## PRP Records

### Probable Primes Top 10000

#### (295461 PRPs in the top)

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) !!!

See the Top discoverers
See the Latest PRPs
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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 3501 2^491851+1871453 148062 Enzo Doria 05/2016 3502 (68*10^148060-257)/9 148061 Robert Price 07/2019 3503 (151*10^148020-1)/3 148022 Robert Price 03/2020 3504 39153^6032+6032^39153 148017 Hans Havermann 10/2020 3505 36798^10507+10507^36798 147983 Hans Havermann 12/2020 3506 (26*10^147973-23)/3 147974 Robert Price 12/2019 3507 2^491521-1865323 147963 Enzo Doria 02/2016 3508 (2^491476+7)/71 147948 Lelio R Paula 10/2015 3509 2*10^147928+47 147929 Robert Price 12/2021 3510 2^491391-7807 147924 Lelio R Paula 01/2013 3511 39736^5279+5279^39736 147920 Hans Havermann 11/2020 3512 2^491370-113297 147918 Enzo Doria 07/2014 3513 (32760^32760+32759^32759)/95546586737133567708319 147900 Robert Price 07/2016 3514 44368^2155+2155^44368 147899 Hans Havermann 12/2020 3515 (17*10^147890+79)/3 147891 Robert Price 04/2019 3516 94*10^147871-3 147873 Robert Price 05/2020 3517 10^147843+620967 147844 Patrick De Geest 05/2021 3518 10^147843-50000000001 147843 Robert Price 12/2020 3519 10^147843-182891 147843 Patrick De Geest 05/2021 3520 35805^13346+13346^35805 147709 Hans Havermann 11/2020 3521 2^490672+255255 147707 Paul Bourdelais 10/2021 3522 2^490660-17 147704 Lelio R Paula 12/2017 3523 (229*10^147699-1)/3 147701 Robert Price 07/2020 3524 40656^4289+4289^40656 147678 Hans Havermann 11/2020 3525 2^490550+1179439 147671 Enzo Doria 06/2016 3526 27249^33292-33292^27249 147662 Frank Doornink 06/2024 3527 (23*10^147649-59)/9 147650 Robert Price 05/2018 3528 2^490303+2793653 147596 Enzo Doria 03/2016 3529 2^490266+255255 147585 Paul Bourdelais 10/2021 3530 199^64181-2 147543 Lelio R Paula 11/2017 3531 32849^30958+30958^32849 147518 Hans Havermann 11/2020 3532 2^489871-286987 147466 Enzo Doria 07/2015 3533 2^489864-351899 147464 Enzo Doria 07/2015 3534 175^65724-2 147422 Lelio R Paula 11/2017 3535 2^489712+1874851 147419 Enzo Doria 06/2016 3536 34473^18830+18830^34473 147367 Hans Havermann 11/2020 3537 63^81896-2 147359 Lelio R Paula 10/2017 3538 34580^18237+18237^34580 147344 Hans Havermann 11/2020 3539 (11*10^147313-107)/3 147314 Robert Price 09/2018 3540 (397*10^147310+17)/9 147312 Robert Price 03/2022 3541 2^489305-59815 147296 Enzo Doria 10/2015 3542 (2^489280-7)/6381 147285 Lelio R Paula 09/2015 3543 2*10^147264-61 147265 Robert Price 10/2021 3544 2*10^147260+29 147261 Robert Price 02/2021 3545 33556^24457+24457^33556 147258 Hans Havermann 11/2020 3546 2^489125+80357 147242 Enzo Doria 06/2016 3547 10^147240-40000001 147240 Robert Price 07/2022 3548 32835^30452+30452^32835 147220 Hans Havermann 12/2020 3549 (19*10^147213-97)/3 147214 Robert Price 10/2021 3550 27123^33190-33190^27123 147143 Frank Doornink 01/2024 3551 (148*10^147139-1)/3 147141 Robert Price 03/2020 3552 34338^19255+19255^34338 147123 Hans Havermann 11/2020 3553 2^488648-112799 147098 Enzo Doria 07/2014 3554 2^488627-350317 147092 Enzo Doria 06/2015 3555 33432^25075+25075^33432 147076 Hans Havermann 12/2020 3556 (2^488441-1)/(61543567*30051203516986199) 147012 Dario Alpern 12/2014 3557 2^488280-2165 146987 Yves Minet 07/2014 3558 2^488278+45 146987 Lelio R Paula 12/2017 3559 2^487927-39 146881 Lelio R Paula 12/2017 3560 (7*10^146860-13)/3 146861 Robert Price 07/2018 3561 (26*10^146856-77)/3 146857 Robert Price 11/2019 3562 32948^28611+28611^32948 146834 Hans Havermann 11/2020 3563 42596^2799+2799^42596 146829 Hans Havermann 12/2020 3564 2^487726-1863341 146821 Enzo Doria 12/2015 3565 43838^2229+2229^43838 146775 Hans Havermann 11/2020 3566 35005^15594+15594^35005 146775 Hans Havermann 11/2020 3567 (167*10^146764+7)/3 146766 Robert Price 04/2021 3568 53^85114+85114 146761 Kellen Shenton 05/2022 3569 (59*10^146738+157)/9 146739 Robert Price 12/2021 3570 ((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9 146728 Hans Havermann 09/2019 3571 32963^28234+28234^32963 146711 Hans Havermann 12/2020 3572 (22*10^146661-19)/3 146662 Robert Price 04/2019 3573 33958^20825+20825^33958 146651 Hans Havermann 12/2020 3574 26289^33178-33178^26289 146640 Frank Doornink 03/2024 3575 2^487121-39523 146639 Enzo Doria 09/2015 3576 61063^252+252^61063 146637 Hans Havermann 12/2020 3577 (7*2^486967+1)/39 146591 Lelio R Paula 09/2015 3578 34099^19900+19900^34099 146587 Hans Havermann 11/2020 3579 2^486893-79 146570 Yves Minet 09/2017 3580 36818^9567+9567^36818 146565 Hans Havermann 12/2020 3581 2^486840+1879141 146554 Enzo Doria 08/2016 3582 2^486774-87 146534 Lelio R Paula 12/2017 3583 38655^6176+6176^38655 146530 Hans Havermann 11/2020 3584 8*10^146522-81 146523 Robert Price 02/2021 3585 32820^29059+29059^32820 146485 Hans Havermann 12/2020 3586 37261^8530+8530^37261 146472 Hans Havermann 12/2020 3587 66953^154+154^66953 146462 Hans Havermann 12/2020 3588 96^73877-95^73877 146445 Robert Price 10/2015 3589 8*10^146421+81 146422 Robert Price 08/2019 3590 33153^26090+26090^33153 146420 Hans Havermann 11/2020 3591 2^486275+23961 146384 Enzo Doria 10/2023 3592 (52^85259+1)/53 146304 Paul Bourdelais 09/2017 3593 179^64935+2 146290 Lelio R Paula 10/2017 3594 32595^30758+30758^32595 146285 Hans Havermann 11/2020 3595 34972^15157+15157^34972 146205 Hans Havermann 12/2020 3596 (16*10^146200+131)/3 146201 Robert Price 03/2022 3597 (19*10^146181-49)/3 146182 Robert Price 05/2019 3598 2^485531-114621 146160 Enzo Doria 05/2015 3599 2^485473-933075 146142 Paul Bourdelais 06/2021 3600 (2^485461-9)/4249 146135 Lelio R Paula 09/2015 3601 (22*10^146130-193)/9 146131 Robert Price 07/2022 3602 2^485389+81887 146117 Enzo Doria 08/2016 3603 32554^30773+30773^32554 146108 Hans Havermann 11/2020 3604 28075^32844-32844^28075 146101 Frank Doornink 06/2024 3605 (10^146063+71)/9 146063 Serge Batalov 07/2015 3606 2*10^146051-63 146052 Robert Price 01/2022 3607 (2^485119+7)/2745 146032 Lelio R Paula 09/2015 3608 (22*10^146029+257)/9 146030 Robert Price 06/2018 3609 7*10^145982-53 145983 Robert Price 06/2020 3610 2^484743+1872923 145923 Enzo Doria 05/2016 3611 33140^25287+25287^33140 145913 Hans Havermann 01/2021 3612 37875^7112+7112^37875 145895 Hans Havermann 01/2021 3613 30542^32529-32529^30542 145890 Frank Doornink 06/2024 3614 32862^27473+27473^32862 145872 Hans Havermann 01/2021 3615 32836^27587+27587^32836 145815 Hans Havermann 01/2021 3616 2^484341+1879157 145802 Enzo Doria 08/2016 3617 2*10^145784-91 145785 Robert Price 04/2020 3618 2^484271-51 145781 Lelio R Paula 11/2017 3619 (188*10^145750-11)/3 145752 Robert Price 02/2022 3620 70^78989-69^78989 145743 Robert Price 01/2014 3621 51^85334+2 145714 Robert Price 07/2015 3622 2^483886-1857101 145665 Enzo Doria 10/2015 3623 29312^32607-32607^29312 145657 Frank