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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See the Latest PRPs
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 5501 | (6*32^89076+4241)/31 | 134073 | Eric Chen | 11/2023 |
| 5502 | (277*10^134059-7)/9 | 134061 | Robert Price | 02/2022 |
| 5503 | 2^445328-216917 | 134058 | Enzo Doria | 05/2014 |
| 5504 | 2^445202+1874899 | 134020 | Enzo Doria | 06/2016 |
| 5505 | 5^191739-3^191739-1 | 134020 | Jon Grantham | 08/2023 |
| 5506 | (35*10^134003-89)/9 | 134004 | Robert Price | 02/2022 |
| 5507 | (13*2^445102+1)/17 | 133989 | Lelio R Paula | 07/2015 |
| 5508 | (35*10^133979-593)/9 | 133980 | Robert Price | 07/2018 |
| 5509 | 2*10^133955+51 | 133956 | Robert Price | 05/2018 |
| 5510 | (49*10^133952+437)/9 | 133953 | Robert Price | 09/2021 |
| 5511 | 2^444964-113639 | 133948 | Enzo Doria | 08/2014 |
| 5512 | 31811^16240+16240^31811 | 133943 | Hans Havermann | 04/2021 |
| 5513 | 10^133902+167841 | 133903 | Patrick De Geest | 05/2021 |
| 5515 | 28118^30097-30097^28118 | 133902 | Norbert Schneider | 01/2015 |
| 5514 | 10^133902-100001 | 133902 | Robert Price | 07/2020 |
| 5516 | 2^444784-113859 | 133894 | Enzo Doria | 10/2014 |
| 5517 | (132^63127-1)/131 | 133864 | Anonymous | 06/2024 |
| 5518 | 32303^13914+13914^32303 | 133846 | Hans Havermann | 04/2021 |
| 5519 | (29^91493-3^91493)/26 | 133798 | Robert Price | 06/2025 |
| 5520 | (2276213*2^444444+1)/3 | 133797 | Alex_soldier | 11/2022 |
| 5521 | (1403559*2^444444+1)/5 | 133797 | Alex_soldier | 11/2022 |
| 5522 | (1209887*2^444444+1)/9 | 133797 | Alex_soldier | 11/2022 |
| 5523 | (608239*2^444444+1)/25 | 133796 | Alex_soldier | 11/2022 |
| 5524 | (1824587*2^444444+1)/27 | 133796 | Alex_soldier | 11/2022 |
| 5525 | (40795*2^444444+1)/7 | 133795 | Alex_soldier | 11/2022 |
| 5526 | 30739^22458+22458^30739 | 133757 | Hans Havermann | 04/2021 |
| 5527 | 34942^6721+6721^34942 | 133739 | Hans Havermann | 04/2021 |
| 5528 | (3^280229-1)/1120918 | 133698 | Aurel Gibier | 03/2025 |
| 5529 | (2^444046+100280245065) | 133672 | Paul Bourdelais | 05/2022 |
| 5530 | 34792^6935+6935^34792 | 133638 | Hans Havermann | 04/2021 |
| 5531 | (266*10^133603+1)/3 | 133605 | Robert Price | 04/2020 |
| 5532 | 32261^13842+13842^32261 | 133600 | Hans Havermann | 04/2021 |
| 5533 | (89*10^133580+1)/9 | 133581 | Serge Batalov | 05/2010 |
| 5534 | (134*10^133573-11)/3 | 133575 | Robert Price | 01/2022 |
| 5535 | 26726^30173-30173^26726 | 133574 | Frank Doornink | 03/2024 |
| 5536 | 2^443721+39527 | 133574 | Enzo Doria | 11/2024 |
| 5537 | 62^74521-61^74521 | 133571 | Robert Price | 05/2013 |
| 5538 | (182*10^133543+1)/3 | 133545 | Robert Price | 02/2020 |
| 5539 | (103*10^133535+11)/3 | 133537 | Robert Price | 01/2021 |
