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
See the Top discoverers
See the Latest PRPs
Search by form
| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 3501 | (10^181996+41)/3 | 181996 | Robert Price | 12/2017 |
| 3502 | (17*10^181979+91)/9 | 181980 | Robert Price | 02/2022 |
| 3503 | (10^181960+3)/7 | 181960 | Jinyuan Wang | 11/2024 |
| 3504 | (5*10^181950-101)/3 | 181951 | Robert Price | 04/2018 |
| 3505 | 2^603915+75233 | 181797 | Enzo Doria | 04/2016 |
| 3506 | 39470^39537+39537^39470 | 181723 | Norbert Schneider | 12/2022 |
| 3507 | (10^181710+7)/563747/2019847 | 181698 | Alfred Reich | 08/2021 |
| 3508 | 7*10^181594-57 | 181595 | Robert Price | 06/2020 |
| 3509 | 8*10^181580+29 | 181581 | Robert Price | 11/2021 |
| 3510 | (83*10^181544+61)/9 | 181545 | Serge Batalov | 01/2023 |
| 3511 | (2*10^181457+7)/9 | 181457 | Rytis Slatkevicius | 01/2023 |
| 3512 | 3*10^181445+23 | 181446 | Robert Price | 03/2022 |
| 3513 | Phi(306341,-5) | 181375 | Henri Lifchitz | 02/2026 |
| 3514 | (194*10^181369-11)/3 | 181371 | Robert Price | 09/2020 |
| 3515 | 11^174145-360 | 181354 | Enzo Doria | 10/2012 |
| 3516 | 2^602351-396765 | 181326 | Enzo Doria | 08/2013 |
| 3517 | 6*10^181306+17 | 181307 | Robert Price | 04/2019 |
| 3518 | (353^71143-1)/352 | 181254 | Anonymous | 04/2024 |
| 3519 | (286*10^181220-1)/3 | 181222 | Robert Price | 11/2020 |
| 3520 | 2^601957-113833 | 181208 | Enzo Doria | 09/2014 |
| 3521 | 66^99581-65^99581 | 181193 | Robert Price | 09/2013 |
| 3522 | 10^181182+383973 | 181183 | Patrick De Geest | 04/2016 |
| 3523 | 10^181182-21 | 181182 | Serge Batalov | 12/2014 |
| 3524 | (797*10^181171-41)/9 | 181173 | Robert Price | 04/2022 |
| 3525 | 33385^40046-40046^33385 | 181151 | Norbert Schneider | 02/2026 |
| 3526 | 2^601722+74209 | 181137 | Enzo Doria | 08/2023 |
| 3527 | (5*10^181127-29)/3 | 181128 | Robert Price | 03/2018 |
| 3528 | 2^601521-29143 | 181076 | Enzo Doria | 07/2015 |
| 3529 | 2^601442-2797811 | 181053 | Enzo Doria | 04/2016 |
| 3530 | 44*10^181029+3 | 181031 | Robert Price | 04/2020 |
| 3531 | 5*10^180992-9 | 180993 | Robert Price | 05/2015 |
| 3532 | 10^180979+79477 | 180980 | Patrick De Geest | 04/2016 |
| 3533 | 10^180979+107739 | 180980 | Patrick De Geest | 04/2016 |
| 3534 | 10^180979-11 | 180979 | Serge Batalov | 12/2014 |
| 3535 | 2^601023-113851 | 180926 | Enzo Doria | 10/2014 |
| 3536 | (23*10^180862-143)/3 | 180863 | Robert Price | 12/2019 |
| 3537 | 3*10^180852+29 | 180853 | Robert Price | 05/2018 |
| 3538 | (277*10^180782-7)/9 | 180784 | Robert Price | 02/2022 |
| 3539 | 2^600412+29851 | 180743 | Enzo Doria | 03/2024 |
| 3540 | (8*10^180725-629)/9 | 180725 | Robert Price | 01/2022 |
