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 | 2^415290-113591 | 125015 | Enzo Doria | 08/2014 |
| 3502 | 2^415276-460919 | 125011 | Enzo Doria | 06/2015 |
| 3503 | 2^415259+77243 | 125006 | Enzo Doria | 05/2016 |
| 3504 | (67*10^124990+77)/9 | 124991 | Robert Price | 10/2021 |
| 3505 | 2^415144-3683 | 124971 | Yves Minet | 10/2011 |
| 3506 | 2^415092+111546435 | 124956 | Paul Bourdelais | 10/2021 |
| 3507 | 31936^8173+8173^31936 | 124946 | Hans Havermann | 03/2021 |
| 3508 | 5^178715-4 | 124916 | Tyler NeSmith | 07/2021 |
| 3509 | 29767^15700+15700^29767 | 124900 | Hans Havermann | 03/2021 |
| 3510 | 2^414874+79 | 124890 | Lelio R Paula | 01/2015 |
| 3511 | (2^414765+7)/1389 | 124854 | Lelio R Paula | 05/2014 |
| 3512 | 2^414618+79459 | 124813 | Enzo Doria | 06/2016 |
| 3513 | (61*10^124809-1)/3 | 124811 | Robert Price | 01/2020 |
| 3514 | (29*10^124765-71)/3 | 124766 | Robert Price | 07/2021 |
| 3515 | 2^414432-1846709 | 124757 | Enzo Doria | 07/2015 |
| 3516 | 2*10^124751-51 | 124752 | Robert Price | 04/2018 |
| 3517 | (56*10^124735+367)/9 | 124736 | Robert Price | 06/2019 |
| 3518 | (13*2^414274-1)/153 | 124708 | Lelio R Paula | 05/2014 |
| 3519 | 56*10^124656-3 | 124658 | Robert Price | 03/2020 |
| 3520 | (7*10^124648+197)/3 | 124649 | Robert Price | 07/2018 |
| 3522 | 2^414032-5 | 124637 | Henri Lifchitz | 07/2006 |
| 3521 | 2^414032+1872331 | 124637 | Enzo Doria | 05/2016 |
| 3523 | 37373^2158+2158^37373 | 124604 | Hans Havermann | 03/2021 |
| 3524 | 29811^15112+15112^29811 | 124590 | Hans Havermann | 03/2021 |
| 3525 | 14120^30009-30009^14120 | 124533 | Norbert Schneider | 02/2015 |
| 3526 | 29757^15296+15296^29757 | 124521 | Hans Havermann | 03/2021 |
| 3527 | 35056^3561+3561^35056 | 124504 | Hans Havermann | 03/2021 |
| 3528 | 40588^1167+1167^40588 | 124487 | Hans Havermann | 02/2021 |
| 3529 | (85*10^124485-49)/9 | 124486 | Robert Price | 12/2020 |
| 3530 | 64^68909-63^68909 | 124463 | Robert Price | 07/2013 |
| 3531 | 35016^3581+3581^35016 | 124448 | Hans Havermann | 03/2021 |
| 3532 | 2^413387+76253 | 124442 | Enzo Doria | 04/2016 |
| 3533 | 28749^21298+21298^28749 | 124436 | Hans Havermann | 03/2021 |
| 3534 | 2^413352+524287 | 124432 | Paul Underwood | 09/2018 |
| 3535 | 287117#+391613 | 124424 | Nicolas PALAU | 01/2017 |
| 3536 | (4*10^124420+83)/3 | 124421 | Robert Price | 02/2018 |
| 3537 | 34578^3965+3965^34578 | 124421 | Hans Havermann | 03/2021 |
| 3538 | (68*10^124392-329)/9 | 124393 | Robert Price | 03/2021 |
| 3539 | (27*2^413207-1)/108335 | 124385 | Lelio R Paula | 05/2014 |
| 3540 | 10^124383+58407 | 124384 | Patrick De Geest | 08/2021 |
| 3542 | 10^124383-8000001 | 124383 | Robert Price | 04/2021 |