| 5540 | 32589^12520+12520^32589 | 133537 | Hans Havermann | 03/2021 |
| 5541 | L(638839)/274700771 | 133502 | Serge Batalov | 07/2024 |
| 5542 | 34516^7373+7373^34516 | 133496 | Hans Havermann | 04/2021 |
| 5543 | 8*10^133487-37 | 133488 | Robert Price | 03/2022 |
| 5544 | 30135^26882+26882^30135 | 133482 | Hans Havermann | 04/2021 |
| 5545 | 2^443198-1867301 | 133416 | Enzo Doria | 03/2016 |
| 5546 | 27^93192+26 | 133392 | Anonymous | 09/2024 |
| 5547 | (19*10^133390+101)/3 | 133391 | Robert Price | 09/2019 |
| 5548 | (71^72043-1)/70 | 133369 | Paul Bourdelais | 09/2017 |
| 5549 | (17508!^2+1)/(1453817*25094393) | 133366 | Michael Porter | 09/2025 |
| 5550 | 36117^4910+4910^36117 | 133311 | Hans Havermann | 04/2021 |
| 5551 | 2^442799+1874633 | 133296 | Enzo Doria | 06/2016 |
| 5552 | L(637751) | 133283 | Henri Lifchitz | 09/2008 |
| 5553 | 109^65410-2 | 133269 | Lelio R Paula | 10/2017 |
| 5554 | 2^442688-113489 | 133263 | Enzo Doria | 08/2014 |
| 5555 | (7*2^442640-1)/783 | 133246 | Lelio R Paula | 07/2015 |
| 5556 | (9*2^442463+1)/17441 | 133192 | Lelio R Paula | 07/2015 |
| 5557 | 2^442437-1849993 | 133187 | Enzo Doria | 08/2015 |
| 5558 | 2^442430-2791721 | 133185 | Enzo Doria | 03/2016 |
| 5559 | (13*2^442428-1)/309 | 133183 | Lelio R Paula | 07/2015 |
| 5560 | 29959^27870+27870^29959 | 133172 | Hans Havermann | 03/2021 |
| 5561 | (25*2^442379-1)/71 | 133169 | Lelio R Paula | 07/2015 |
| 5562 | 2^442368+213691 | 133167 | Enzo Doria | 09/2023 |
| 5563 | 34240^7737+7737^34240 | 133145 | Hans Havermann | 03/2021 |
| 5564 | 452^50145+50145^452 | 133142 | Norbert Schneider | 09/2020 |
| 5565 | (355^52201-1)/354 | 133122 | Tom Wu | 08/2024 |
| 5566 | (3^278981-1)/14507014 | 133101 | Paul Vanderveen | 05/2025 |
| 5567 | 30659^21796+21796^30659 | 133011 | Hans Havermann | 04/2021 |
| 5568 | 33276^9935+9935^33276 | 133010 | Hans Havermann | 04/2021 |
| 5569 | 30111^26122+26122^30111 | 133001 | Hans Havermann | 04/2021 |
| 5570 | 30790^20869+20869^30790 | 132998 | Hans Havermann | 04/2021 |
| 5572 | (2^441799+78557)/5 | 132995 | Lelio R Paula | 07/2015 |
| 5571 | 8*10^132994-27 | 132995 | Robert Price | 10/2021 |
| 5573 | (109*10^132992+11)/3 | 132994 | Robert Price | 06/2022 |
| 5574 | 2^441781-2787883 | 132990 | Enzo Doria | 03/2016 |
| 5575 | fibonacci(636232)+4 | 132965 | Jon Grantham | 08/2023 |
| 5576 | (3*2^441685+1)/749 | 132959 | Lelio R Paula | 07/2015 |
| 5577 | 2^441618+37 | 132941 | Lelio R Paula | 08/2017 |
| 5578 | 34857^6514+6514^34857 | 132940 | Hans Havermann | 04/2021 |
| 5579 | 34065^7988+7988^34065 | 132937 | Hans Havermann | 04/2021 |
| 5580 | 35571^5452+5452^35571 | 132914 | Hans Havermann | 04/2021 |
| 5581 | 2^441521-113575 | 132912 | Enzo Doria | 08/2014 |
