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) !!!
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
7501 | 2^338406-184175 | 101871 | Stefano Morozzi | 04/2022 |
7502 | 2^338405+94451 | 101871 | Stefano Morozzi | 09/2022 |
7503 | 2^338406-161217 | 101871 | Stefano Morozzi | 12/2022 |
7504 | 2^338406+199929 | 101871 | Stefano Morozzi | 02/2023 |
7505 | 2^338404+55717 | 101870 | Stefano Morozzi | 01/2022 |
7506 | 2^338403+36261 | 101870 | Stefano Morozzi | 04/2022 |
7507 | 2^338402-34431 | 101870 | Stefano Morozzi | 04/2022 |
7508 | 2^338404-159215 | 101870 | Stefano Morozzi | 04/2022 |
7509 | 2^338403+18363 | 101870 | Stefano Morozzi | 09/2022 |
7510 | 2^338403+170235 | 101870 | Stefano Morozzi | 11/2022 |
7511 | 2^338399+23045 | 101869 | Stefano Morozzi | 11/2022 |
7512 | 2^338399-65535 | 101869 | Stefano Morozzi | 01/2023 |
7513 | 2^338395-127449 | 101868 | Stefano Morozzi | 12/2021 |
7514 | 2^338398-127637 | 101868 | Stefano Morozzi | 01/2022 |
7515 | 2^338398-166533 | 101868 | Stefano Morozzi | 01/2023 |
7516 | 2^338394+100317 | 101867 | Stefano Morozzi | 11/2021 |
7517 | 2^338393-152749 | 101867 | Stefano Morozzi | 01/2022 |
7518 | 2^338393+163025 | 101867 | Stefano Morozzi | 04/2022 |
7519 | 2^338393+89229 | 101867 | Stefano Morozzi | 05/2022 |
7520 | 2^338393+99647 | 101867 | Stefano Morozzi | 02/2023 |
7521 | 2^338394-192471 | 101867 | Stefano Morozzi | 02/2023 |
7522 | 2^338390+76627 | 101866 | Stefano Morozzi | 12/2021 |
7523 | 2^338389-85081 | 101866 | Stefano Morozzi | 06/2022 |
7524 | 2^338390+148113 | 101866 | Stefano Morozzi | 11/2022 |
7525 | 2^338389-14253 | 101866 | Stefano Morozzi | 01/2023 |
7526 | 2^338390-114297 | 101866 | Stefano Morozzi | 01/2023 |
7527 | 2^338391-64225 | 101866 | Stefano Morozzi | 01/2023 |
7528 | 2^338389-16971 | 101866 | Stefano Morozzi | 02/2023 |
7529 | 2^338387-75685 | 101865 | Stefano Morozzi | 12/2021 |
7530 | 2^338388-53459 | 101865 | Stefano Morozzi | 01/2022 |
7531 | 2^338388-36575 | 101865 | Stefano Morozzi | 12/2022 |
7532 | 2^338385-190311 | 101865 | Stefano Morozzi | 01/2023 |
7533 | 2^338384+131563 | 101864 | Stefano Morozzi | 01/2022 |
7534 | 2^338382+109069 | 101864 | Stefano Morozzi | 03/2022 |
7535 | 2^338384+168987 | 101864 | Stefano Morozzi | 09/2022 |
7536 | 2^338383-42367 | 101864 | Stefano Morozzi | 02/2023 |
7537 | 2^338380+77125 | 101863 | Stefano Morozzi | 12/2021 |
7538 | 2^338381-35539 | 101863 | Stefano Morozzi | 06/2022 |
7539 | 2^338378-125841 | 101862 | Stefano Morozzi | 12/2021 |
7540 | 2^338375+27815 | 101862 | Stefano Morozzi | 01/2022 |
7541 | 2^338375-28509 | 101862 | Stefano Morozzi | 01/2022 |
7542 | 2^338375+29985 | 101862 | Stefano Morozzi | 01/2022 |
7543 | 2^338377+157881 | 101862 | Stefano Morozzi | 02/2022 |
7544 | 2^338375+59589 | 101862 | Stefano Morozzi | 03/2022 |
7545 | 2^338378+36399 | 101862 | Stefano Morozzi | 04/2022 |
7546 | 2^338378-159773 | 101862 | Stefano Morozzi | 04/2022 |