| 3541 | 10^124383-5801 | 124383 | Patrick De Geest | 08/2021 |
| 3543 | (41*10^124335-383)/9 | 124336 | Robert Price | 11/2018 |
| 3544 | (304*10^124329-43)/9 | 124331 | Robert Price | 02/2020 |
| 3545 | 34716^3811+3811^34716 | 124320 | Hans Havermann | 03/2021 |
| 3546 | 2^412868-120599 | 124286 | Paul Bourdelais | 02/2012 |
| 3547 | 10^124248+899089 | 124249 | Patrick De Geest | 05/2021 |
| 3549 | 10^124248-1000001 | 124248 | Robert Price | 08/2020 |
| 3548 | 10^124248-501903 | 124248 | Patrick De Geest | 05/2021 |
| 3550 | 45^75145-2 | 124231 | Lelio R Paula | 08/2015 |
| 3551 | 29901^14272+14272^29901 | 124224 | Hans Havermann | 03/2021 |
| 3552 | 2^412645-112213 | 124219 | Enzo Doria | 06/2014 |
| 3553 | 29837^14500+14500^29837 | 124163 | Hans Havermann | 03/2021 |
| 3554 | 28074^26455+26455^28074 | 124158 | Hans Havermann | 03/2021 |
| 3555 | 2^412248+74611 | 124100 | Enzo Doria | 04/2016 |
| 3556 | (22*10^124096-13)/9 | 124097 | Robert Price | 06/2018 |
| 3557 | (455*10^124093+31)/9 | 124095 | Robert Price | 06/2021 |
| 3558 | 2^412192-3329 | 124083 | Yves Minet | 12/2014 |
| 3559 | (25*2^412191-1)/23 | 124082 | Lelio R Paula | 05/2014 |
| 3561 | (25*10^124076-67)/3 | 124077 | Robert Price | 06/2019 |
| 3560 | 28132^25735+25735^28132 | 124077 | Hans Havermann | 03/2021 |
| 3562 | F(593689) | 124074 | Henri Lifchitz | 01/2005 |
| 3563 | (11*2^412161+1)/19 | 124073 | Lelio R Paula | 05/2014 |
| 3564 | 35364^3215+3215^35364 | 124028 | Hans Havermann | 03/2021 |
| 3566 | (266*10^124022-11)/3 | 124024 | Robert Price | 04/2020 |
| 3565 | 29987^13674+13674^29987 | 124024 | Hans Havermann | 03/2021 |
| 3567 | 2^411932-111546435 | 124004 | Paul Bourdelais | 10/2021 |
| 3568 | 2^411884-113279 | 123990 | Enzo Doria | 07/2014 |
| 3569 | (2^411832+1)/257 | 123972 | Lelio R Paula | 05/2014 |
| 3570 | (2^411833+2)/514 | 123972 | Stefano Morozzi | 03/2020 |
| 3571 | (26*10^123970-89)/9 | 123971 | Robert Price | 06/2018 |
| 3572 | 2^411790-1853531 | 123962 | Enzo Doria | 08/2015 |
| 3573 | (5^177337+1)/6 | 123953 | Paul Bourdelais | 11/2008 |
| 3574 | 2^411711-113257 | 123938 | Enzo Doria | 07/2014 |
| 3575 | (23*2^411675-1)/3 | 123928 | Lelio R Paula | 05/2014 |
| 3576 | 36289^2598+2598^36289 | 123914 | Hans Havermann | 03/2021 |
| 3577 | (11*10^123899-179)/3 | 123900 | Robert Price | 09/2018 |
| 3578 | 32276^6879+6879^32276 | 123860 | Hans Havermann | 02/2021 |
| 3579 | 2^411325-351103 | 123822 | Enzo Doria | 06/2015 |
| 3580 | (646*10^123817+11)/9 | 123819 | Robert Price | 10/2021 |
| 3581 | 30738^10643+10643^30738 | 123784 | Hans Havermann | 03/2021 |
| 3582 | 31074^9607+9607^31074 | 123755 | Hans Havermann | 03/2021 |
| 3583 | 2^411052+1872481 | 123739 | Enzo Doria | 05/2016 |
