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 ? |
| 3501 | (71*10^148306-539)/9 | 148307 | Robert Price | 07/2019 |
| 3502 | 30814^33039-33039^30814 | 148304 | Frank Doornink | 06/2024 |
| 3503 | 38042^7875+7875^38042 | 148222 | Hans Havermann | 10/2020 |
| 3504 | 5^211959-12874 | 148153 | Enzo Doria | 05/2014 |
| 3505 | 34142^21831+21831^34142 | 148145 | Hans Havermann | 10/2020 |
| 3506 | 10^148112+34059 | 148113 | Patrick De Geest | 05/2021 |
| 3507 | 10^148112-70000001 | 148112 | Robert Price | 03/2021 |
| 3508 | 10^148112-106593 | 148112 | Patrick De Geest | 05/2021 |
| 3509 | 36303^12016+12016^36303 | 148108 | Hans Havermann | 10/2020 |
| 3510 | (77*10^148089-149)/9 | 148090 | Robert Price | 03/2022 |
| 3511 | (16*10^148071+41)/3 | 148072 | Robert Price | 03/2019 |
| 3512 | 187^65175-2 | 148068 | Lelio R Paula | 11/2017 |
| 3513 | 2^491851+1871453 | 148062 | Enzo Doria | 05/2016 |
| 3514 | (68*10^148060-257)/9 | 148061 | Robert Price | 07/2019 |
| 3515 | (151*10^148020-1)/3 | 148022 | Robert Price | 03/2020 |
| 3516 | 39153^6032+6032^39153 | 148017 | Hans Havermann | 10/2020 |
| 3517 | 36798^10507+10507^36798 | 147983 | Hans Havermann | 12/2020 |
| 3518 | (26*10^147973-23)/3 | 147974 | Robert Price | 12/2019 |
| 3519 | 2^491521-1865323 | 147963 | Enzo Doria | 02/2016 |
| 3520 | (2^491476+7)/71 | 147948 | Lelio R Paula | 10/2015 |
| 3521 | 2*10^147928+47 | 147929 | Robert Price | 12/2021 |
| 3522 | 2^491391-7807 | 147924 | Lelio R Paula | 01/2013 |
| 3523 | 39736^5279+5279^39736 | 147920 | Hans Havermann | 11/2020 |
| 3524 | 2^491370-113297 | 147918 | Enzo Doria | 07/2014 |
| 3525 | (32760^32760+32759^32759)/95546586737133567708319 | 147900 | Robert Price | 07/2016 |
| 3526 | 44368^2155+2155^44368 | 147899 | Hans Havermann | 12/2020 |
| 3527 | (17*10^147890+79)/3 | 147891 | Robert Price | 04/2019 |
| 3528 | 94*10^147871-3 | 147873 | Robert Price | 05/2020 |
| 3529 | 10^147843+620967 | 147844 | Patrick De Geest | 05/2021 |
| 3530 | 10^147843-50000000001 | 147843 | Robert Price | 12/2020 |
| 3531 | 10^147843-182891 | 147843 | Patrick De Geest | 05/2021 |
| 3532 | 35805^13346+13346^35805 | 147709 | Hans Havermann | 11/2020 |
| 3533 | 2^490672+255255 | 147707 | Paul Bourdelais | 10/2021 |
| 3534 | 2^490660-17 | 147704 | Lelio R Paula | 12/2017 |
| 3535 | (229*10^147699-1)/3 | 147701 | Robert Price | 07/2020 |
| 3536 | 40656^4289+4289^40656 | 147678 | Hans Havermann | 11/2020 |
| 3537 | 2^490550+1179439 | 147671 | Enzo Doria | 06/2016 |
| 3538 | 27249^33292-33292^27249 | 147662 | Frank Doornink | 06/2024 |
| 3539 | (23*10^147649-59)/9 | 147650 | Robert Price | 05/2018 |
| 3540 | 2^490303+2793653 | 147596 | Enzo Doria | 03/2016 |