Doornink 06/2024 3624 33350^23307+23307^33350 145656 Hans Havermann 01/2021 3625 (19*10^145585+131)/3 145586 Robert Price 06/2020 3626 31815^32332-32332^31815 145580 Frank Doornink 01/2024 3627 2^483563-1863457 145567 Enzo Doria 12/2015 3628 4*10^145563-69 145564 Robert Price 01/2022 3629 2^483516-1861409 145553 Enzo Doria 11/2015 3630 2^483384-115019 145514 Enzo Doria 06/2015 3631 (259*10^145501-1)/3 145503 Robert Price 12/2020 3632 (19*10^145499-61)/3 145500 Robert Price 05/2019 3633 2^483302-3221 145489 Lelio R Paula 12/2012 3634 (23*10^145463+61)/3 145464 Robert Price 01/2022 3635 35523^12434+12434^35523 145453 Hans Havermann 01/2021 3636 (29121^32761-1)/(29121^181-1) 145444 Ryan Propper 11/2023 3637 2^483046+1874029 145412 Enzo Doria 06/2016 3638 2^482991-2789317 145395 Enzo Doria 12/2015 3639 2^482978-2789711 145391 Enzo Doria 12/2015 3640 2^482966-2789711 145388 Enzo Doria 12/2015 3641 2^482817-1858843 145343 Enzo Doria 10/2015 3642 2^482751-113635 145323 Enzo Doria 08/2014 3643 2^482705-459763 145309 Enzo Doria 05/2015 3644 (4^241306+11)/3 145281 Robert Price 03/2017 3645 (238*10^145276-1)/3 145278 Robert Price 04/2020 3646 (19*2^482534+1)/7 145258 Lelio R Paula 09/2015 3647 53^84239-52^84239 145252 Robert Price 01/2013 3648 2^482386+212419 145213 Enzo Doria 08/2023 3649 47952^1067+1067^47952 145207 Hans Havermann 01/2021 3650 (2^482333+5)/9287 145193 Lelio R Paula 09/2015 3651 2^482087+72623 145123 Enzo Doria 04/2016 3652 2^482016-286565 145102 Enzo Doria 07/2015 3653 (19*10^145093+101)/3 145094 Robert Price 09/2019 3654 2^481956+121 145084 Stefano Morozzi 04/2021 3655 27535^32676-32676^27535 145078 Frank Doornink 06/2024 3656 2^481840+15 145049 Robert Price 09/2015 3657 (23*10^145040+7)/3 145041 Robert Price 05/2023 3658 2^481801-481801 145037 Henri Lifchitz 03/2005 3659 2^481775+1869083 145029 Enzo Doria 05/2016 3660 29^99167+2 145022 Ray Chandler 08/2011 3661 2^481663+1875653 144996 Enzo Doria 07/2016 3662 8*10^144977+27 144978 Robert Price 09/2021 3663 29840^32393-32393^29840 144953 Frank Doornink 06/2024 3664 36486^9379+9379^36486 144929 Hans Havermann 12/2020 3665 31580^32209-32209^31580 144922 Frank Doornink 01/2024 3666 35111^13378+13378^35111 144882 Hans Havermann 01/2021 3667 2^481149-459073 144841 Enzo Doria 05/2015 3668 2^481113+181419 144830 Boyan Hu 04/2024 3669 34619^15246+15246^34619 144817 Hans Havermann 01/2021 3670 2^481045-113215 144809 Enzo Doria 07/2014 3671 (64*10^144797+287)/9 144798 Robert Price 04/2019 3672 27320^32629-32629^27320 144758 Frank Doornink 06/2024 3673 2^480859-113695 144753 Enzo Doria 09/2014 3674 (106*10^144744+17)/3 144746 Robert Price 04/2021 3675 7*10^144742-27 144743 Robert Price 11/2022 3676 2^480766-2787191 144725 Enzo Doria 11/2015 3677 (21*27^101106-151)/26 144720 Curtis Bright 05/2015 3678 28915^32438-32438^28915 144710 Frank Doornink 06/2024 3679 2^480678+1874239 144699 Enzo Doria 06/2016 3680 (8*10^144683+1)/9 144683 Serge Batalov 05/2010 3681 L(692147) 144651 Henri Lifchitz 10/2008 3682 (76*10^144648+77)/9 144649 Robert Price 10/2019 3683 32672^26721+26721^32672 144635 Hans Havermann 01/2021 3684 31478^32153-32153^31478 144625 Frank Doornink 01/2024 3685 2^480417+35 144620 Robert Price 11/2015 3686 2^480296-59879 144584 Enzo Doria 10/2015 3687 33157^22878+22878^33157 144546 Hans Havermann 12/2020 3688 27520^32541-32541^27520 144471 Frank Doornink 06/2024 3689 45494^1497+1497^45494 144454 Hans