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) !!!
Submit your PRPs
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 3501 | 2^570980-2782289 | 171883 | Enzo Doria | 09/2015 |
| 3502 | (25*10^171849-37)/3 | 171850 | Robert Price | 10/2019 |
| 3503 | 10^171832+387909 | 171833 | Patrick De Geest | 08/2021 |
| 3504 | 10^171832-10001 | 171832 | Robert Price | 02/2021 |
| 3506 | (2^(12*47563+13)-9)/7 | 171818 | Kevin Acres | 11/2013 |
| 3505 | (2^570769-9)/7 | 171818 | Stefano Morozzi | 08/2022 |
| 3507 | 2^570545+11025 | 171752 | Henri Lifchitz | 01/2025 |
| 3508 | 24^124375-124375^24 | 171664 | Henri Lifchitz | 08/2024 |
| 3509 | (74*10^171651-29)/9 | 171652 | Robert Price | 06/2022 |
| 3510 | (536*10^171601-23)/9 | 171603 | Robert Price | 02/2020 |
| 3511 | 7*10^171535-99 | 171536 | Robert Price | 06/2019 |
| 3512 | (28*10^171534+101)/3 | 171535 | Robert Price | 09/2020 |
| 3513 | 2^569563-1854607 | 171456 | Enzo Doria | 09/2015 |
| 3514 | 32133^38042-38042^32133 | 171454 | Frank Doornink | 02/2024 |
| 3515 | 3*10^171391+59 | 171392 | Robert Price | 08/2018 |
| 3516 | (13*10^171306-37)/3 | 171307 | Robert Price | 01/2019 |
| 3517 | 8*10^171296+87 | 171297 | Robert Price | 10/2019 |
| 3518 | (55^98419-1)/54 | 171284 | Paul Bourdelais | 12/2017 |
| 3519 | (29*10^171275+67)/3 | 171276 | Robert Price | 12/2019 |
| 3520 | (457*10^171248-7)/9 | 171250 | Robert Price | 09/2022 |
| 3521 | (194*10^171193+1)/3 | 171195 | Robert Price | 01/2022 |
| 3522 | 2^568642+1876129 | 171179 | Enzo Doria | 07/2016 |
| 3523 | 4*10^171146-47 | 171147 | Robert Price | 10/2021 |
| 3524 | (19*10^170970+131)/3 | 170971 | Robert Price | 06/2020 |
| 3525 | (46*10^170932+143)/9 | 170933 | Robert Price | 01/2019 |
| 3526 | (79*10^170901-1)/3 | 170903 | Robert Price | 02/2020 |
| 3527 | (58*10^170842+221)/9 | 170843 | Robert Price | 02/2017 |
| 3528 | (29*10^170830+583)/9 | 170831 | Robert Price | 06/2021 |
| 3529 | 3*10^170800+73 | 170801 | Robert Price | 08/2018 |
| 3530 | (29*10^170799-119)/9 | 170800 | Robert Price | 12/2021 |
| 3531 | 11^164009-270 | 170798 | Enzo Doria | 10/2012 |
| 3532 | 2*10^170767+41 | 170768 | Robert Price | 05/2018 |
| 3533 | 3^357706-112358 | 170670 | Enzo Doria | 07/2014 |
| 3534 | TheodorusPrime(170657) | 170657 | Eric W. Weisstein | 08/2013 |
| 3535 | 2^566871+1876163 | 170646 | Enzo Doria | 07/2016 |
| 3536 | (10657#+(404267#)/(10657#))/(1675379) | 170624 | Makoto Morimoto | 10/2017 |
| 3537 | 33^112337-32^112337 | 170586 | Alfred Reich | 11/2025 |
| 3538 | 2^566496+7 | 170533 | Donovan Johnson | 07/2006 |
| 3539 | (7^201653+1)/8 | 170416 | Paul Bourdelais | 02/2010 |
| 3540 | 32150^37807-37807^32150 | 170403 | Frank Doornink | 02/2024 |