| 3541 | 2^490266+255255 | 147585 | Paul Bourdelais | 10/2021 |
| 3542 | 199^64181-2 | 147543 | Lelio R Paula | 11/2017 |
| 3543 | 32849^30958+30958^32849 | 147518 | Hans Havermann | 11/2020 |
| 3544 | 2^489871-286987 | 147466 | Enzo Doria | 07/2015 |
| 3545 | 2^489864-351899 | 147464 | Enzo Doria | 07/2015 |
| 3546 | 175^65724-2 | 147422 | Lelio R Paula | 11/2017 |
| 3547 | 2^489712+1874851 | 147419 | Enzo Doria | 06/2016 |
| 3548 | 34473^18830+18830^34473 | 147367 | Hans Havermann | 11/2020 |
| 3549 | 63^81896-2 | 147359 | Lelio R Paula | 10/2017 |
| 3550 | 34580^18237+18237^34580 | 147344 | Hans Havermann | 11/2020 |
| 3551 | (11*10^147313-107)/3 | 147314 | Robert Price | 09/2018 |
| 3552 | (397*10^147310+17)/9 | 147312 | Robert Price | 03/2022 |
| 3553 | 2^489305-59815 | 147296 | Enzo Doria | 10/2015 |
| 3554 | (2^489280-7)/6381 | 147285 | Lelio R Paula | 09/2015 |
| 3555 | 2*10^147264-61 | 147265 | Robert Price | 10/2021 |
| 3556 | 2*10^147260+29 | 147261 | Robert Price | 02/2021 |
| 3557 | 33556^24457+24457^33556 | 147258 | Hans Havermann | 11/2020 |
| 3558 | 2^489125+80357 | 147242 | Enzo Doria | 06/2016 |
| 3559 | 10^147240-40000001 | 147240 | Robert Price | 07/2022 |
| 3560 | 32835^30452+30452^32835 | 147220 | Hans Havermann | 12/2020 |
| 3561 | (19*10^147213-97)/3 | 147214 | Robert Price | 10/2021 |
| 3562 | 27123^33190-33190^27123 | 147143 | Frank Doornink | 01/2024 |
| 3563 | (148*10^147139-1)/3 | 147141 | Robert Price | 03/2020 |
| 3564 | 34338^19255+19255^34338 | 147123 | Hans Havermann | 11/2020 |
| 3565 | 2^488648-112799 | 147098 | Enzo Doria | 07/2014 |
| 3566 | 2^488627-350317 | 147092 | Enzo Doria | 06/2015 |
| 3567 | 33432^25075+25075^33432 | 147076 | Hans Havermann | 12/2020 |
| 3568 | (2^488441-1)/(61543567*30051203516986199) | 147012 | Dario Alpern | 12/2014 |
| 3569 | 2^488280-2165 | 146987 | Yves Minet | 07/2014 |
| 3570 | 2^488278+45 | 146987 | Lelio R Paula | 12/2017 |
| 3571 | 2^487927-39 | 146881 | Lelio R Paula | 12/2017 |
| 3572 | (7*10^146860-13)/3 | 146861 | Robert Price | 07/2018 |
| 3573 | (26*10^146856-77)/3 | 146857 | Robert Price | 11/2019 |
| 3574 | 32948^28611+28611^32948 | 146834 | Hans Havermann | 11/2020 |
| 3575 | 42596^2799+2799^42596 | 146829 | Hans Havermann | 12/2020 |
| 3576 | 2^487726-1863341 | 146821 | Enzo Doria | 12/2015 |
| 3577 | 43838^2229+2229^43838 | 146775 | Hans Havermann | 11/2020 |
| 3578 | 35005^15594+15594^35005 | 146775 | Hans Havermann | 11/2020 |
| 3579 | (167*10^146764+7)/3 | 146766 | Robert Price | 04/2021 |
| 3580 | 53^85114+85114 | 146761 | Kellen Shenton | 05/2022 |
| 3581 | (59*10^146738+157)/9 | 146739 | Robert Price | 12/2021 |
| 3582 | ((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9 | 146728 | Hans Havermann | 09/2019 |