| 3541 | (79*10^180710-1)/3 | 180712 | Robert Price | 02/2020 |
| 3542 | 2^600300-1852559 | 180709 | Enzo Doria | 08/2015 |
| 3543 | (2*10^180706-77)/3 | 180706 | Robert Price | 02/2021 |
| 3544 | (156^82393-1)/155 | 180696 | Anonymous | 06/2024 |
| 3545 | (10^180689+71)/9 | 180689 | Serge Batalov | 07/2015 |
| 3546 | 2^600209+76487 | 180681 | Enzo Doria | 05/2016 |
| 3547 | 2^599999+378461 | 180618 | Norman Luhn | 09/2023 |
| 3548 | (8*10^180536-269)/9 | 180536 | Robert Price | 09/2021 |
| 3549 | 2^599702-369885 | 180529 | Enzo Doria | 11/2013 |
| 3550 | Tau(643^11688) | 180524 | Nik Lygeros / Olivier Rozier | 05/2015 |
| 3551 | (2951*29^123418-3)/4 | 180490 | Curtis Bright | 05/2015 |
| 3552 | (29*10^180432-17)/3 | 180433 | Robert Price | 09/2019 |
| 3553 | 4*10^180360+93 | 180361 | Robert Price | 08/2018 |
| 3554 | 2^599035+219323 | 180328 | Enzo Doria | 03/2024 |
| 3555 | 2^598942+80779 | 180300 | Enzo Doria | 07/2016 |
| 3556 | (38*10^180296+403)/9 | 180297 | Robert Price | 10/2018 |
| 3557 | (85*10^180241+77)/9 | 180242 | Robert Price | 07/2022 |
| 3558 | 2^598591-1844797 | 180194 | Enzo Doria | 06/2015 |
| 3559 | (100^90089+1)/101 | 180176 | Paul Bourdelais | 08/2017 |
| 3560 | Phi(90089,-100) | 180176 | Henri Lifchitz | 12/2025 |
| 3561 | 2^598301+28517 | 180107 | Enzo Doria | 01/2024 |
| 3562 | (29*10^180072+691)/9 | 180073 | Robert Price | 08/2021 |
| 3563 | (59*10^180038+157)/9 | 180039 | Robert Price | 12/2021 |
| 3564 | 95*10^180019-9 | 180021 | Robert Price | 01/2022 |
| 3565 | 6*10^179970+91 | 179971 | Robert Price | 05/2019 |
| 3566 | (4*10^179963-79)/3 | 179964 | Robert Price | 02/2018 |
| 3567 | (403*10^179944-43)/9 | 179946 | Robert Price | 06/2021 |
| 3568 | Gamma-Prime(179849) | 179849 | Eric W. Weisstein | 06/2011 |
| 3569 | 2^597424-1859729 | 179843 | Enzo Doria | 11/2015 |
| 3570 | Phi(180683,10) | 179760 | Maksym Voznyy | 09/2015 |
| 3571 | (10^180683-1)*9/(10^643-1)/(10^281-1) | 179760 | Robert Price | 07/2016 |
| 3572 | (3^376657-2^376657)/22301107657 | 179701 | Mike Oakes | 04/2017 |
| 3573 | (29*10^179697+223)/9 | 179698 | Robert Price | 09/2018 |
| 3574 | U(1289697) | 179687 | Serge Batalov | 07/2024 |
| 3576 | 2^596884+73 | 179680 | Stefano Morozzi | 04/2021 |
| 3575 | (11*10^179679+13)/3 | 179680 | Robert Price | 03/2022 |
| 3577 | (68*10^179656+7)/3 | 179658 | Robert Price | 01/2020 |
| 3578 | 26952^40547-40547^26952 | 179648 | Norbert Schneider | 01/2026 |
| 3579 | (10^179643+173)/3 | 179643 | Robert Price | 05/2021 |
| 3580 | 2^596690-461261 | 179622 | Enzo Doria | 07/2015 |
| 3581 | 2^596684-113939 | 179620 | Enzo Doria | 10/2014 |
| 3582 | 2^596642+39 | 179608 | Jon Grantham | 08/2023 |