| 3584 | 34365^3986+3986^34365 | 123733 | Hans Havermann | 03/2021 |
| 3585 | 2^410997+39 | 123723 | Lelio R Paula | 05/2014 |
| 3586 | (649^43987-1)/648 | 123700 | Michael Stocker | 05/2020 |
| 3587 | (148*10^123688-1)/3 | 123690 | Robert Price | 03/2020 |
| 3588 | 36825^2284+2284^36825 | 123684 | Hans Havermann | 03/2021 |
| 3589 | 29582^15171+15171^29582 | 123683 | Hans Havermann | 03/2021 |
| 3590 | 10^123671+3593037 | 123672 | Paul Bourdelais | 10/2021 |
| 3591 | 8*10^123657+87 | 123658 | Robert Price | 10/2019 |
| 3592 | 30505^11302+11302^30505 | 123642 | Hans Havermann | 03/2021 |
| 3593 | 29956^13401+13401^29956 | 123633 | Hans Havermann | 03/2021 |
| 3594 | 155^56438+154 | 123618 | Norbert Schneider | 01/2019 |
| 3595 | 2^410596-39 | 123602 | Lelio R Paula | 05/2014 |
| 3596 | (41*10^123600-221)/9 | 123601 | Robert Price | 10/2021 |
| 3597 | 28995^18302+18302^28995 | 123592 | Hans Havermann | 03/2021 |
| 3598 | 28302^23269+23269^28302 | 123589 | Hans Havermann | 03/2021 |
| 3599 | 2^410540-115079 | 123585 | Enzo Doria | 06/2015 |
| 3600 | (7*10^123563+107)/3 | 123564 | Robert Price | 02/2018 |
| 3601 | 9*10^123549+89 | 123550 | Robert Price | 11/2019 |
| 3602 | (197*10^123545+7)/3 | 123547 | Robert Price | 12/2020 |
| 3603 | (3*2^410392-1)/9229 | 123537 | Lelio R Paula | 05/2014 |
| 3604 | (29*10^123510+277)/9 | 123511 | Robert Price | 11/2021 |
| 3605 | 28118^24687+24687^28118 | 123508 | Hans Havermann | 03/2021 |
| 3606 | 39994^1225+1225^39994 | 123507 | Hans Havermann | 03/2021 |
| 3607 | 2^410206-113081 | 123485 | Enzo Doria | 07/2014 |
| 3608 | (25*2^410192+1)/10397 | 123478 | Lelio R Paula | 04/2014 |
| 3609 | 28974^18215+18215^28974 | 123442 | Hans Havermann | 03/2021 |
| 3610 | 28901^18618+18618^28901 | 123406 | Hans Havermann | 03/2021 |
| 3611 | 2^409909-189 | 123395 | Enzo Doria | 05/2014 |
| 3612 | 2^409896-109043 | 123391 | Enzo Doria | 04/2014 |
| 3613 | 2^409890+75409 | 123390 | Enzo Doria | 04/2016 |
| 3614 | 81254^33+33^81254 | 123386 | Hans Havermann | 03/2021 |
| 3615 | 33463^4854+4854^33463 | 123348 | Hans Havermann | 03/2021 |
| 3616 | 34061^4182+4182^34061 | 123348 | Hans Havermann | 03/2021 |
| 3617 | 133^58076-2 | 123345 | Lelio R Paula | 10/2017 |
| 3618 | F(590041) | 123311 | Henri Lifchitz | 01/2005 |
| 3619 | 2^409566-113501 | 123292 | Enzo Doria | 08/2014 |
| 3620 | 2^409533+77747 | 123282 | Enzo Doria | 05/2016 |
| 3621 | 2^409436-112799 | 123253 | Enzo Doria | 06/2014 |
| 3622 | 28212^23321+23321^28212 | 123223 | Hans Havermann | 03/2021 |
| 3623 | 2^409225+1873787 | 123189 | Enzo Doria | 06/2016 |
| 3624 | 2^409174+73009 | 123174 | Enzo Doria | 04/2016 |
| 3625 | 2^409058-112685 | 123139 | Enzo Doria | 06/2014 |