| 5582 | 7*10^132884-99 | 132885 | Robert Price | 06/2019 |
| 5583 | 26987^29988-29988^26987 | 132882 | Frank Doornink | 03/2024 |
| 5584 | (103*10^132879+17)/3 | 132881 | Robert Price | 08/2020 |
| 5585 | 2^441396-65 | 132874 | Lelio R Paula | 08/2017 |
| 5586 | 33350^9633+9633^33350 | 132859 | Hans Havermann | 04/2021 |
| 5587 | 2^441330+1871959 | 132854 | Enzo Doria | 05/2016 |
| 5588 | 25772^30111-30111^25772 | 132825 | Frank Doornink | 02/2024 |
| 5589 | 2^441063+383 | 132774 | Lelio R Paula | 06/2012 |
| 5590 | (10^132753+7)/17/19 | 132751 | Alfred Reich | 06/2021 |
| 5591 | (22*10^132746+53)/3 | 132747 | Robert Price | 07/2019 |
| 5592 | (77*10^132744-149)/9 | 132745 | Robert Price | 03/2022 |
| 5593 | (22*10^132732+119)/3 | 132733 | Robert Price | 04/2021 |
| 5594 | 2^440846+1870909 | 132708 | Enzo Doria | 05/2016 |
| 5595 | (948^44579-1)/947 | 132701 | Jinyuan Wang | 04/2023 |
| 5596 | 2^440656-113489 | 132651 | Enzo Doria | 08/2014 |
| 5597 | numbpart(14180123587) | 132646 | Serge Batalov | 04/2017 |
| 5598 | 32950^10591+10591^32950 | 132622 | Hans Havermann | 04/2021 |
| 5599 | 33302^9597+9597^33302 | 132614 | Hans Havermann | 04/2021 |
| 5600 | (19*10^132550+191)/3 | 132551 | Robert Price | 05/2019 |
| 5601 | (2^440399-1)/(16210820281161978209*31518475633*880799) | 132538 | Dario Alpern | 01/2015 |
| 5602 | (38^83891+1)/39 | 132529 | Robert Price | 09/2013 |
| 5603 | 2*10^132493-43 | 132494 | Robert Price | 04/2018 |
| 5604 | 31352^16809+16809^31352 | 132480 | Hans Havermann | 04/2021 |
| 5605 | (418*10^132441+23)/9 | 132443 | Robert Price | 02/2020 |
| 5606 | 2^439931-21 | 132433 | Lelio R Paula | 08/2017 |
| 5607 | 47^79201-46^79201 | 132432 | Robert Price | 10/2012 |
| 5608 | 2^439897-113653 | 132423 | Enzo Doria | 08/2014 |
| 5609 | 35505^5362+5362^35505 | 132410 | Hans Havermann | 03/2021 |
| 5610 | 30079^25222+25222^30079 | 132402 | Hans Havermann | 04/2021 |
| 5611 | (5*2^439822+1)/9 | 132400 | Lelio R Paula | 06/2015 |
| 5612 | (695*10^132356+7)/9 | 132358 | Robert Price | 12/2021 |
| 5613 | (112*10^132337-1)/3 | 132339 | Serge Batalov | 12/2014 |
| 5614 | 2^439576-113247 | 132326 | Enzo Doria | 07/2014 |
| 5615 | (7^156589-1)/65346468774 | 132323 | Paul Vanderveen | 05/2025 |
| 5616 | 30059^25230+25230^30059 | 132318 | Hans Havermann | 04/2021 |
| 5617 | 2^439497-29143 | 132302 | Enzo Doria | 07/2015 |
| 5618 | 2^439409-114193 | 132276 | Enzo Doria | 12/2014 |
| 5619 | (39^83137+2^83137)/41 | 132275 | Robert Price | 12/2024 |
| 5620 | (44*10^132233-233)/9 | 132234 | Robert Price | 01/2019 |
| 5621 | 25507^30000-30000^25507 | 132200 | Frank Doornink | 02/2024 |
| 5622 | 9*10^132148-7 | 132149 | Robert Price | 09/2015 |
| 5623 | V(790390) | 132144 | Serge Batalov | 07/2024 |
