozzi | 03/2022 |
7728 | 2^338906+92617 | 102021 | Stefano Morozzi | 09/2022 |
7729 | 2^338904+47065 | 102021 | Stefano Morozzi | 11/2022 |
7730 | 2^338905+70427 | 102021 | Stefano Morozzi | 11/2022 |
7731 | 2^338905-163975 | 102021 | Stefano Morozzi | 12/2022 |
7732 | 2^338903+4155 | 102020 | Stefano Morozzi | 01/2022 |
7733 | 2^338901+55571 | 102020 | Stefano Morozzi | 01/2022 |
7734 | 2^338901-55479 | 102020 | Stefano Morozzi | 02/2022 |
7735 | 2^338903+33555 | 102020 | Stefano Morozzi | 03/2022 |
7736 | 2^338901+39777 | 102020 | Stefano Morozzi | 05/2022 |
7737 | 2^338903+165981 | 102020 | Stefano Morozzi | 06/2022 |
7738 | 2^338901-34863 | 102020 | Stefano Morozzi | 06/2022 |
7739 | 2^338899-150051 | 102019 | Stefano Morozzi | 12/2021 |
7740 | 2^338899+125951 | 102019 | Stefano Morozzi | 12/2021 |
7741 | 2^338898+179623 | 102019 | Stefano Morozzi | 01/2022 |
7742 | 2^338899-154467 | 102019 | Stefano Morozzi | 02/2022 |
7743 | 2^338898-60753 | 102019 | Stefano Morozzi | 06/2022 |
7744 | 2^338898+68635 | 102019 | Stefano Morozzi | 09/2022 |
7745 | 2^338897-85963 | 102019 | Stefano Morozzi | 12/2022 |
7746 | 2^338898+174129 | 102019 | Stefano Morozzi | 02/2023 |
7747 | 2^338894-133295 | 102018 | Stefano Morozzi | 04/2022 |
7748 | 2^338894+165573 | 102018 | Stefano Morozzi | 06/2022 |
7749 | 2^338894-60957 | 102018 | Stefano Morozzi | 06/2022 |
7750 | 2^338894-89463 | 102018 | Stefano Morozzi | 01/2023 |