Havermann 12/2020 3690 2^479844+3 144448 Donovan Johnson 06/2006 3691 33442^20803+20803^33442 144407 Hans Havermann 01/2021 3692 (441*33^95095-3833)/32 144405 Eric Chen 12/2023 3693 31892^32061-32061^31892 144393 Norbert Schneider 01/2023 3694 (27*2^479642+1)/733 144386 Lelio R Paula 08/2015 3695 (56*10^144380+169)/9 144381 Robert Price 03/2022 3696 44917^1638+1638^44917 144378 Hans Havermann 12/2020 3697 (21*2^479605-1)/11 144376 Lelio R Paula 09/2015 3698 (56*10^144336+583)/9 144337 Robert Price 08/2021 3699 5*2^479430-3 144324 Jon Grantham 07/2023 3700 2^479348-2792219 144299 Enzo Doria 02/2016 3701 31134^32111-32111^31134 144283 Frank Doornink 01/2024 3702 3^302389-6242 144277 Enzo Doria 05/2014 3703 31665^32056-32056^31665 144271 Frank Doornink 01/2024 3704 33778^18641+18641^33778 144248 Hans Havermann 01/2021 3705 29083^32312-32312^29083 144230 Frank Doornink 06/2024 3706 2*10^144220-3 144221 Robert Price 07/2015 3707 25313^32750-32750^25313 144210 Frank Doornink 01/2024 3708 2^478904-109109 144165 Enzo Doria 04/2014 3709 43698^1987+1987^43698 144125 Hans Havermann 12/2020 3710 79^75948+75948 144121 Kellen Shenton 06/2023 3711 26941^32522-32522^26941 144086 Frank Doornink 06/2024 3712 36128^9723+9723^36128 144072 Hans Havermann 01/2021 3713 32817^24518+24518^32817 144050 Hans Havermann 12/2020 3714 (772*10^144036-7)/9 144038 Robert Price 06/2022 3715 34295^15828+15828^34295 144020 Hans Havermann 01/2021 3716 2^478337-115333 143994 Enzo Doria 07/2015 3717 (7*2^478330-1)/3 143993 Lelio R Paula 08/2015 3718 88^74047-87^74047 143984 Robert Price 05/2015 3719 33242^21441+21441^33242 143980 Hans Havermann 01/2021 3720 (19*10^143963+467)/9 143964 Robert Price 02/2018 3721 (71^77761+1)/72 143954 Paul Bourdelais 09/2017 3722 33490^19859+19859^33490 143939 Hans Havermann 01/2021 3723 (853*10^143931-7)/9 143933 Robert Price 07/2021 3724 2^478088+27 143919 Robert Price 11/2015 3725 (8*10^143898-137)/3 143899 Robert Price 03/2022 3726 7*10^143857-93 143858 Robert Price 08/2020 3727 3*10^143844+61 143845 Robert Price 09/2020 3728 41358^3005+3005^41358 143837 Hans Havermann 01/2021 3729 2^477475-22071 143735 Enzo Doria 07/2013 3730 2^477417-22123 143717 Enzo Doria 07/2013 3731 2^477359-3577 143700 Yves Minet 03/2017 3732 39435^4402+4402^39435 143688 Hans Havermann 01/2021 3733 (14*10^143662-71)/3 143663 Robert Price 12/2018 3734 6^184614+5 143658 Paul Bourdelais 01/2021 3735 46371^1252+1252^46371 143640 Hans Havermann 12/2020 3736 34975^12748+12748^34975 143588 Hans Havermann 01/2021 3737 2^476936-396765 143573 Enzo Doria 07/2013 3738 2^476888-2791229 143558 Enzo Doria 01/2016 3739 2^476868-1859939 143552 Enzo Doria 11/2015 3740 40807^3294+3294^40807 143548 Hans Havermann 12/2020 3741 755^49878+49878^755 143547 Norbert Schneider 04/2019 3742 (19^112247-4^112247)/15 143536 Robert Price 03/2021 3743 35561^10872+10872^35561 143536 Hans Havermann 06/2021 3744 37637^6492+6492^37637 143487 Hans Havermann 05/2021 3745 61567^214+214^61567 143477 Hans Havermann 05/2021 3746 25933^32504-32504^25933 143468 Frank Doornink 03/2024 3747 2^476558-113627 143459 Enzo Doria 08/2014 3748 2^476478-45 143435 Lelio R Paula 11/2017 3749 36380^8757+8757^36380 143423 Hans Havermann 06/2021 3750 32510^25707+25707^32510 143371 Hans Havermann 05/2021

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 19 2024 15:29 (Time in France)

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