| 5624 | (47*10^132125-119)/9 | 132126 | Robert Price | 05/2019 |
| 5625 | 2^438900+214051 | 132123 | Enzo Doria | 10/2023 |
| 5626 | 2^438845+1870217 | 132106 | Enzo Doria | 05/2016 |
| 5627 | Phi(293229,-5) | 132106 | Henri Lifchitz | 02/2026 |
| 5628 | 2^438789+87855 | 132089 | Lelio R Paula | 01/2016 |
| 5629 | 2^438774-2786411 | 132085 | Enzo Doria | 03/2016 |
| 5630 | 2^438755-1848205 | 132079 | Enzo Doria | 07/2015 |
| 5631 | 30502^21381+21381^30502 | 132075 | Hans Havermann | 04/2021 |
| 5632 | 2^438739-112087 | 132074 | Enzo Doria | 06/2014 |
| 5633 | (588859*29^90289-19)/28 | 132043 | Eric Chen | 06/2025 |
| 5634 | (2^438438+100280245065) | 131983 | Paul Bourdelais | 05/2022 |
| 5635 | 35872^4777+4777^35872 | 131979 | Hans Havermann | 04/2021 |
| 5636 | 31198^16945+16945^31198 | 131938 | Hans Havermann | 03/2021 |
| 5637 | 13907#+(318259#)/(13907#) | 131923 | Makoto Morimoto | 10/2017 |
| 5638 | L(631181) | 131910 | Henri Lifchitz | 09/2008 |
| 5639 | (47*10^131886-119)/9 | 131887 | Robert Price | 05/2019 |
| 5640 | 5*2^438096-3 | 131881 | Jon Grantham | 07/2023 |
| 5641 | (3*2^438121+1)/4308193883 | 131879 | Lelio R Paula | 06/2015 |
| 5642 | 2^438079-1863877 | 131875 | Enzo Doria | 03/2016 |
| 5643 | (16*10^131872-37)/3 | 131873 | Robert Price | 05/2021 |
| 5644 | (2^438067+5)/329 | 131869 | Lelio R Paula | 06/2015 |
| 5645 | 2^437908-113855 | 131824 | Enzo Doria | 09/2014 |
| 5646 | 2^437884-286349 | 131817 | Enzo Doria | 07/2015 |
| 5647 | 15^112072+14 | 131807 | Alfred Reich | 10/2023 |
| 5648 | 5^188558+4 | 131797 | Tyler NeSmith | 05/2021 |
| 5649 | (11*10^131784-17)/3 | 131785 | Robert Price | 06/2018 |
| 5650 | (166^59357-1)/165 | 131777 | Anonymous | 06/2024 |
| 5651 | 4*10^131719-93 | 131720 | Robert Price | 07/2020 |
| 5652 | 31629^14606+14606^31629 | 131720 | Hans Havermann | 04/2021 |
| 5653 | 3^276062-112292 | 131716 | Enzo Doria | 07/2014 |
| 5654 | 2^437539+2025 | 131713 | Henri Lifchitz | 01/2025 |
| 5655 | 11*31^88313+322688 | 131708 | Eric Chen | 05/2024 |
| 5656 | (7*10^131682+89)/3 | 131683 | Robert Price | 08/2020 |
| 5657 | 29512^28969+28969^29512 | 131681 | Hans Havermann | 03/2021 |
| 5658 | 2^437343+75953 | 131654 | Enzo Doria | 04/2016 |
| 5659 | 35^85243-34^85243 | 131621 | Robert Price | 05/2012 |
| 5660 | (28*10^131586+59)/3 | 131587 | Robert Price | 05/2021 |
| 5661 | (59*10^131575+391)/9 | 131576 | Robert Price | 03/2021 |
| 5662 | Phi(51051,-17#) | 131513 | Henri Lifchitz | 12/2025 |
| 5663 | 39984^1945+1945^39984 | 131505 | Hans Havermann | 03/2021 |
| 5664 | 25842^29801-29801^25842 | 131492 | Frank Doornink | 03/2024 |
| 5665 | 28592^29505-29505^28592 | 131482 | Frank Doornink | 05/2024 |
| 5666 | 25647^29818-29818^25647 | 131469 | Frank Doornink | 02/2024 |