| 3583 | 2*10^179602+63 | 179603 | Robert Price | 05/2018 |
| 3584 | 3^376380+531440 | 179579 | Alfred Reich | 03/2026 |
| 3585 | 32262^39815-39815^32262 | 179514 | Frank Doornink | 02/2024 |
| 3586 | (25*10^179488-403)/9 | 179489 | Robert Price | 01/2021 |
| 3587 | 7*10^179460+99 | 179461 | Robert Price | 05/2021 |
| 3588 | 2^596127+74333 | 179453 | Enzo Doria | 07/2023 |
| 3589 | 3^375887-112696 | 179344 | Enzo Doria | 07/2014 |
| 3590 | 4*10^179265-71 | 179266 | Robert Price | 12/2018 |
| 3591 | 2*10^179193+83 | 179194 | Robert Price | 12/2021 |
| 3592 | 2^595144-1850429 | 179157 | Enzo Doria | 08/2015 |
| 3593 | 2^595122-5 | 179150 | Stefano Morozzi | 07/2022 |
| 3594 | 3*10^179138+89 | 179139 | Robert Price | 10/2018 |
| 3595 | (52*10^179062-133)/9 | 179063 | Robert Price | 09/2021 |
| 3596 | 2^594531+82253 | 178972 | Enzo Doria | 09/2016 |
| 3597 | (664*10^178939-61)/9 | 178941 | Robert Price | 09/2021 |
| 3598 | 2^594260-2787899 | 178891 | Enzo Doria | 11/2015 |
| 3599 | (14*10^178822+67)/9 | 178823 | Robert Price | 05/2022 |
| 3600 | (29*10^178732-119)/9 | 178733 | Robert Price | 12/2021 |
| 3601 | 2^593631+101381 | 178701 | Jorge Menendez | 04/2018 |
| 3602 | 10^178695+136719 | 178696 | Patrick De Geest | 05/2016 |
| 3603 | 10^178695-71 | 178695 | Serge Batalov | 12/2014 |
| 3604 | (2*10^178649-161)/3 | 178649 | Robert Price | 12/2020 |
| 3605 | (691^62903-1)/690 | 178609 | Michael Stocker | 05/2020 |
| 3606 | (2^148330+1)^4-2 | 178608 | Cletus Emmanuel | 12/2003 |
| 3607 | 2^593242+28309 | 178584 | Enzo Doria | 01/2024 |
| 3608 | 2^593222-14145 | 178578 | Jorge Menendez | 10/2017 |
| 3609 | 7*10^178566+33 | 178567 | Robert Price | 06/2020 |
| 3610 | 2^593178+1867219 | 178565 | Enzo Doria | 03/2016 |
| 3611 | 2^593152+22441 | 178557 | Enzo Doria | 09/2023 |
| 3612 | (38*10^178456+151)/9 | 178457 | Robert Price | 03/2022 |
| 3613 | (302*10^178369+13)/9 | 178371 | Robert Price | 02/2020 |
| 3614 | (26*10^178296-113)/3 | 178297 | Robert Price | 06/2020 |
| 3615 | (18^142031-1)/17 | 178287 | Paul Bourdelais | 03/2010 |
| 3616 | (13*10^178233+137)/3 | 178234 | Robert Price | 06/2021 |
| 3617 | (5*10^178206+91)/3 | 178207 | Robert Price | 04/2018 |
| 3618 | 2^591872-291929 | 178172 | Enzo Doria | 07/2015 |
| 3619 | 2^591682-286871 | 178115 | Enzo Doria | 07/2015 |
| 3620 | (7^210761-5^210761)/2 | 178114 | Jon Grantham | 08/2023 |
| 3621 | 4*10^178091+9 | 178092 | Robert Price | 05/2015 |
| 3622 | 2^591435+335931 | 178040 | Enzo Doria | 09/2024 |
| 3623 | Phi(148280,2^11) | 178018 | Henri Lifchitz | 12/2025 |
| 3624 | 410747#+478483 | 178007 | Makoto Morimoto | 02/2016 |
| 3625 | 3*10^177872+73 | 177873 | Robert Price | 08/2018 |
