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 | 2^437884-286349 | 131817 | Enzo Doria | 07/2015 |
3502 | 5^188558+4 | 131797 | Tyler NeSmith | 05/2021 |
3503 | (11*10^131784-17)/3 | 131785 | Robert Price | 06/2018 |
3505 | 4*10^131719-93 | 131720 | Robert Price | 07/2020 |
3504 | 31629^14606+14606^31629 | 131720 | Hans Havermann | 04/2021 |
3506 | 3^276062-112292 | 131716 | Enzo Doria | 07/2014 |
3507 | (7*10^131682+89)/3 | 131683 | Robert Price | 08/2020 |
3508 | 29512^28969+28969^29512 | 131681 | Hans Havermann | 03/2021 |
3509 | 2^437343+75953 | 131654 | Enzo Doria | 04/2016 |
3510 | 35^85243-34^85243 | 131621 | Robert Price | 05/2012 |
3511 | (28*10^131586+59)/3 | 131587 | Robert Price | 05/2021 |
3512 | (59*10^131575+391)/9 | 131576 | Robert Price | 03/2021 |
3513 | 39984^1945+1945^39984 | 131505 | Hans Havermann | 03/2021 |
3514 | (203*10^131457+1)/3 | 131459 | Robert Price | 03/2020 |
3515 | 7*10^131421-41 | 131422 | Robert Price | 08/2021 |
3516 | 87309^32+32^87309 | 131414 | Hans Havermann | 03/2021 |
3517 | (68^71713+1)/69 | 131413 | Paul Bourdelais | 09/2017 |
3518 | (650*10^131391+43)/9 | 131393 | Tyler Busby | 01/2023 |
3519 | 2^436451+1884713 | 131385 | Enzo Doria | 03/2017 |
3520 | 2^436365+35 | 131359 | Robert Price | 11/2015 |
3521 | 2^436300+1866871 | 131340 | Enzo Doria | 03/2016 |
3522 | (7*10^131339+179)/3 | 131340 | Robert Price | 09/2018 |
3523 | 14^114592-3 | 131338 | Paul Bourdelais | 12/2020 |
3524 | 36197^4236+4236^36197 | 131285 | Hans Havermann | 04/2021 |
3525 | (37*10^131270+341)/9 | 131271 | Robert Price | 08/2018 |
3526 | 29863^24790+24790^29863 | 131227 | Hans Havermann | 03/2021 |
3527 | (5*10^131223-29)/3 | 131224 | Robert Price | 03/2018 |
3528 | 29524^27825+27825^29524 | 131218 | Hans Havermann | 03/2021 |
3529 | (23*2^435891-1)/699 | 131215 | Lelio R Paula | 07/2015 |
3530 | (11*2^435879+1)/3337 | 131211 | Lelio R Paula | 06/2015 |
3531 | 30639^19136+19136^30639 | 131192 | Hans Havermann | 04/2021 |
3532 | (2^435808+1)/641/6700417 | 131182 | Lelio R Paula | 02/2012 |
3533 | (2^435808+1)/4294967297 | 131182 | Serge Batalov | 12/2016 |
3534 | 2^435773+1875557 | 131181 | Enzo Doria | 06/2016 |
3535 | (16*10^131180+167)/3 | 131181 | Robert Price | 06/2019 |
3536 | (26*10^131180-77)/3 | 131181 | Robert Price | 11/2019 |
3537 | (25*10^131144-7)/9 | 131145 | Robert Price | 05/2018 |
3538 | 29299^29358-29358^29299 | 131138 | Norbert Schneider | 03/2022 |
3539 | 2^435612-2789939 | 131133 | Enzo Doria | 12/2015 |
3540 | 33976^7231+7231^33976 | 131121 | Hans Havermann | 03/2021 |
3541 | 33715^7746+7746^33715 | 131121 | Hans Havermann | 03/2021 |