| 3541 | 7*10^170348+33 | 170349 | Robert Price | 06/2020 |
| 3542 | 2^565799+216011 | 170323 | Enzo Doria | 12/2023 |
| 3543 | 2^565183-352021 | 170138 | Enzo Doria | 07/2015 |
| 3544 | 2^565143-114457 | 170125 | Enzo Doria | 02/2015 |
| 3545 | 3*2^565024-5 | 170090 | Jon Grantham | 07/2023 |
| 3546 | 2^564976-49869 | 170075 | Enzo Doria | 10/2015 |
| 3547 | 2^564561+225 | 169950 | Henri Lifchitz | 11/2024 |
| 3548 | (7*10^169944+23)/3 | 169945 | Robert Price | 06/2020 |
| 3549 | (37*10^169943+251)/9 | 169944 | Robert Price | 09/2021 |
| 3550 | 2^564526-351401 | 169940 | Enzo Doria | 07/2015 |
| 3551 | 3^355902+4 | 169809 | Aurel Gibier | 10/2024 |
| 3552 | 4*10^169759+19 | 169760 | Robert Price | 10/2018 |
| 3553 | (2^563903-13)/5 | 169752 | Stefano Morozzi | 08/2022 |
| 3554 | 21^128327-20^128327 | 169677 | Jean-Louis Charton | 11/2014 |
| 3555 | 2^563583+89 | 169656 | Stefano Morozzi | 04/2021 |
| 3556 | 2^563311+215813 | 169574 | Enzo Doria | 11/2023 |
| 3557 | (4*10^169559+83)/3 | 169560 | Robert Price | 02/2018 |
| 3558 | (194*10^169461-17)/3 | 169463 | Robert Price | 09/2020 |
| 3559 | 2^562749+2793047 | 169405 | Enzo Doria | 02/2016 |
| 3560 | (154*10^169337-1)/9 | 169339 | Serge Batalov | 12/2014 |
| 3561 | (109*10^169337+11)/3 | 169339 | Robert Price | 06/2022 |
| 3562 | (56*10^169311+691)/9 | 169312 | Robert Price | 05/2019 |
| 3563 | 2^562369-29503 | 169290 | Enzo Doria | 08/2015 |
| 3564 | (17*10^169283+19)/9 | 169284 | Robert Price | 03/2021 |
| 3565 | 390151#-2322911 | 169082 | Hayden Chesnut | 07/2024 |
| 3566 | 10^169074-5000000001 | 169074 | Robert Price | 09/2022 |
| 3567 | 8*10^169071+59 | 169072 | Robert Price | 11/2021 |
| 3568 | (10^169044+173)/3 | 169044 | Robert Price | 05/2021 |
| 3569 | (22*10^169019+383)/9 | 169020 | Robert Price | 05/2018 |
| 3570 | (64*10^168935+143)/9 | 168936 | Robert Price | 05/2021 |
| 3571 | (22*10^168906+47)/3 | 168907 | Robert Price | 06/2021 |
| 3572 | 5*10^168807+87 | 168808 | Robert Price | 02/2019 |
| 3573 | (77*10^168803-149)/9 | 168804 | Robert Price | 03/2022 |
| 3574 | 4*10^168788-47 | 168789 | Robert Price | 10/2021 |
| 3575 | (154*10^168781+17)/9 | 168783 | Robert Price | 06/2022 |
| 3576 | (418*10^168751-31)/9 | 168753 | Robert Price | 05/2022 |
| 3577 | (29*10^168711+691)/9 | 168712 | Robert Price | 08/2021 |
| 3578 | 2^560405-39943 | 168699 | Enzo Doria | 09/2015 |
| 3579 | (397*10^168634+17)/9 | 168636 | Robert Price | 03/2022 |
| 3580 | 2^560189+36587 | 168634 | Enzo Doria | 09/2024 |
| 3581 | 89*10^168614-7 | 168616 | Robert Price | 04/2020 |
| 3582 | (23*10^168608-83)/3 | 168609 | Robert Price | 08/2019 |
| 3583 | (94*10^168541+11)/3 | 168543 | Robert Price | 04/2020 |