| 3626 | 2^590762-396765 | 177838 | Enzo Doria | 08/2013 |
| 3627 | (136*10^177754-1)/9 | 177756 | Serge Batalov | 12/2014 |
| 3628 | ReverseConsecutiveIntegerPrime(37765) | 177719 | Eric W. Weisstein | 04/2010 |
| 3629 | Smr(37765) | 177719 | Eric W. Weisstein | 12/2021 |
| 3630 | 598^128^209+209^128^598 | 177594 | Henri Lifchitz | 03/2025 |
| 3631 | (266*10^177577-11)/3 | 177579 | Robert Price | 04/2020 |
| 3632 | Phi(100093,2^7) | 177512 | Henri Lifchitz | 10/2025 |
| 3633 | (11*10^177466-113)/3 | 177467 | Robert Price | 10/2018 |
| 3634 | 3*10^177373-97 | 177374 | Robert Price | 07/2018 |
| 3635 | 2^589204+1881151 | 177369 | Enzo Doria | 11/2016 |
| 3636 | 2^589132-69479 | 177347 | Enzo Doria | 01/2016 |
| 3637 | (3^371666)/(371666^3) | 177314 | Henri Lifchitz | 05/2025 |
| 3638 | (101*10^177302-17)/3 | 177304 | Robert Price | 02/2020 |
| 3639 | 2^588912-113519 | 177281 | Enzo Doria | 08/2014 |
| 3640 | (682*10^177266-7)/9 | 177268 | Robert Price | 08/2021 |
| 3641 | 15^150706+2 | 177245 | Robert Price | 06/2015 |
| 3642 | 2^588403+335931 | 177127 | Enzo Doria | 09/2024 |
| 3643 | (31208^39601-1)/(31208^199-1) | 177084 | Ryan Propper | 11/2023 |
| 3644 | 2^588194-1861001 | 177065 | Enzo Doria | 11/2015 |
| 3645 | 5*10^177016-37 | 177017 | Robert Price | 11/2021 |
| 3646 | fibonacci(846926)-4 | 176997 | Jon Grantham | 08/2023 |
| 3647 | (23*10^176964-47)/3 | 176965 | Robert Price | 09/2019 |
| 3648 | 20530^41031+41031^20530 | 176942 | Norbert Schneider | 07/2022 |
| 3649 | (19*10^176932+521)/9 | 176933 | Robert Price | 05/2018 |
| 3650 | (8*10^176908+43)/3 | 176909 | Robert Price | 06/2018 |
| 3651 | Phi(146979,2^7) | 176905 | Henri Lifchitz | 10/2025 |
| 3652 | Phi(342951,2^3) | 176905 | Henri Lifchitz | 12/2025 |
| 3653 | (85*10^176900+203)/9 | 176901 | Robert Price | 09/2020 |
| 3654 | 2^587560-113699 | 176874 | Enzo Doria | 09/2014 |
| 3655 | 20596^40995+40995^20596 | 176844 | Norbert Schneider | 07/2022 |
| 3656 | (101*10^176815-17)/3 | 176817 | Robert Price | 02/2020 |
| 3657 | (25*10^176715-37)/3 | 176716 | Robert Price | 10/2019 |
| 3658 | 5^252763-12862 | 176674 | Enzo Doria | 05/2014 |
| 3659 | 38442^38531+38531^38442 | 176658 | Norbert Schneider | 09/2022 |
| 3660 | 2^586829+23961 | 176654 | Enzo Doria | 10/2023 |
| 3661 | 2^586804+81721 | 176646 | Enzo Doria | 08/2016 |
| 3662 | (10^176584+77)/3 | 176584 | Robert Price | 01/2018 |
| 3663 | 2^586570+1874419 | 176576 | Enzo Doria | 06/2016 |
| 3664 | (157*10^176482-1)/3 | 176484 | Robert Price | 01/2022 |
| 3665 | 5*2^586202+3 | 176466 | Jon Grantham | 07/2023 |
| 3666 | 27122^39799-39799^27122 | 176442 | Frank Doornink | 01/2024 |