7547 | 2^338378+14883 | 101862 | Stefano Morozzi | 05/2022 |
7548 | 2^338376+140173 | 101862 | Stefano Morozzi | 06/2022 |
7549 | 2^338375+18761 | 101862 | Stefano Morozzi | 09/2022 |
7550 | 2^338373-75103 | 101861 | Stefano Morozzi | 12/2021 |
7551 | 2^338372+128877 | 101861 | Stefano Morozzi | 01/2022 |
7552 | 2^338374-28731 | 101861 | Stefano Morozzi | 01/2022 |
7553 | 2^338374-128427 | 101861 | Stefano Morozzi | 01/2022 |
7554 | 2^338372+37875 | 101861 | Stefano Morozzi | 04/2022 |
7555 | 2^338373+161541 | 101861 | Stefano Morozzi | 04/2022 |
7556 | 2^338374+37759 | 101861 | Stefano Morozzi | 04/2022 |
7557 | 2^338372+93235 | 101861 | Stefano Morozzi | 09/2022 |
7558 | 2^338373-63273 | 101861 | Stefano Morozzi | 12/2022 |
7559 | 2^338369+29427 | 101860 | Stefano Morozzi | 01/2022 |
7560 | 2^338370+179133 | 101860 | Stefano Morozzi | 01/2022 |
7561 | 2^338369+131501 | 101860 | Stefano Morozzi | 01/2022 |
7562 | 2^338369+181649 | 101860 | Stefano Morozzi | 02/2022 |
7563 | 2^338370-4787 | 101860 | Stefano Morozzi | 02/2022 |
7564 | 2^338371-133491 | 101860 | Stefano Morozzi | 04/2022 |
7565 | 2^338371+42023 | 101860 | Stefano Morozzi | 09/2022 |
7566 | 2^338371+145323 | 101860 | Stefano Morozzi | 11/2022 |
7567 | 2^338371-138145 | 101860 | Stefano Morozzi | 12/2022 |
7574 | 2^338368-20369 | 101859 | Enzo Doria | 06/2013 |
7575 | 2^338366+74179 | 101859 | Enzo Doria | 04/2016 |
7568 | 2^338366+53853 | 101859 | Stefano Morozzi | 01/2022 |
7569 | 2^338365-31665 | 101859 | Stefano Morozzi | 03/2022 |
7570 | 2^338368-156345 | 101859 | Stefano Morozzi | 03/2022 |
7571 | 2^338366-159867 | 101859 | Stefano Morozzi | 04/2022 |
7572 | 2^338368-63509 | 101859 | Stefano Morozzi | 12/2022 |
7573 | 2^338365-190975 | 101859 | Stefano Morozzi | 01/2023 |
7576 | 2^338362-180845 | 101858 | Stefano Morozzi | 02/2022 |
7577 | 2^338364-155769 | 101858 | Stefano Morozzi | 02/2022 |
7578 | 2^338362+142843 | 101858 | Stefano Morozzi | 09/2022 |
7579 | 2^338362+170019 | 101858 | Stefano Morozzi | 11/2022 |
7580 | 2^338361-100875 | 101857 | Stefano Morozzi | 12/2021 |
7581 | 2^338361+154169 | 101857 | Stefano Morozzi | 01/2022 |
7582 | 2^338359-189645 | 101857 | Stefano Morozzi | 01/2023 |
7583 | 2^338356+101271 | 101856 | Stefano Morozzi | 12/2021 |
7584 | 2^338356+53383 | 101856 | Stefano Morozzi | 01/2022 |
7585 | 2^338355+59393 | 101856 | Stefano Morozzi | 03/2022 |
7586 | 2^338356+60775 | 101856 | Stefano Morozzi | 03/2022 |
7587 | 2^338356-106257 | 101856 | Stefano Morozzi | 03/2022 |
7588 | 2^338357-58921 | 101856 | Stefano Morozzi | 04/2022 |
7589 | 2^338356+94605 | 101856 | Stefano Morozzi | 09/2022 |
7590 | 2^338356+117813 | 101856 | Stefano Morozzi | 09/2022 |
7591 | 2^338358-38475 | 101856 | Stefano Morozzi | 12/2022 |
7592 | 2^338353-190291 | 101855 | Stefano Morozzi | 01/2023 |
7593 | 2^338350-152933 | 101854 | Stefano Morozzi | 01/2022 |
7594 | 2^338350+6337 | 101854 | Stefano Morozzi | 01/2022 |