3542 | 66^72047-65^72047 | 131093 | Robert Price | 09/2013 |
3543 | (5*10^131090+37)/3 | 131091 | Robert Price | 03/2018 |
3544 | 2^435468+75631 | 131089 | Enzo Doria | 04/2016 |
3545 | 37^83588-2 | 131083 | Lelio R Paula | 08/2015 |
3546 | (4^217720+11)/3 | 131081 | Robert Price | 02/2017 |
3547 | 30407^20448+20448^30407 | 131074 | Hans Havermann | 04/2021 |
3548 | (22*10^131070+179)/3 | 131071 | Robert Price | 02/2022 |
3549 | 29487^27836+27836^29487 | 131059 | Hans Havermann | 04/2021 |
3550 | 29962^23615+23615^29962 | 131030 | Hans Havermann | 03/2021 |
3551 | 2^435202-113193 | 131009 | Enzo Doria | 07/2014 |
3552 | 41705^1384+1384^41705 | 131002 | Hans Havermann | 04/2021 |
3553 | 9*10^130998-19 | 130999 | Robert Price | 07/2019 |
3554 | 36243^4108+4108^36243 | 130969 | Hans Havermann | 04/2021 |
3555 | floor((sqrt(5)-1)/2*10^130911) | 130911 | Serge Batalov | 06/2017 |
3556 | 2^434835-111937 | 130899 | Enzo Doria | 05/2014 |
3557 | (62*10^130895-629)/9 | 130896 | Robert Price | 07/2021 |
3558 | 2^434685+72257 | 130854 | Enzo Doria | 04/2016 |
3559 | (7*10^130825+113)/3 | 130826 | Robert Price | 02/2018 |
3560 | 2^434539-29317 | 130810 | Enzo Doria | 07/2015 |
3561 | (74*10^130791+637)/9 | 130792 | Robert Price | 01/2022 |
3562 | 2^434469-114259 | 130789 | Enzo Doria | 01/2015 |
3563 | (5*10^130763+103)/9 | 130763 | Robert Price | 04/2022 |
3564 | 2^434246+33 | 130722 | Robert Price | 11/2015 |
3565 | 30156^21599+21599^30156 | 130710 | Hans Havermann | 04/2021 |
3566 | (17*10^130695-161)/9 | 130695 | Robert Price | 02/2021 |
3567 | 30513^19148+19148^30513 | 130661 | Hans Havermann | 03/2021 |
3568 | 29736^24761+24761^29736 | 130654 | Hans Havermann | 04/2021 |
3569 | 9*10^130638+41 | 130639 | Robert Price | 08/2020 |
3570 | 2^433911-91 | 130621 | Lelio R Paula | 06/2017 |
3571 | 30786^17449+17449^30786 | 130588 | Hans Havermann | 03/2021 |
3572 | 2^433744-114419 | 130570 | Enzo Doria | 02/2015 |
3574 | 2^433708+1869451 | 130560 | Enzo Doria | 05/2016 |
3573 | 2^433710+93 | 130560 | Lelio R Paula | 06/2017 |
3575 | 7*10^130535-27 | 130536 | Robert Price | 11/2022 |
3576 | (9629^32768+1)/120501441265666 | 130520 | Kellen Shenton | 05/2021 |
3577 | (29*2^433547-1)/27 | 130511 | Lelio R Paula | 06/2015 |
3578 | 3^273521+10 | 130503 | Tyler NeSmith | 01/2021 |
3579 | 41659^1356+1356^41659 | 130487 | Hans Havermann | 03/2021 |
3580 | 4*10^130480+9 | 130481 | Robert Price | 05/2015 |
3581 | (23*2^433449-1)/75 | 130481 | Lelio R Paula | 06/2015 |
3582 | (23*2^433334-1)/3731 | 130445 | Lelio R Paula | 06/2015 |
3583 | (31*10^130414-49)/9 | 130415 | Robert Price | 11/2021 |