| 3667 | 2^585994-3311 | 176402 | Yves Minet | 12/2014 |
| 3668 | 8*10^176383-81 | 176384 | Robert Price | 02/2021 |
| 3669 | (23*10^176357+61)/3 | 176358 | Robert Price | 01/2022 |
| 3670 | 2^585832-112799 | 176354 | Enzo Doria | 07/2014 |
| 3671 | 128^83686+127 | 176344 | Alfred Reich | 06/2026 |
| 3672 | fibonacci(843383)+4 | 176257 | Jon Grantham | 08/2023 |
| 3673 | (29*10^176240+49)/3 | 176241 | Robert Price | 09/2021 |
| 3674 | (2^585387-11)/3 | 176219 | Stefano Morozzi | 08/2022 |
| 3675 | 2^585336-461039 | 176204 | Enzo Doria | 06/2015 |
| 3676 | (25*10^176164+143)/3 | 176165 | Robert Price | 08/2020 |
| 3677 | 2^585095-1848127 | 176132 | Enzo Doria | 08/2015 |
| 3678 | (5*10^176101-311)/9 | 176101 | Robert Price | 12/2021 |
| 3679 | 6*10^176092+77 | 176093 | Robert Price | 06/2020 |
| 3680 | 2^584950-115451 | 176088 | Enzo Doria | 07/2015 |
| 3681 | (646*10^176044+11)/9 | 176046 | Robert Price | 10/2021 |
| 3682 | (7^208283-5^208283)/2 | 176020 | Jon Grantham | 08/2023 |
| 3683 | 2^584671-3697 | 176004 | Yves Minet | 03/2017 |
| 3684 | (13*10^175965-37)/3 | 175966 | Robert Price | 01/2019 |
| 3685 | 31728^39089-39089^31728 | 175957 | Frank Doornink | 01/2024 |
| 3686 | 2*10^175860-87 | 175861 | Robert Price | 04/2018 |
| 3687 | 27009^39670-39670^27009 | 175798 | Frank Doornink | 01/2024 |
| 3688 | (86*10^175774-221)/9 | 175775 | Robert Price | 09/2019 |
| 3689 | 2^583614+216037 | 175686 | Enzo Doria | 11/2023 |
| 3690 | 9*10^175654+47 | 175655 | Robert Price | 01/2022 |
| 3691 | 25430^39869-39869^25430 | 175637 | Frank Doornink | 01/2024 |
| 3692 | 10^175608+2971 | 175609 | Mike Oakes | 05/2010 |
| 3693 | 10^175608-55829 | 175608 | Patrick De Geest | 09/2013 |
| 3694 | 2^583051+1879793 | 175516 | Enzo Doria | 09/2016 |
| 3695 | (76*10^175514+491)/9 | 175515 | Robert Price | 10/2021 |
| 3697 | 2^582860-23829 | 175459 | Enzo Doria | 08/2013 |
| 3696 | (200^76253-1)/199 | 175459 | Anonymous | 06/2024 |
| 3698 | (8*10^175428-53)/9 | 175428 | Serge Batalov | 11/2022 |
| 3699 | (28*10^175417-67)/3 | 175418 | Robert Price | 10/2020 |
| 3700 | 2^582670-23913 | 175402 | Enzo Doria | 08/2013 |
| 3701 | 2^582573-29563 | 175372 | Enzo Doria | 08/2015 |
| 3702 | 2^582435-1862767 | 175331 | Enzo Doria | 12/2015 |
| 3703 | 10^175295-40000001 | 175295 | Robert Price | 07/2022 |
| 3704 | 31093^39018-39018^31093 | 175295 | Frank Doornink | 01/2024 |
| 3705 | (11*10^175250-149)/3 | 175251 | Robert Price | 09/2018 |
| 3706 | (29*10^175236+31)/3 | 175237 | Robert Price | 04/2021 |
| 3707 | 2^582072-1848599 | 175222 | Enzo Doria | 08/2015 |
| 3708 | (404267#+465)/(3^4*5^2*31) | 175208 | Makoto Morimoto | 06/2019 |
| 3709 | Phi(262767,10)/259613797 | 175168 | Makoto Kamada | 12/2022 |