| 3584 | 2^559686-350471 | 168483 | Enzo Doria | 06/2015 |
| 3585 | 2^559672-1855889 | 168479 | Enzo Doria | 09/2015 |
| 3586 | (5*10^168379-473)/9 | 168379 | Robert Price | 01/2018 |
| 3587 | 2024^50920+3 | 168353 | Martin Hopf | 01/2024 |
| 3588 | 2^559000-59939 | 168276 | Enzo Doria | 11/2015 |
| 3589 | 2^558830+25009 | 168225 | Enzo Doria | 11/2023 |
| 3590 | (16*10^168181+41)/3 | 168182 | Robert Price | 03/2019 |
| 3591 | (19*10^168173+77)/3 | 168174 | Robert Price | 05/2019 |
| 3592 | (74*10^168170+529)/9 | 168171 | Robert Price | 02/2022 |
| 3593 | 2^558640-114149 | 168168 | Enzo Doria | 12/2014 |
| 3594 | 2^558498-1849277 | 168125 | Enzo Doria | 08/2015 |
| 3595 | 2^558476-1850249 | 168119 | Enzo Doria | 08/2015 |
| 3596 | (7*10^168067+71)/3 | 168068 | Robert Price | 05/2018 |
| 3597 | 2^558150-1852211 | 168020 | Enzo Doria | 08/2015 |
| 3598 | 2^558125-113661 | 168013 | Enzo Doria | 09/2014 |
| 3599 | 393^64747-392^64747 | 167980 | Jean-Louis Charton | 08/2012 |
| 3600 | (8*10^167965-11)/3 | 167966 | Robert Price | 07/2023 |
| 3601 | 2^557916+216151 | 167950 | Enzo Doria | 12/2023 |
| 3602 | (13*10^167911+179)/3 | 167912 | Robert Price | 11/2018 |
| 3603 | (26*10^167861-167)/3 | 167862 | Robert Price | 10/2019 |
| 3604 | 36^107827-107827 | 167812 | Kellen Shenton | 06/2023 |
| 3605 | 32027^37242-37242^32027 | 167795 | Frank Doornink | 01/2024 |
| 3606 | 39^105456+2 | 167788 | Robert Price | 04/2015 |
| 3607 | 2^557322+217519 | 167771 | Enzo Doria | 01/2024 |
| 3608 | (28^115877-1)/27 | 167691 | Paul Bourdelais | 12/2017 |
| 3609 | 6*10^167662-13 | 167663 | Robert Price | 07/2022 |
| 3610 | 10^167639+121911 | 167640 | Patrick De Geest | 07/2018 |
| 3611 | 10^167639-8001 | 167639 | Robert Price | 03/2018 |
| 3612 | 2^556504-462059 | 167525 | Enzo Doria | 07/2015 |
| 3613 | (88*10^167522-637)/9 | 167523 | Robert Price | 11/2020 |
| 3614 | 5*10^167510+9 | 167511 | Robert Price | 08/2015 |
| 3615 | 7*10^167437-93 | 167438 | Robert Price | 08/2020 |
| 3616 | (43^102451-1)/7138097213378082 | 167335 | Paul Vanderveen | 05/2025 |
| 3617 | 25455^37978-37978^25455 | 167323 | Frank Doornink | 01/2024 |
| 3618 | 11^160663+6 | 167314 | Paul Bourdelais | 02/2021 |
| 3619 | (7*10^167308-493)/9 | 167308 | Robert Price | 04/2021 |
| 3620 | 2^555759+74333 | 167301 | Enzo Doria | 07/2023 |
| 3621 | 26084^37871-37871^26084 | 167253 | Frank Doornink | 03/2024 |
| 3622 | 2^555343+1874333 | 167175 | Enzo Doria | 06/2016 |
| 3623 | 2^555210-461261 | 167135 | Enzo Doria | 07/2015 |
| 3624 | 9*10^166996+59 | 166997 | Robert Price | 01/2020 |
| 3625 | (68*10^166976-329)/9 | 166977 | Robert Price | 03/2021 |
| 3626 | (64*10^166901+683)/9 | 166902 | Robert Price | 06/2022 |