| 3583 | 32963^28234+28234^32963 | 146711 | Hans Havermann | 12/2020 |
| 3584 | (22*10^146661-19)/3 | 146662 | Robert Price | 04/2019 |
| 3585 | 33958^20825+20825^33958 | 146651 | Hans Havermann | 12/2020 |
| 3586 | 26289^33178-33178^26289 | 146640 | Frank Doornink | 03/2024 |
| 3587 | 2^487121-39523 | 146639 | Enzo Doria | 09/2015 |
| 3588 | 61063^252+252^61063 | 146637 | Hans Havermann | 12/2020 |
| 3589 | (7*2^486967+1)/39 | 146591 | Lelio R Paula | 09/2015 |
| 3590 | 34099^19900+19900^34099 | 146587 | Hans Havermann | 11/2020 |
| 3591 | 2^486893-79 | 146570 | Yves Minet | 09/2017 |
| 3592 | 36818^9567+9567^36818 | 146565 | Hans Havermann | 12/2020 |
| 3593 | 2^486840+1879141 | 146554 | Enzo Doria | 08/2016 |
| 3594 | 2^486774-87 | 146534 | Lelio R Paula | 12/2017 |
| 3595 | 38655^6176+6176^38655 | 146530 | Hans Havermann | 11/2020 |
| 3596 | 8*10^146522-81 | 146523 | Robert Price | 02/2021 |
| 3597 | 32820^29059+29059^32820 | 146485 | Hans Havermann | 12/2020 |
| 3598 | 37261^8530+8530^37261 | 146472 | Hans Havermann | 12/2020 |
| 3599 | 66953^154+154^66953 | 146462 | Hans Havermann | 12/2020 |
| 3600 | 96^73877-95^73877 | 146445 | Robert Price | 10/2015 |
| 3601 | 8*10^146421+81 | 146422 | Robert Price | 08/2019 |
| 3602 | 33153^26090+26090^33153 | 146420 | Hans Havermann | 11/2020 |
| 3603 | 2^486275+23961 | 146384 | Enzo Doria | 10/2023 |
| 3604 | (52^85259+1)/53 | 146304 | Paul Bourdelais | 09/2017 |
| 3605 | 179^64935+2 | 146290 | Lelio R Paula | 10/2017 |
| 3606 | 32595^30758+30758^32595 | 146285 | Hans Havermann | 11/2020 |
| 3607 | 34972^15157+15157^34972 | 146205 | Hans Havermann | 12/2020 |
| 3608 | (16*10^146200+131)/3 | 146201 | Robert Price | 03/2022 |
| 3609 | (19*10^146181-49)/3 | 146182 | Robert Price | 05/2019 |
| 3610 | 2^485531-114621 | 146160 | Enzo Doria | 05/2015 |
| 3611 | 2^485473-933075 | 146142 | Paul Bourdelais | 06/2021 |
| 3612 | (2^485461-9)/4249 | 146135 | Lelio R Paula | 09/2015 |
| 3613 | (22*10^146130-193)/9 | 146131 | Robert Price | 07/2022 |
| 3614 | 2^485389+81887 | 146117 | Enzo Doria | 08/2016 |
| 3615 | 32554^30773+30773^32554 | 146108 | Hans Havermann | 11/2020 |
| 3616 | 28075^32844-32844^28075 | 146101 | Frank Doornink | 06/2024 |
| 3617 | (10^146063+71)/9 | 146063 | Serge Batalov | 07/2015 |
| 3618 | 2*10^146051-63 | 146052 | Robert Price | 01/2022 |
| 3619 | (2^485119+7)/2745 | 146032 | Lelio R Paula | 09/2015 |
| 3620 | (22*10^146029+257)/9 | 146030 | Robert Price | 06/2018 |
| 3621 | 7*10^145982-53 | 145983 | Robert Price | 06/2020 |
| 3622 | 2^484743+1872923 | 145923 | Enzo Doria | 05/2016 |
| 3623 | 33140^25287+25287^33140 | 145913 | Hans Havermann | 01/2021 |
| 3624 | 37875^7112+7112^37875 | 145895 | Hans Havermann | 01/2021 |