3584 | 33481^7848+7848^33481 | 130401 | Hans Havermann | 03/2021 |
3585 | (22*10^130392+203)/9 | 130393 | Robert Price | 10/2021 |
3586 | 29773^23950+23950^29773 | 130386 | Hans Havermann | 04/2021 |
3587 | 2^433023-113497 | 130353 | Enzo Doria | 08/2014 |
3588 | 31175^15178+15178^31175 | 130350 | Hans Havermann | 04/2021 |
3589 | 2^433002+1179379 | 130347 | Enzo Doria | 06/2016 |
3590 | 2^432974+19 | 130339 | Robert Price | 08/2015 |
3591 | 31903^12168+12168^31903 | 130331 | Hans Havermann | 04/2021 |
3592 | 29387^27112+27112^29387 | 130278 | Hans Havermann | 04/2021 |
3593 | 29577^25370+25370^29577 | 130267 | Hans Havermann | 04/2021 |
3594 | 31738^12685+12685^31738 | 130231 | Hans Havermann | 03/2021 |
3595 | 44235^878+878^44235 | 130206 | Hans Havermann | 04/2021 |
3596 | 32160^11171+11171^32160 | 130187 | Hans Havermann | 04/2021 |
3597 | 29489^25956+25956^29489 | 130172 | Hans Havermann | 04/2021 |
3598 | (2^432457-1)/1672739247834685086279697 | 130159 | Tony Prest / Never Odd Or Even | 09/2013 |
3599 | 33005^8766+8766^33005 | 130133 | Hans Havermann | 04/2021 |
3600 | (35*10^130132-611)/9 | 130133 | Robert Price | 02/2022 |
3601 | 2^432217+41 | 130111 | Lelio R Paula | 06/2017 |
3602 | (2^216089*(2^216091-1)-339)/25 | 130098 | Makoto Morimoto | 03/2017 |
3603 | ((2^216091+1066)^2+(2^216091+1066)+41)/47/2069 | 130095 | Makoto Morimoto | 05/2016 |
3604 | 97^65480-2 | 130094 | Lelio R Paula | 05/2017 |
3605 | 36007^4102+4102^36007 | 130094 | Hans Havermann | 04/2021 |
3606 | 4*10^130088-89 | 130089 | Robert Price | 11/2018 |
3607 | 2^432117-113215 | 130081 | Enzo Doria | 07/2014 |
3608 | (4*10^130080+41)/9 | 130080 | Serge Batalov | 11/2022 |
3609 | 2^431804+72511 | 129986 | Enzo Doria | 04/2016 |
3610 | (13*10^129896+137)/3 | 129897 | Robert Price | 06/2021 |
3611 | (13*10^129890+71)/3 | 129891 | Robert Price | 06/2021 |
3612 | 29048^29101-29101^29048 | 129882 | Norbert Schneider | 03/2022 |
3613 | 37832^2709+2709^37832 | 129871 | Hans Havermann | 04/2021 |
3614 | 31055^15184+15184^31055 | 129853 | Hans Havermann | 04/2021 |
3615 | (3^272141-3^136071+1)/7 | 129844 | Serge Batalov | 03/2014 |
3616 | 31385^13702+13702^31385 | 129833 | Hans Havermann | 04/2021 |
3617 | (13*10^129826+41)/9 | 129827 | Tyler Busby | 02/2023 |
3618 | 28901^29102-29102^28901 | 129822 | Norbert Schneider | 03/2022 |
3619 | (47*10^129789-119)/9 | 129790 | Robert Price | 05/2019 |
3620 | (9*2^431141+1)/17 | 129787 | Lelio R Paula | 06/2015 |
3621 | (166*10^129712+17)/3 | 129714 | Robert Price | 07/2022 |
3622 | (29*2^430881-1)/21 | 129709 | Lelio R Paula | 06/2015 |
3623 | 2^430807+1869563 | 129686 | Enzo Doria | 05/2016 |