| 3627 | 2^554372+1880527 | 166883 | Enzo Doria | 11/2016 |
| 3628 | 2^554299+72173 | 166861 | Enzo Doria | 04/2016 |
| 3629 | (185*10^166837+7)/3 | 166839 | Robert Price | 03/2020 |
| 3630 | (14*10^166813+139)/9 | 166814 | Robert Price | 11/2021 |
| 3631 | 26084^37767-37767^26084 | 166794 | Frank Doornink | 03/2024 |
| 3632 | 2^554037-2797063 | 166782 | Enzo Doria | 03/2016 |
| 3633 | 31861^37028-37028^31861 | 166747 | Frank Doornink | 01/2024 |
| 3634 | (49*10^166721-139)/9 | 166722 | Robert Price | 03/2019 |
| 3635 | 2*10^166646+69 | 166647 | Robert Price | 06/2020 |
| 3636 | 2^553484-29819 | 166616 | Enzo Doria | 08/2015 |
| 3637 | (188*10^166611+7)/3 | 166613 | Robert Price | 03/2020 |
| 3638 | 2^553383-2784217 | 166585 | Enzo Doria | 10/2015 |
| 3639 | 2^553069+76427 | 166491 | Enzo Doria | 05/2016 |
| 3640 | 25218^37819-37819^25218 | 166469 | Frank Doornink | 12/2023 |
| 3641 | 2*10^166458+51 | 166459 | Robert Price | 05/2018 |
| 3642 | 589^60089-588^60089 | 166454 | Jean-Louis Charton | 09/2012 |
| 3643 | 25214^37799-37799^25214 | 166378 | Frank Doornink | 11/2023 |
| 3644 | 11^159756-2424 | 166369 | Mike Oakes | 06/2010 |
| 3645 | 2^552649-361275 | 166364 | Enzo Doria | 05/2014 |
| 3646 | 2^552628-113669 | 166358 | Enzo Doria | 09/2014 |
| 3647 | (19*10^166325+137)/3 | 166326 | Robert Price | 03/2022 |
| 3648 | 10^166324+550603 | 166325 | Patrick De Geest | 07/2018 |
| 3649 | 10^166324-801 | 166324 | Robert Price | 02/2018 |
| 3650 | (85*10^166297-1)/3 | 166299 | Robert Price | 02/2020 |
| 3651 | (19*10^166280-7)/3 | 166281 | Robert Price | 12/2023 |
| 3652 | 25533^37726-37726^25533 | 166263 | Frank Doornink | 02/2024 |
| 3653 | 8*10^166227+87 | 166228 | Robert Price | 10/2019 |
| 3654 | 2^552137+1879397 | 166210 | Enzo Doria | 09/2016 |
| 3655 | 262273205671539190984629()252475512364409752762433 | 166141 | Anonymous | 01/2025 |
| 3656 | 490079063773165613318095()218182139934160868002603 | 166141 | Anonymous | 01/2025 |
| 3657 | 140717254840416411192803()712689271538459396766869 | 166140 | Anonymous | 01/2025 |
| 3658 | 122398296040696255481419()271117913237372866926417 | 166140 | Anonymous | 01/2025 |
| 3659 | (103*10^166126+11)/3 | 166128 | Robert Price | 01/2021 |
| 3660 | (22*10^166077+179)/3 | 166078 | Robert Price | 02/2022 |
| 3661 | (23^121949-1)/22 | 166061 | Paul Bourdelais | 10/2017 |
| 3662 | 2^551576+236221 | 166041 | Enzo Doria | 05/2025 |
| 3663 | 2^551542+19249 | 166031 | Payam Samidoost | 08/2002 |
| 3664 | 2^551535-23821 | 166029 | Enzo Doria | 08/2013 |
| 3665 | 2^551507-23557 | 166021 | Enzo Doria | 08/2013 |
| 3666 | 32030^36841-36841^32030 | 165990 | Frank Doornink | 01/2024 |