| 3625 | 30542^32529-32529^30542 | 145890 | Frank Doornink | 06/2024 |
| 3626 | 32862^27473+27473^32862 | 145872 | Hans Havermann | 01/2021 |
| 3627 | 32836^27587+27587^32836 | 145815 | Hans Havermann | 01/2021 |
| 3628 | 2^484341+1879157 | 145802 | Enzo Doria | 08/2016 |
| 3629 | 2*10^145784-91 | 145785 | Robert Price | 04/2020 |
| 3630 | 2^484271-51 | 145781 | Lelio R Paula | 11/2017 |
| 3631 | (188*10^145750-11)/3 | 145752 | Robert Price | 02/2022 |
| 3632 | 70^78989-69^78989 | 145743 | Robert Price | 01/2014 |
| 3633 | 51^85334+2 | 145714 | Robert Price | 07/2015 |
| 3634 | 2^483886-1857101 | 145665 | Enzo Doria | 10/2015 |
| 3635 | 29312^32607-32607^29312 | 145657 | Frank Doornink | 06/2024 |
| 3636 | 33350^23307+23307^33350 | 145656 | Hans Havermann | 01/2021 |
| 3637 | (19*10^145585+131)/3 | 145586 | Robert Price | 06/2020 |
| 3638 | 31815^32332-32332^31815 | 145580 | Frank Doornink | 01/2024 |
| 3639 | 2^483563-1863457 | 145567 | Enzo Doria | 12/2015 |
| 3640 | 4*10^145563-69 | 145564 | Robert Price | 01/2022 |
| 3641 | 2^483516-1861409 | 145553 | Enzo Doria | 11/2015 |
| 3642 | 2^483384-115019 | 145514 | Enzo Doria | 06/2015 |
| 3643 | (259*10^145501-1)/3 | 145503 | Robert Price | 12/2020 |
| 3644 | (19*10^145499-61)/3 | 145500 | Robert Price | 05/2019 |
| 3645 | 2^483302-3221 | 145489 | Lelio R Paula | 12/2012 |
| 3646 | (23*10^145463+61)/3 | 145464 | Robert Price | 01/2022 |
| 3647 | 35523^12434+12434^35523 | 145453 | Hans Havermann | 01/2021 |
| 3648 | (29121^32761-1)/(29121^181-1) | 145444 | Ryan Propper | 11/2023 |
| 3649 | 2^483046+1874029 | 145412 | Enzo Doria | 06/2016 |
| 3650 | 2^482991-2789317 | 145395 | Enzo Doria | 12/2015 |
| 3651 | 2^482978-2789711 | 145391 | Enzo Doria | 12/2015 |
| 3652 | 2^482966-2789711 | 145388 | Enzo Doria | 12/2015 |
| 3653 | 2^482817-1858843 | 145343 | Enzo Doria | 10/2015 |
| 3654 | 2^482751-113635 | 145323 | Enzo Doria | 08/2014 |
| 3655 | 2^482705-459763 | 145309 | Enzo Doria | 05/2015 |
| 3656 | (4^241306+11)/3 | 145281 | Robert Price | 03/2017 |
| 3657 | (238*10^145276-1)/3 | 145278 | Robert Price | 04/2020 |
| 3658 | (19*2^482534+1)/7 | 145258 | Lelio R Paula | 09/2015 |
| 3659 | 53^84239-52^84239 | 145252 | Robert Price | 01/2013 |
| 3660 | 2^482386+212419 | 145213 | Enzo Doria | 08/2023 |
| 3661 | 47952^1067+1067^47952 | 145207 | Hans Havermann | 01/2021 |
| 3662 | (2^482333+5)/9287 | 145193 | Lelio R Paula | 09/2015 |
| 3663 | 2^482087+72623 | 145123 | Enzo Doria | 04/2016 |
| 3664 | 2^482016-286565 | 145102 | Enzo Doria | 07/2015 |
| 3665 | (19*10^145093+101)/3 | 145094 | Robert Price | 09/2019 |
| 3666 | 2^481956+121 | 145084 | Stefano Morozzi | 04/2021 |