| 5667 | (203*10^131457+1)/3 | 131459 | Robert Price | 03/2020 |
| 5668 | 7*10^131421-41 | 131422 | Robert Price | 08/2021 |
| 5669 | 87309^32+32^87309 | 131414 | Hans Havermann | 03/2021 |
| 5670 | (68^71713+1)/69 | 131413 | Paul Bourdelais | 09/2017 |
| 5671 | 2^436521+224885 | 131406 | Enzo Doria | 07/2024 |
| 5672 | (650*10^131391+43)/9 | 131393 | Tyler Busby | 01/2023 |
| 5673 | 2^436451+1884713 | 131385 | Enzo Doria | 03/2017 |
| 5674 | 2^436365+35 | 131359 | Robert Price | 11/2015 |
| 5676 | 2^436300+1866871 | 131340 | Enzo Doria | 03/2016 |
| 5675 | (7*10^131339+179)/3 | 131340 | Robert Price | 09/2018 |
| 5677 | 14^114592-3 | 131338 | Paul Bourdelais | 12/2020 |
| 5678 | 36197^4236+4236^36197 | 131285 | Hans Havermann | 04/2021 |
| 5679 | (37*10^131270+341)/9 | 131271 | Robert Price | 08/2018 |
| 5680 | 29863^24790+24790^29863 | 131227 | Hans Havermann | 03/2021 |
| 5681 | (5*10^131223-29)/3 | 131224 | Robert Price | 03/2018 |
| 5682 | 29524^27825+27825^29524 | 131218 | Hans Havermann | 03/2021 |
| 5683 | (23*2^435891-1)/699 | 131215 | Lelio R Paula | 07/2015 |
| 5684 | (11*2^435879+1)/3337 | 131211 | Lelio R Paula | 06/2015 |
| 5685 | 30639^19136+19136^30639 | 131192 | Hans Havermann | 04/2021 |
| 5686 | (2^435808+1)/641/6700417 | 131182 | Lelio R Paula | 02/2012 |
| 5687 | (2^435808+1)/4294967297 | 131182 | Serge Batalov | 12/2016 |
| 5688 | 2^435773+1875557 | 131181 | Enzo Doria | 06/2016 |
| 5690 | (16*10^131180+167)/3 | 131181 | Robert Price | 06/2019 |
| 5689 | (26*10^131180-77)/3 | 131181 | Robert Price | 11/2019 |
| 5691 | (25*10^131144-7)/9 | 131145 | Robert Price | 05/2018 |
| 5692 | 29299^29358-29358^29299 | 131138 | Norbert Schneider | 03/2022 |
| 5693 | 2^435612-2789939 | 131133 | Enzo Doria | 12/2015 |
| 5694 | 33976^7231+7231^33976 | 131121 | Hans Havermann | 03/2021 |
| 5695 | 33715^7746+7746^33715 | 131121 | Hans Havermann | 03/2021 |
| 5696 | 66^72047-65^72047 | 131093 | Robert Price | 09/2013 |
| 5697 | (5*10^131090+37)/3 | 131091 | Robert Price | 03/2018 |
| 5698 | 2^435468+75631 | 131089 | Enzo Doria | 04/2016 |
| 5699 | 37^83588-2 | 131083 | Lelio R Paula | 08/2015 |
| 5700 | (4^217720+11)/3 | 131081 | Robert Price | 02/2017 |
| 5701 | 30407^20448+20448^30407 | 131074 | Hans Havermann | 04/2021 |
| 5702 | (22*10^131070+179)/3 | 131071 | Robert Price | 02/2022 |
| 5703 | 28831^29388-29388^28831 | 131067 | Frank Doornink | 05/2024 |
| 5704 | 29487^27836+27836^29487 | 131059 | Hans Havermann | 04/2021 |
| 5705 | 29962^23615+23615^29962 | 131030 | Hans Havermann | 03/2021 |
| 5706 | 2^435202-113193 | 131009 | Enzo Doria | 07/2014 |
| 5707 | 41705^1384+1384^41705 | 131002 | Hans Havermann | 04/2021 |
| 5708 | 9*10^130998-19 | 130999 | Robert Price | 07/2019 |