3624 | 2^430721-21429 | 129660 | Enzo Doria | 07/2013 |
3625 | (4*10^129618+89)/3 | 129619 | Robert Price | 08/2021 |
3626 | 2^430415-276271 | 129568 | Enzo Doria | 07/2015 |
3627 | 32282^10311+10311^32282 | 129558 | Hans Havermann | 04/2021 |
3628 | 29486^24741+24741^29486 | 129545 | Hans Havermann | 04/2021 |
3629 | (29*10^129543+313)/9 | 129544 | Robert Price | 04/2021 |
3630 | 37095^3104+3104^37095 | 129533 | Hans Havermann | 04/2021 |
3631 | 31132^14459+14459^31132 | 129514 | Hans Havermann | 04/2021 |
3632 | 32582^9435+9435^32582 | 129506 | Hans Havermann | 03/2021 |
3633 | 30442^17953+17953^30442 | 129505 | Hans Havermann | 03/2021 |
3634 | (199*10^129487-7)/3 | 129489 | Robert Price | 05/2020 |
3635 | 2^430142-2791721 | 129486 | Enzo Doria | 03/2016 |
3636 | (7*10^129472-13)/3 | 129473 | Robert Price | 07/2018 |
3637 | (8*10^129469+79)/3 | 129470 | Robert Price | 10/2020 |
3638 | 31678^12213+12213^31678 | 129463 | Hans Havermann | 04/2021 |
3639 | (772*10^129406-7)/9 | 129408 | Robert Price | 06/2022 |
3640 | 31100^14439+14439^31100 | 129362 | Hans Havermann | 04/2021 |
3641 | 33009^8288+8288^33009 | 129345 | Hans Havermann | 04/2021 |
3642 | 29675^22804+22804^29675 | 129324 | Hans Havermann | 04/2021 |
3643 | 29068^28099+28099^29068 | 129315 | Hans Havermann | 04/2021 |
3644 | 2^429568-21017 | 129313 | Enzo Doria | 07/2013 |
3645 | (10^129295+83)/3 | 129295 | Robert Price | 08/2021 |
3646 | (853*10^129274-7)/9 | 129276 | Robert Price | 07/2021 |
3647 | 30958^14961+14961^30958 | 129249 | Hans Havermann | 04/2021 |
3648 | (11*10^129239-179)/3 | 129240 | Robert Price | 09/2018 |
3649 | 28659^28988+28988^28659 | 129208 | Norbert Schneider | 02/2021 |
3650 | 29423^24616+24616^29423 | 129203 | Hans Havermann | 03/2021 |
3651 | 2^429194-112685 | 129201 | Enzo Doria | 06/2014 |
3652 | 2^429145-2780449 | 129186 | Enzo Doria | 04/2016 |
3653 | 32500^9427+9427^32500 | 129168 | Hans Havermann | 04/2021 |
3654 | 33577^7014+7014^33577 | 129136 | Hans Havermann | 03/2021 |
3655 | 2^428892-113453 | 129110 | Enzo Doria | 07/2014 |
3656 | (11*2^428881-7)/15 | 129106 | Renaud Lifchitz | 03/2011 |
3657 | 2^428727-113959 | 129060 | Enzo Doria | 10/2014 |
3658 | (7*2^428725-1)/13 | 129059 | Lelio R Paula | 05/2014 |
3659 | (10^129051-31)/3 | 129051 | Serge Batalov | 12/2014 |
3660 | (134*10^129038+7)/3 | 129040 | Robert Price | 02/2020 |
3661 | 2^428564+71161 | 129011 | Enzo Doria | 04/2016 |
3662 | 28781^28930+28930^28781 | 129002 | Norbert Schneider | 02/2021 |
3663 | 29065^27424+27424^29065 | 128995 | Hans Havermann | 04/2021 |
3664 | 2^428502-113285 | 128992 | Enzo Doria | 07/2014 |
3665 | 2^428421-21373 | 128968 | Enzo Doria | 06/2013 |