| 3667 | 10^165947-7000000001 | 165947 | Robert Price | 12/2021 |
| 3668 | 4*10^165938-47 | 165939 | Robert Price | 10/2021 |
| 3669 | 7*10^165916-3 | 165917 | Robert Price | 08/2015 |
| 3670 | (29*10^165796+67)/3 | 165797 | Robert Price | 12/2019 |
| 3671 | 81^86837-80^86837 | 165728 | Robert Price | 01/2015 |
| 3672 | (71*10^165716-17)/9 | 165717 | Serge Batalov | 01/2023 |
| 3673 | fibonacci(792909)+3 | 165708 | Jon Grantham | 08/2023 |
| 3674 | (71*10^165663-539)/9 | 165664 | Robert Price | 07/2019 |
| 3675 | 25682^37567-37567^25682 | 165657 | Frank Doornink | 02/2024 |
| 3676 | 2^550270-69551 | 165648 | Enzo Doria | 12/2015 |
| 3677 | 2^550250+29329 | 165642 | Enzo Doria | 03/2024 |
| 3678 | (202*10^165569-13)/9 | 165571 | Robert Price | 01/2020 |
| 3679 | 2^550000-23625 | 165567 | Enzo Doria | 08/2013 |
| 3680 | 31688^36783-36783^31688 | 165557 | Frank Doornink | 01/2024 |
| 3681 | 2^549675-1852057 | 165469 | Enzo Doria | 08/2015 |
| 3682 | 2^549663+212543 | 165466 | Enzo Doria | 08/2023 |
| 3683 | (3^549633)%(2^549633) | 165456 | Henri Lifchitz | 06/2025 |
| 3684 | (529*10^165394-7)/9 | 165396 | Robert Price | 08/2021 |
| 3685 | 26253^37424-37424^26253 | 165384 | Frank Doornink | 03/2024 |
| 3686 | -tau(103^14938) | 165374 | Nik Lygeros / Olivier Rozier | 10/2013 |
| 3687 | (28*10^165358-1)/9 | 165359 | Serge Batalov | 10/2014 |
| 3688 | 2^549278+1879669 | 165350 | Enzo Doria | 09/2016 |
| 3689 | (7*10^165350-439)/9 | 165350 | Robert Price | 02/2018 |
| 3690 | 2^549252-351269 | 165342 | Enzo Doria | 06/2015 |
| 3691 | 2^549221+335931 | 165332 | Enzo Doria | 09/2024 |
| 3692 | 67*10^165327-9 | 165329 | Robert Price | 03/2021 |
| 3693 | (14*10^165282+73)/3 | 165283 | Robert Price | 12/2018 |
| 3694 | (8*10^165283-629)/9 | 165283 | Robert Price | 01/2022 |
| 3695 | 2^549049+2797607 | 165281 | Enzo Doria | 04/2016 |
| 3696 | (218*10^165258+7)/9 | 165260 | Robert Price | 06/2022 |
| 3697 | (7*10^165239+107)/3 | 165240 | Robert Price | 02/2018 |
| 3698 | 2^548880+23961 | 165230 | Enzo Doria | 10/2023 |
| 3699 | 5*2^548778+3 | 165200 | Jon Grantham | 07/2023 |
| 3700 | (44^100511-1)/43 | 165184 | Paul Bourdelais | 11/2017 |
| 3701 | (7*10^165134+107)/3 | 165135 | Robert Price | 02/2018 |
| 3702 | (301*10^165082+23)/9 | 165084 | Robert Price | 06/2021 |
| 3703 | (23*10^165060-83)/3 | 165061 | Robert Price | 08/2019 |
| 3704 | 7*10^165023-27 | 165024 | Robert Price | 11/2022 |
| 3705 | (76*10^164984+77)/9 | 164985 | Robert Price | 10/2019 |
| 3706 | 31058^36715-36715^31058 | 164931 | Frank Doornink | 01/2024 |
| 3707 | (4*10^164929-211)/9 | 164929 | Robert Price | 03/2022 |
| 3708 | 10^164878-500001 | 164878 | Robert Price | 03/2022 |