| 3626 | (13*10^123137-61)/3 | 123138 | Robert Price | 11/2018 |
| 3627 | 4*10^123113+21 | 123114 | Robert Price | 12/2018 |
| 3628 | 2^408778+77689 | 123055 | Enzo Doria | 05/2016 |
| 3629 | 2^408690-75 | 123028 | Lelio R Paula | 11/2013 |
| 3630 | 28327^22032+22032^28327 | 123026 | Hans Havermann | 03/2021 |
| 3631 | (29*10^122996+673)/9 | 122997 | Robert Price | 12/2018 |
| 3632 | (65*10^122994-101)/9 | 122995 | Robert Price | 01/2022 |
| 3633 | 2^408574-2787341 | 122994 | Enzo Doria | 03/2016 |
| 3634 | 3*10^122977+37 | 122978 | Robert Price | 08/2018 |
| 3635 | (7*10^122976-67)/3 | 122977 | Robert Price | 10/2021 |
| 3636 | Phi(157825,10) | 122961 | Maksym Voznyy | 06/2015 |
| 3637 | (68*10^122933-419)/9 | 122934 | Robert Price | 07/2019 |
| 3638 | 29712^13721+13721^29712 | 122931 | Hans Havermann | 03/2021 |
| 3639 | (13*2^408283+1)/1665 | 122904 | Lelio R Paula | 05/2014 |
| 3640 | (266*10^122872-17)/3 | 122874 | Robert Price | 07/2020 |
| 3641 | (16*10^122871+77)/3 | 122872 | Robert Price | 03/2019 |
| 3642 | 30395^11022+11022^30395 | 122865 | Hans Havermann | 03/2021 |
| 3643 | (10^122857+167)/3 | 122857 | Robert Price | 05/2021 |
| 3644 | 33331^4852+4852^33331 | 122856 | Hans Havermann | 03/2021 |
| 3645 | (11*2^408100-1)/35 | 122850 | Lelio R Paula | 04/2014 |
| 3646 | (19*10^122836-43)/3 | 122837 | Robert Price | 05/2019 |
| 3647 | 28420^20969+20969^28420 | 122820 | Hans Havermann | 03/2021 |
| 3648 | (16*10^122818+179)/3 | 122819 | Robert Price | 11/2021 |
| 3649 | 29865^12934+12934^29865 | 122797 | Hans Havermann | 03/2021 |
| 3650 | (2^407821-lucasV(1,2,407821)+1)/2 | 122767 | Mike Oakes | 11/2016 |
| 3651 | (32*10^122733-77)/9 | 122734 | Robert Price | 06/2018 |
| 3652 | (21*2^407604-1)/215 | 122701 | Lelio R Paula | 04/2014 |
| 3654 | (22*10^122681+161)/3 | 122682 | Robert Price | 05/2019 |
| 3653 | 29513^14350+14350^29513 | 122682 | Hans Havermann | 03/2021 |
| 3655 | (21*2^407433-1)/13 | 122650 | Lelio R Paula | 04/2014 |
| 3656 | (26*10^122625-131)/3 | 122626 | Robert Price | 10/2019 |
| 3657 | 27925^24562+24562^27925 | 122599 | Hans Havermann | 03/2021 |
| 3658 | (73*10^122592-1)/9 | 122593 | Robert Price | 01/2015 |
| 3659 | (5*10^122592+91)/3 | 122593 | Robert Price | 04/2018 |
| 3660 | 36751^2166+2166^36751 | 122589 | Hans Havermann | 03/2021 |
| 3661 | (85*10^122585-1)/3 | 122587 | Robert Price | 02/2020 |
| 3662 | 29368^14931+14931^29368 | 122585 | Hans Havermann | 03/2021 |
| 3663 | 2^407179-112075 | 122574 | Enzo Doria | 06/2014 |
| 3664 | (21*2^407131+1)/207517523 | 122552 | Lelio R Paula | 04/2014 |
| 3665 | (66^67349+1)/67 | 122543 | Paul Bourdelais | 09/2017 |
| 3666 | (646*10^122533+11)/9 | 122535 | Robert Price | 10/2021 |