3666 | L(616787) | 128901 | Henri Lifchitz | 09/2008 |
3667 | 20^99055-3 | 128874 | Paul Bourdelais | 12/2020 |
3668 | 91^65772-2 | 128851 | Lelio R Paula | 05/2017 |
3669 | 2^428022+43 | 128848 | Lelio R Paula | 05/2017 |
3670 | 2^427999-459397 | 128841 | Enzo Doria | 05/2015 |
3671 | 2^427993+76847 | 128839 | Enzo Doria | 05/2016 |
3672 | 31059^14060+14060^31059 | 128833 | Hans Havermann | 03/2021 |
3673 | 10^128805+152871 | 128806 | Patrick De Geest | 05/2021 |
3674 | 10^128805-10001 | 128805 | Robert Price | 02/2021 |
3675 | 2^427824-1851507 | 128788 | Enzo Doria | 08/2015 |
3676 | 2^427807-21469 | 128783 | Enzo Doria | 07/2013 |
3677 | 29082^26783+26783^29082 | 128772 | Hans Havermann | 04/2021 |
3678 | 40055^1638+1638^40055 | 128750 | Hans Havermann | 04/2021 |
3679 | 11^123594-240 | 128710 | Enzo Doria | 09/2012 |
3680 | 2^427504-21503 | 128692 | Enzo Doria | 07/2013 |
3681 | 37727^2574+2574^37727 | 128673 | Hans Havermann | 04/2021 |
3682 | 29686^21591+21591^29686 | 128668 | Hans Havermann | 04/2021 |
3683 | 10^128668-70000000001 | 128668 | Robert Price | 08/2021 |
3684 | 2^427420+91 | 128667 | Lelio R Paula | 05/2017 |
3685 | 8*10^128651-37 | 128652 | Robert Price | 03/2022 |
3686 | (68*10^128645-257)/9 | 128646 | Robert Price | 07/2019 |
3687 | 2^427269-113635 | 128621 | Enzo Doria | 08/2014 |
3688 | 2^427130+1877569 | 128579 | Enzo Doria | 08/2016 |
3689 | 2^427016-115349 | 128545 | Enzo Doria | 07/2015 |
3690 | (4*10^128510+137)/3 | 128511 | Robert Price | 03/2018 |
3691 | 2^426889-112879 | 128507 | Enzo Doria | 06/2014 |
3692 | 2^426804+1869931 | 128481 | Enzo Doria | 05/2016 |
3693 | 2^426750+77635 | 128465 | Enzo Doria | 05/2016 |
3694 | 36988^2969+2969^36988 | 128445 | Hans Havermann | 03/2021 |
3695 | 36664^3185+3185^36664 | 128439 | Hans Havermann | 03/2021 |
3696 | 32618^8649+8649^32618 | 128416 | Hans Havermann | 04/2021 |
3697 | 28883^27874+27874^28883 | 128391 | Hans Havermann | 04/2021 |
3698 | 2^426425-91 | 128367 | Lelio R Paula | 05/2017 |
3699 | (15*2^426398-1)/11 | 128359 | Lelio R Paula | 05/2014 |
3700 | 2^426352+74971 | 128345 | Enzo Doria | 04/2016 |
3701 | (199*10^128343-7)/3 | 128345 | Robert Price | 05/2020 |
3702 | 4*10^128343-21 | 128344 | Robert Price | 09/2018 |
3703 | (65*10^128338+493)/9 | 128339 | Robert Price | 08/2021 |
3704 | 35632^3997+3997^35632 | 128337 | Hans Havermann | 04/2021 |
3705 | 2^426300-1863689 | 128330 | Enzo Doria | 03/2016 |
3706 | 2^426293+1881017 | 128327 | Enzo Doria | 11/2016 |
3707 | (88*10^128324-637)/9 | 128325 | Robert Price | 11/2020 |
3708 | (491*10^128285+31)/9 | 128287 | Robert Price | 04/2022 |