| 3709 | 9*10^164791-89 | 164792 | Robert Price | 04/2020 |
| 3710 | (2^788414)%F(788414) | 164769 | Henri Lifchitz | 05/2025 |
| 3711 | 2^547178-1856501 | 164717 | Enzo Doria | 10/2015 |
| 3712 | 11^158160-60 | 164707 | Enzo Doria | 07/2012 |
| 3713 | (26*10^164643-167)/3 | 164644 | Robert Price | 10/2019 |
| 3714 | (10^164643+83)/3 | 164643 | Robert Price | 08/2021 |
| 3715 | 2^546398-59201 | 164483 | Enzo Doria | 10/2015 |
| 3716 | 2^546332-114893 | 164463 | Enzo Doria | 05/2015 |
| 3717 | 36087^36087-36080^36080 | 164462 | Henri Lifchitz | 08/2024 |
| 3718 | 32003^36504-36504^32003 | 164458 | Frank Doornink | 01/2024 |
| 3719 | (65*10^164427+277)/9 | 164428 | Robert Price | 08/2021 |
| 3720 | 2^545958+1876189 | 164350 | Enzo Doria | 07/2016 |
| 3721 | 2^545878-49841 | 164326 | Enzo Doria | 10/2015 |
| 3722 | (10^164284+77)/3 | 164284 | Robert Price | 01/2018 |
| 3723 | 2^545668-4019 | 164263 | Yves Minet | 04/2017 |
| 3724 | 10^164216+780639 | 164217 | Patrick De Geest | 08/2021 |
| 3726 | 10^164216-50000000001 | 164216 | Robert Price | 12/2020 |
| 3725 | 10^164216-891051 | 164216 | Patrick De Geest | 08/2021 |
| 3727 | (13*53^238539*617^9)/10^247183 | 164151 | Hans Havermann | 07/2017 |
| 3728 | (16*10^164122+197)/3 | 164123 | Robert Price | 04/2019 |
| 3729 | 2^545185+76757 | 164118 | Enzo Doria | 05/2016 |
| 3730 | 2^545076-114329 | 164085 | Enzo Doria | 01/2015 |
| 3731 | (2*10^164043-143)/3 | 164043 | Robert Price | 03/2018 |
| 3732 | (33085^36481-1)/(33085^191-1) | 164018 | Ryan Propper | 11/2023 |
| 3733 | (29^112153+1)/30 | 164011 | Lelio R Paula | 03/2017 |
| 3734 | 2^544757+1874777 | 163989 | Enzo Doria | 06/2016 |
| 3735 | 2^544723+211193 | 163978 | Enzo Doria | 08/2023 |
| 3736 | 2^544444-457199 | 163894 | Enzo Doria | 01/2015 |
| 3737 | (32804^36481-1)/(32804^191-1) | 163883 | Ryan Propper | 11/2023 |
| 3738 | 2^544264-343529 | 163840 | Enzo Doria | 07/2015 |
| 3739 | 7*10^163780+9 | 163781 | Robert Price | 09/2015 |
| 3740 | (2^783598)%L(783598) | 163761 | Henri Lifchitz | 05/2025 |
| 3741 | 2^543989+2793047 | 163758 | Enzo Doria | 02/2016 |
| 3742 | (28*10^163709+113)/3 | 163710 | Robert Price | 03/2020 |
| 3743 | (2^543398)/(543398^2) | 163568 | Henri Lifchitz | 05/2025 |
| 3744 | (2013^49729-1)/(2013^223-1) | 163561 | Ryan Propper | 11/2023 |
| 3745 | L(2*543272)%(2^543272) | 163541 | Henri Lifchitz | 07/2025 |
| 3746 | (23*10^163523+301)/9 | 163524 | Robert Price | 06/2021 |
| 3747 | (68*10^163521-329)/9 | 163522 | Robert Price | 03/2021 |
| 3748 | 35820^35899+35899^35820 | 163489 | Norbert Schneider | 11/2021 |
| 3749 | 2^542870-69551 | 163421 | Enzo Doria | 12/2015 |
| 3750 | 2^542502+24799 | 163310 | Enzo Doria | 10/2023 |