| 5709 | 36243^4108+4108^36243 | 130969 | Hans Havermann | 04/2021 |
| 5710 | (32^86981-5^86981)/27 | 130919 | Robert Price | 04/2026 |
| 5711 | (445^49433+1)/446 | 130914 | Jinyuan Wang | 05/2024 |
| 5712 | floor((sqrt(5)-1)/2*10^130911) | 130911 | Serge Batalov | 06/2017 |
| 5713 | 2^434835-111937 | 130899 | Enzo Doria | 05/2014 |
| 5714 | (62*10^130895-629)/9 | 130896 | Robert Price | 07/2021 |
| 5715 | 2^434807+225 | 130890 | Henri Lifchitz | 11/2024 |
| 5716 | 2^434685+72257 | 130854 | Enzo Doria | 04/2016 |
| 5717 | Phi(64497,-1105) | 130853 | Henri Lifchitz | 12/2025 |
| 5718 | (7*10^130825+113)/3 | 130826 | Robert Price | 02/2018 |
| 5719 | 2^434539-29317 | 130810 | Enzo Doria | 07/2015 |
| 5720 | (74*10^130791+637)/9 | 130792 | Robert Price | 01/2022 |
| 5721 | 2^434469-114259 | 130789 | Enzo Doria | 01/2015 |
| 5722 | (5*10^130763+103)/9 | 130763 | Robert Price | 04/2022 |
| 5723 | 2^434246+33 | 130722 | Robert Price | 11/2015 |
| 5724 | 30156^21599+21599^30156 | 130710 | Hans Havermann | 04/2021 |
| 5725 | (41^81041-3^81041)/38 | 130701 | Robert Price | 09/2025 |
| 5726 | (17*10^130695-161)/9 | 130696 | Robert Price | 02/2021 |
| 5727 | 30513^19148+19148^30513 | 130661 | Hans Havermann | 03/2021 |
| 5728 | 29736^24761+24761^29736 | 130654 | Hans Havermann | 04/2021 |
| 5729 | 9*10^130638+41 | 130639 | Robert Price | 08/2020 |
| 5730 | 2^433911-91 | 130621 | Lelio R Paula | 06/2017 |
| 5731 | 30786^17449+17449^30786 | 130588 | Hans Havermann | 03/2021 |
| 5732 | 2^433744-114419 | 130570 | Enzo Doria | 02/2015 |
| 5734 | 2^433708+1869451 | 130560 | Enzo Doria | 05/2016 |
| 5733 | 2^433710+93 | 130560 | Lelio R Paula | 06/2017 |
| 5735 | 7*10^130535-27 | 130536 | Robert Price | 11/2022 |
| 5736 | (17^130533)%(10^130533) | 130533 | Henri Lifchitz | 05/2025 |
| 5737 | (9629^32768+1)/120501441265666 | 130520 | Kellen Shenton | 05/2021 |
| 5738 | 804*34^85220+713 | 130516 | Eric Chen | 08/2023 |
| 5739 | (29*2^433547-1)/27 | 130511 | Lelio R Paula | 06/2015 |
| 5740 | 3^273521+10 | 130503 | Tyler NeSmith | 01/2021 |
| 5741 | 41659^1356+1356^41659 | 130487 | Hans Havermann | 03/2021 |
| 5742 | 4*10^130480+9 | 130481 | Robert Price | 05/2015 |
| 5743 | (23*2^433449-1)/75 | 130481 | Lelio R Paula | 06/2015 |
| 5744 | 3*2^433422+5 | 130474 | Jon Grantham | 07/2023 |
| 5745 | (23*2^433334-1)/3731 | 130445 | Lelio R Paula | 06/2015 |
| 5746 | (31*10^130414-49)/9 | 130415 | Robert Price | 11/2021 |
| 5747 | 26462^29485-29485^26462 | 130402 | Frank Doornink | 03/2024 |
| 5748 | 33481^7848+7848^33481 | 130401 | Hans Havermann | 03/2021 |
| 5749 | (17*10^130393+7)/3 | 130394 | Robert Price | 06/2023 |
| 5750 | (22*10^130392+203)/9 | 130393 | Robert Price | 10/2021 |