| 3667 | 2^407008-1867919 | 122522 | Enzo Doria | 04/2016 |
| 3668 | 11^117642-300 | 122512 | Enzo Doria | 10/2012 |
| 3669 | (F(3*97700+1)^2+L(3*97700+1)^2)/2 | 122509 | Henri Lifchitz | 10/2017 |
| 3670 | 2^406949+72197 | 122504 | Enzo Doria | 04/2016 |
| 3671 | (19*10^122501+149)/3 | 122502 | Robert Price | 05/2019 |
| 3672 | 28632^18977+18977^28632 | 122495 | Hans Havermann | 03/2021 |
| 3673 | 31815^7076+7076^31815 | 122481 | Hans Havermann | 03/2021 |
| 3674 | 2^406826-65 | 122467 | Lelio R Paula | 11/2013 |
| 3675 | 2^406821-2797363 | 122466 | Enzo Doria | 04/2016 |
| 3676 | 2^406758-17 | 122447 | Lelio R Paula | 11/2013 |
| 3677 | 29941^12282+12282^29941 | 122437 | Hans Havermann | 03/2021 |
| 3678 | (30^82883-1)/29 | 122427 | Robert Price | 12/2011 |
| 3679 | 27496^27577+27577^27496 | 122422 | Norbert Schneider | 12/2020 |
| 3680 | 28732^18215+18215^28732 | 122411 | Hans Havermann | 03/2021 |
| 3681 | (2^406583-1)/813167 | 122388 | Jens K. Andersen | 02/2009 |
| 3682 | 4*10^122377+19 | 122378 | Robert Price | 10/2018 |
| 3683 | 28227^21634+21634^28227 | 122368 | Hans Havermann | 03/2021 |
| 3684 | Phi(246362,10) | 122365 | Makoto Kamada | 09/2019 |
| 3685 | 3*10^122345-97 | 122346 | Robert Price | 07/2018 |
| 3686 | 97^61575-2 | 122336 | Lelio R Paula | 12/2014 |
| 3687 | 2*10^122319+47 | 122320 | Robert Price | 12/2021 |
| 3688 | 208^52765+52765^208 | 122313 | Norbert Schneider | 11/2020 |
| 3689 | 2^406298+2799109 | 122308 | Enzo Doria | 04/2016 |
| 3690 | 7*10^122294+57 | 122295 | Robert Price | 06/2019 |
| 3691 | (27*2^406241-1)/10277 | 122289 | Lelio R Paula | 04/2014 |
| 3692 | 2^406229-1849993 | 122288 | Enzo Doria | 08/2015 |
| 3693 | 3*10^122274+7 | 122275 | Robert Price | 07/2015 |
| 3694 | 2^406117+1876577 | 122254 | Enzo Doria | 07/2016 |
| 3695 | 29308^14835+14835^29308 | 122253 | Hans Havermann | 03/2021 |
| 3696 | 28119^22268+22268^28119 | 122253 | Hans Havermann | 03/2021 |
| 3697 | 32167^6312+6312^32167 | 122240 | Hans Havermann | 03/2021 |
| 3698 | 3^256199-2^256199 | 122238 | Mike Oakes | 06/2005 |
| 3699 | 27678^26053+26053^27678 | 122223 | Hans Havermann | 03/2021 |
| 3700 | 2^405992-78557 | 122216 | Jorge Menendez | 03/2018 |
| 3701 | (8*10^122203+43)/3 | 122204 | Robert Price | 06/2018 |
| 3702 | (58*10^122170+329)/9 | 122171 | Robert Price | 05/2019 |
| 3703 | 2^405774+179149 | 122151 | Enzo Doria | 06/2016 |
| 3704 | 29189^15246+15246^29189 | 122103 | Hans Havermann | 03/2021 |
| 3706 | 34*10^122082-9 | 122084 | Robert Price | 06/2020 |
| 3705 | 33442^4473+4473^33442 | 122084 | Hans Havermann | 03/2021 |
| 3707 | 5*10^122082+41 | 122083 | Robert Price | 03/2019 |