| 3667 | 27535^32676-32676^27535 | 145078 | Frank Doornink | 06/2024 |
| 3668 | 2^481840+15 | 145049 | Robert Price | 09/2015 |
| 3669 | (23*10^145040+7)/3 | 145041 | Robert Price | 05/2023 |
| 3670 | 2^481801-481801 | 145037 | Henri Lifchitz | 03/2005 |
| 3671 | 2^481775+1869083 | 145029 | Enzo Doria | 05/2016 |
| 3672 | 29^99167+2 | 145022 | Ray Chandler | 08/2011 |
| 3673 | 2^481663+1875653 | 144996 | Enzo Doria | 07/2016 |
| 3674 | 8*10^144977+27 | 144978 | Robert Price | 09/2021 |
| 3675 | 29840^32393-32393^29840 | 144953 | Frank Doornink | 06/2024 |
| 3676 | 36486^9379+9379^36486 | 144929 | Hans Havermann | 12/2020 |
| 3677 | 31580^32209-32209^31580 | 144922 | Frank Doornink | 01/2024 |
| 3678 | 35111^13378+13378^35111 | 144882 | Hans Havermann | 01/2021 |
| 3679 | 2^481149-459073 | 144841 | Enzo Doria | 05/2015 |
| 3680 | 2^481113+181419 | 144830 | Boyan Hu | 04/2024 |
| 3681 | 34619^15246+15246^34619 | 144817 | Hans Havermann | 01/2021 |
| 3682 | 2^481045-113215 | 144809 | Enzo Doria | 07/2014 |
| 3683 | (64*10^144797+287)/9 | 144798 | Robert Price | 04/2019 |
| 3684 | 27320^32629-32629^27320 | 144758 | Frank Doornink | 06/2024 |
| 3685 | 2^480859-113695 | 144753 | Enzo Doria | 09/2014 |
| 3686 | (106*10^144744+17)/3 | 144746 | Robert Price | 04/2021 |
| 3687 | 7*10^144742-27 | 144743 | Robert Price | 11/2022 |
| 3688 | 2^480766-2787191 | 144725 | Enzo Doria | 11/2015 |
| 3689 | (21*27^101106-151)/26 | 144720 | Curtis Bright | 05/2015 |
| 3690 | 28915^32438-32438^28915 | 144710 | Frank Doornink | 06/2024 |
| 3691 | 2^480678+1874239 | 144699 | Enzo Doria | 06/2016 |
| 3692 | (8*10^144683+1)/9 | 144683 | Serge Batalov | 05/2010 |
| 3693 | L(692147) | 144651 | Henri Lifchitz | 10/2008 |
| 3694 | (76*10^144648+77)/9 | 144649 | Robert Price | 10/2019 |
| 3695 | 32672^26721+26721^32672 | 144635 | Hans Havermann | 01/2021 |
| 3696 | 31478^32153-32153^31478 | 144625 | Frank Doornink | 01/2024 |
| 3697 | 2^480417+35 | 144620 | Robert Price | 11/2015 |
| 3698 | 2^480296-59879 | 144584 | Enzo Doria | 10/2015 |
| 3699 | 33157^22878+22878^33157 | 144546 | Hans Havermann | 12/2020 |
| 3700 | 27520^32541-32541^27520 | 144471 | Frank Doornink | 06/2024 |
| 3701 | 45494^1497+1497^45494 | 144454 | Hans Havermann | 12/2020 |
| 3702 | 2^479844+3 | 144448 | Donovan Johnson | 06/2006 |
| 3703 | 33442^20803+20803^33442 | 144407 | Hans Havermann | 01/2021 |
| 3704 | (441*33^95095-3833)/32 | 144405 | Eric Chen | 12/2023 |
| 3705 | 31892^32061-32061^31892 | 144393 | Norbert Schneider | 01/2023 |
| 3706 | (27*2^479642+1)/733 | 144386 | Lelio R Paula | 08/2015 |
| 3707 | (56*10^144380+169)/9 | 144381 | Robert Price | 03/2022 |
| 3708 | 44917^1638+1638^44917 | 144378 | Hans Havermann | 12/2020 |