| 3710 | (2^581871-15)/7 | 175160 | Stefano Morozzi | 08/2022 |
| 3711 | (5*10^175117-311)/9 | 175117 | Robert Price | 12/2021 |
| 3712 | 31193^38966-38966^31193 | 175116 | Frank Doornink | 01/2024 |
| 3713 | 2^581695+225893 | 175108 | Enzo Doria | 08/2024 |
| 3714 | 10^175093-89 | 175093 | Riley Fisher | 10/2023 |
| 3715 | (220221^32768+1)/2 | 175075 | Serge Batalov | 03/2018 |
| 3716 | 2^581560+1874911 | 175068 | Enzo Doria | 06/2016 |
| 3717 | (25*10^174987-97)/9 | 174988 | Robert Price | 01/2022 |
| 3718 | (75^93307-1)/74 | 174955 | Paul Bourdelais | 09/2017 |
| 3719 | 26446^39555-39555^26446 | 174927 | Frank Doornink | 03/2024 |
| 3720 | 31522^38883-38883^31522 | 174920 | Frank Doornink | 01/2024 |
| 3721 | (27398^39601-1)/(27398^199-1) | 174855 | Ryan Propper | 11/2023 |
| 3722 | (861^59557-1)/860 | 174798 | Jinyuan Wang | 11/2023 |
| 3723 | 31492^38859-38859^31492 | 174796 | Frank Doornink | 01/2024 |
| 3724 | (47*10^174790+493)/9 | 174791 | Robert Price | 03/2019 |
| 3725 | 2^580528-114035 | 174757 | Enzo Doria | 11/2014 |
| 3726 | (19*10^174754+737)/9 | 174755 | Robert Price | 07/2018 |
| 3727 | V(1045270)/4181081/12543241/81333115129561 | 174730 | Serge Batalov | 07/2024 |
| 3728 | (35*10^174704-377)/9 | 174705 | Robert Price | 07/2018 |
| 3729 | 23181^40018-40018^23181 | 174684 | Norbert Schneider | 07/2025 |
| 3731 | (49*10^174681+293)/9 | 174682 | Robert Price | 03/2021 |
| 3730 | 6*10^174681+11 | 174682 | Robert Price | 07/2022 |
| 3732 | 3*10^174665-97 | 174666 | Robert Price | 07/2018 |
| 3733 | 2^580046-459161 | 174612 | Enzo Doria | 05/2015 |
| 3734 | 2^579992-39779 | 174595 | Enzo Doria | 09/2015 |
| 3735 | 25613^39582-39582^25613 | 174496 | Frank Doornink | 02/2024 |
| 3736 | (29*10^174481-149)/3 | 174482 | Robert Price | 08/2022 |
| 3737 | (4*10^174423+101)/3 | 174424 | Robert Price | 11/2021 |
| 3738 | (2^579371-17)/3 | 174408 | Stefano Morozzi | 08/2022 |
| 3739 | (2*10^174301-71)/3 | 174301 | Robert Price | 12/2017 |
| 3740 | 14^152048+3 | 174267 | Paul Bourdelais | 12/2020 |
| 3741 | (2^578696+1)/257 | 174203 | Lelio R Paula | 09/2015 |
| 3742 | 2^578656-1851809 | 174193 | Enzo Doria | 08/2015 |
| 3743 | 2^578583-113917 | 174171 | Enzo Doria | 10/2014 |
| 3744 | 2^578434-83 | 174126 | Yves Minet | 07/2017 |
| 3745 | 15^148048-2 | 174118 | Robert Price | 06/2015 |
| 3746 | 5*10^174101+81 | 174102 | Robert Price | 03/2019 |
| 3747 | 2^578346+2794249 | 174100 | Enzo Doria | 03/2016 |
| 3748 | 10^173947+1372429 | 173948 | Patrick De Geest | 08/2021 |
| 3750 | 10^173947-500000001 | 173947 | Robert Price | 12/2020 |
| 3749 | 10^173947-286391 | 173947 | Patrick De Geest | 08/2021 |