| 3708 | 31849^6808+6808^31849 | 122078 | Hans Havermann | 03/2021 |
| 3710 | 2^405514-3311 | 122072 | Yves Minet | 12/2014 |
| 3711 | 2^405514-115511 | 122072 | Enzo Doria | 07/2015 |
| 3709 | 23*10^122070-7 | 122072 | Robert Price | 02/2020 |
| 3712 | 2^405422-113261 | 122045 | Enzo Doria | 07/2014 |
| 3713 | 2^405173+71237 | 121970 | Enzo Doria | 04/2016 |
| 3714 | (34*10^121924+191)/9 | 121925 | Robert Price | 08/2021 |
| 3715 | (2^405016+1)/257 | 121920 | Lelio R Paula | 04/2014 |
| 3716 | 28557^18590+18590^28557 | 121918 | Hans Havermann | 03/2021 |
| 3717 | 28641^18002+18002^28641 | 121877 | Hans Havermann | 03/2021 |
| 3718 | 2^404858+71329 | 121875 | Enzo Doria | 04/2016 |
| 3719 | 2^404813-114703 | 121861 | Enzo Doria | 04/2015 |
| 3720 | 2^404764+77791 | 121847 | Enzo Doria | 05/2016 |
| 3721 | 28830^16841+16841^28830 | 121847 | Hans Havermann | 03/2021 |
| 3722 | (4*10^121825+89)/3 | 121826 | Robert Price | 08/2021 |
| 3723 | 317^48694+48694^317 | 121787 | Norbert Schneider | 08/2015 |
| 3724 | 2^404536-115259 | 121778 | Enzo Doria | 06/2015 |
| 3725 | 2^404501-631 | 121767 | Yves Minet | 07/2012 |
| 3726 | 5*10^121764-69 | 121765 | Robert Price | 02/2021 |
| 3727 | 28236^20485+20485^28236 | 121738 | Hans Havermann | 02/2021 |
| 3728 | 63^67620+2 | 121672 | Lelio R Paula | 08/2015 |
| 3729 | (16*10^121633+167)/3 | 121634 | Robert Price | 06/2019 |
| 3730 | 29955^11494+11494^29955 | 121632 | Hans Havermann | 02/2021 |
| 3731 | (17*10^121621+1)/9 | 121622 | Serge Batalov | 05/2010 |
| 3732 | 31088^8163+8163^31088 | 121612 | Hans Havermann | 02/2021 |
| 3733 | (15*2^403912+1)/271 | 121589 | Lelio R Paula | 05/2014 |
| 3734 | (10^121543-79)/3 | 121543 | Robert Price | 01/2018 |
| 3735 | 2^403676+76831 | 121519 | Enzo Doria | 05/2016 |
| 3736 | (7*10^121487+143)/3 | 121488 | Robert Price | 03/2018 |
| 3737 | 27965^22086+22086^27965 | 121484 | Hans Havermann | 02/2021 |
| 3738 | (893*10^121470+7)/9 | 121472 | Robert Price | 06/2021 |
| 3739 | (77*10^121455+67)/9 | 121456 | Robert Price | 12/2021 |
| 3740 | 2^403363-113635 | 121425 | Enzo Doria | 08/2014 |
| 3741 | (17*10^121418-113)/3 | 121419 | Robert Price | 06/2021 |
| 3742 | 2^403336-1861469 | 121417 | Enzo Doria | 03/2016 |
| 3743 | 27929^22186+22186^27929 | 121382 | Hans Havermann | 02/2021 |
| 3744 | p(24442)#/2-64 | 121381 | Robert Price | 04/2017 |
| 3745 | 11^116555-720 | 121380 | Enzo Doria | 11/2012 |
| 3746 | 2^403100-461267 | 121346 | Enzo Doria | 07/2015 |
| 3747 | 2^403093-112213 | 121344 | Enzo Doria | 06/2014 |
| 3748 | 29404^13385+13385^29404 | 121340 | Hans Havermann | 02/2021 |
| 3749 | 28106^20745+20745^28106 | 121332 | Hans Havermann | 02/2021 |
| 3750 | (316^48539+1)/317 | 121330 | Eric Chen | 10/2017 |