| 3709 | (21*2^479605-1)/11 | 144376 | Lelio R Paula | 09/2015 |
| 3710 | (56*10^144336+583)/9 | 144337 | Robert Price | 08/2021 |
| 3711 | 5*2^479430-3 | 144324 | Jon Grantham | 07/2023 |
| 3712 | 2^479348-2792219 | 144299 | Enzo Doria | 02/2016 |
| 3713 | 31134^32111-32111^31134 | 144283 | Frank Doornink | 01/2024 |
| 3714 | 3^302389-6242 | 144277 | Enzo Doria | 05/2014 |
| 3715 | 31665^32056-32056^31665 | 144271 | Frank Doornink | 01/2024 |
| 3716 | 33778^18641+18641^33778 | 144248 | Hans Havermann | 01/2021 |
| 3717 | 29083^32312-32312^29083 | 144230 | Frank Doornink | 06/2024 |
| 3718 | 2*10^144220-3 | 144221 | Robert Price | 07/2015 |
| 3719 | 25313^32750-32750^25313 | 144210 | Frank Doornink | 01/2024 |
| 3720 | 2^478904-109109 | 144165 | Enzo Doria | 04/2014 |
| 3721 | 43698^1987+1987^43698 | 144125 | Hans Havermann | 12/2020 |
| 3722 | 79^75948+75948 | 144121 | Kellen Shenton | 06/2023 |
| 3723 | 26941^32522-32522^26941 | 144086 | Frank Doornink | 06/2024 |
| 3724 | 36128^9723+9723^36128 | 144072 | Hans Havermann | 01/2021 |
| 3725 | 32817^24518+24518^32817 | 144050 | Hans Havermann | 12/2020 |
| 3726 | (772*10^144036-7)/9 | 144038 | Robert Price | 06/2022 |
| 3727 | 34295^15828+15828^34295 | 144020 | Hans Havermann | 01/2021 |
| 3728 | 2^478337-115333 | 143994 | Enzo Doria | 07/2015 |
| 3729 | (7*2^478330-1)/3 | 143993 | Lelio R Paula | 08/2015 |
| 3730 | 88^74047-87^74047 | 143984 | Robert Price | 05/2015 |
| 3731 | 33242^21441+21441^33242 | 143980 | Hans Havermann | 01/2021 |
| 3732 | (19*10^143963+467)/9 | 143964 | Robert Price | 02/2018 |
| 3733 | (71^77761+1)/72 | 143954 | Paul Bourdelais | 09/2017 |
| 3734 | 33490^19859+19859^33490 | 143939 | Hans Havermann | 01/2021 |
| 3735 | (853*10^143931-7)/9 | 143933 | Robert Price | 07/2021 |
| 3736 | 2^478088+27 | 143919 | Robert Price | 11/2015 |
| 3737 | (8*10^143898-137)/3 | 143899 | Robert Price | 03/2022 |
| 3738 | 7*10^143857-93 | 143858 | Robert Price | 08/2020 |
| 3739 | 3*10^143844+61 | 143845 | Robert Price | 09/2020 |
| 3740 | 41358^3005+3005^41358 | 143837 | Hans Havermann | 01/2021 |
| 3741 | 2^477475-22071 | 143735 | Enzo Doria | 07/2013 |
| 3742 | 2^477417-22123 | 143717 | Enzo Doria | 07/2013 |
| 3743 | 2^477359-3577 | 143700 | Yves Minet | 03/2017 |
| 3744 | 39435^4402+4402^39435 | 143688 | Hans Havermann | 01/2021 |
| 3745 | (14*10^143662-71)/3 | 143663 | Robert Price | 12/2018 |
| 3746 | 6^184614+5 | 143658 | Paul Bourdelais | 01/2021 |
| 3747 | 46371^1252+1252^46371 | 143640 | Hans Havermann | 12/2020 |
| 3748 | 34975^12748+12748^34975 | 143588 | Hans Havermann | 01/2021 |
| 3749 | 2^476936-396765 | 143573 | Enzo Doria | 07/2013 |
| 3750 | 2^476888-2791229 | 143558 | Enzo Doria | 01/2016 |