3709 | 39103^1908+1908^39103 | 128281 | Hans Havermann | 04/2021 |
3710 | 2^426043+35 | 128252 | Robert Price | 11/2015 |
3711 | (4*10^128244-19)/3 | 128245 | Robert Price | 03/2018 |
3712 | 35489^4102+4102^35489 | 128222 | Hans Havermann | 04/2021 |
3713 | 34721^4926+4926^34721 | 128208 | Hans Havermann | 04/2021 |
3714 | (305*10^128198+1)/9 | 128200 | Robert Price | 02/2020 |
3715 | 2^425808-459959 | 128181 | Enzo Doria | 06/2015 |
3716 | 30632^15291+15291^30632 | 128178 | Hans Havermann | 04/2021 |
3717 | 35981^3648+3648^35981 | 128167 | Hans Havermann | 04/2021 |
3718 | 2^425627-113605 | 128127 | Enzo Doria | 08/2014 |
3719 | (4*10^128109+119)/3 | 128110 | Robert Price | 12/2021 |
3720 | (22*10^128094+53)/3 | 128095 | Robert Price | 07/2019 |
3721 | (86*10^128086-221)/9 | 128087 | Robert Price | 09/2019 |
3722 | 18565^30002-30002^18565 | 128070 | Norbert Schneider | 01/2015 |
3723 | (2^425287-9)/2737 | 128021 | Lelio R Paula | 05/2015 |
3724 | (3*2^425233-1)/25 | 128007 | Lelio R Paula | 05/2014 |
3725 | Phi(149401,10)/30037901719561 | 128003 | Makoto Kamada | 07/2022 |
3726 | 2^425205+4911 | 128000 | Marek Hubal | 02/2017 |
3727 | 29241^23836+23836^29241 | 127995 | Hans Havermann | 04/2021 |
3728 | 2^425118-113663 | 127974 | Enzo Doria | 08/2014 |
3729 | (86*10^127967-329)/9 | 127968 | Robert Price | 01/2020 |
3730 | 2^425061+1869761 | 127957 | Enzo Doria | 05/2016 |
3731 | 746^44541+44541^746 | 127955 | Norbert Schneider | 07/2019 |
3732 | 30236^17043+17043^30236 | 127946 | Hans Havermann | 03/2021 |
3733 | 2^424918-21141 | 127914 | Enzo Doria | 07/2013 |
3734 | (62*10^127903+91)/9 | 127904 | Robert Price | 07/2021 |
3735 | 2^424864-29489 | 127897 | Enzo Doria | 08/2015 |
3736 | 30438^15893+15893^30438 | 127877 | Hans Havermann | 02/2021 |
3737 | (97*10^127858-1)/3 | 127860 | Serge Batalov | 12/2014 |
3738 | 28929^26258+26258^28929 | 127845 | Hans Havermann | 03/2021 |
3739 | 30563^15220+15220^30563 | 127828 | Hans Havermann | 03/2021 |
3740 | 2^424632-2786639 | 127827 | Enzo Doria | 03/2016 |
3741 | 10^127821-700001 | 127821 | Robert Price | 08/2021 |
3742 | 2^424577-113755 | 127811 | Enzo Doria | 09/2014 |
3743 | (7*2^424512-1)/3 | 127792 | Lelio R Paula | 05/2014 |
3744 | (56*10^127752+691)/9 | 127753 | Robert Price | 05/2019 |
3745 | 11^122629-720 | 127705 | Enzo Doria | 11/2012 |
3746 | 22*10^127645+3 | 127647 | Robert Price | 01/2020 |
3747 | 28715^27844+27844^28715 | 127631 | Hans Havermann | 03/2021 |
3748 | (56*10^127612+187)/9 | 127613 | Robert Price | 10/2021 |
3749 | (5*36^81995+821)/7 | 127609 | Eric Chen | 01/2021 |
3750 | 4*10^127562-39 | 127563 | Robert Price | 09/2020 |