7595 | 2^338350+168759 | 101854 | Stefano Morozzi | 09/2022 |
7598 | 27088^5755+5755^27088 | 101853 | Hans Havermann | 01/2019 |
7596 | 2^338347+125901 | 101853 | Stefano Morozzi | 11/2021 |
7597 | 2^338346-10643 | 101853 | Stefano Morozzi | 06/2022 |
7599 | 2^338343+152271 | 101852 | Stefano Morozzi | 12/2021 |
7600 | 2^338345+154107 | 101852 | Stefano Morozzi | 01/2022 |
7601 | 2^338342+155397 | 101852 | Stefano Morozzi | 01/2022 |
7602 | 2^338342-130767 | 101852 | Stefano Morozzi | 02/2022 |
7603 | 2^338345-30123 | 101852 | Stefano Morozzi | 02/2022 |
7604 | 2^338345+35747 | 101852 | Stefano Morozzi | 03/2022 |
7605 | 2^338345-133131 | 101852 | Stefano Morozzi | 04/2022 |
7606 | 2^338345-134559 | 101852 | Stefano Morozzi | 04/2022 |
7607 | 2^338342+170073 | 101852 | Stefano Morozzi | 11/2022 |
7608 | 2^338344+46567 | 101852 | Stefano Morozzi | 11/2022 |
7609 | 2^338344+97141 | 101852 | Stefano Morozzi | 11/2022 |
7610 | 2^338342-162213 | 101852 | Stefano Morozzi | 12/2022 |
7611 | 2^338339+2753 | 101851 | Stefano Morozzi | 12/2021 |
7612 | 2^338341+128415 | 101851 | Stefano Morozzi | 01/2022 |
7613 | 2^338338+2677 | 101850 | Stefano Morozzi | 12/2021 |
7614 | 2^338336+54607 | 101850 | Stefano Morozzi | 01/2022 |
7615 | 2^338338+109999 | 101850 | Stefano Morozzi | 03/2022 |
7616 | 2^338336+161575 | 101850 | Stefano Morozzi | 04/2022 |
7617 | 2^338335+51975 | 101849 | Stefano Morozzi | 12/2021 |
7618 | 2^338335-152607 | 101849 | Stefano Morozzi | 01/2022 |
7619 | 2^338334+55273 | 101849 | Stefano Morozzi | 01/2022 |
7620 | 2^338332+34315 | 101849 | Stefano Morozzi | 03/2022 |
7621 | 2^338335+158759 | 101849 | Stefano Morozzi | 03/2022 |
7622 | 2^338332+67621 | 101849 | Stefano Morozzi | 09/2022 |
7623 | 2^338332-66099 | 101849 | Stefano Morozzi | 01/2023 |
7624 | 2^338334-191043 | 101849 | Stefano Morozzi | 01/2023 |
7625 | 2^338331+83403 | 101848 | Stefano Morozzi | 02/2022 |
7626 | 2^338330-110865 | 101848 | Stefano Morozzi | 06/2022 |
7627 | 2^338330+71047 | 101848 | Stefano Morozzi | 11/2022 |
7628 | 2^338328-5295 | 101847 | Stefano Morozzi | 02/2022 |
7629 | 2^338327+143585 | 101847 | Stefano Morozzi | 09/2022 |
7630 | 2^338324-179667 | 101846 | Stefano Morozzi | 02/2022 |
7631 | 2^338322+21903 | 101846 | Stefano Morozzi | 11/2022 |
7632 | 2^338324+98047 | 101846 | Stefano Morozzi | 11/2022 |
7633 | 2^338323-87729 | 101846 | Stefano Morozzi | 12/2022 |
7634 | 2^338322-16667 | 101846 | Stefano Morozzi | 01/2023 |
7635 | 2^338325-142159 | 101846 | Stefano Morozzi | 02/2023 |
7636 | 2^338316-175857 | 101844 | Stefano Morozzi | 12/2021 |
7637 | 2^338318+54405 | 101844 | Stefano Morozzi | 01/2022 |
7638 | 2^338316+32961 | 101844 | Stefano Morozzi | 02/2022 |
7639 | 2^338317+68175 | 101844 | Stefano Morozzi | 09/2022 |
7640 | 2^338318-86171 | 101844 | Stefano Morozzi | 12/2022 |
7641 | 2^338315-178635 | 101843 | Stefano Morozzi | 01/2022 |
7642 | 2^338315+34899 | 101843 | Stefano Morozzi | 03/2022 |
7643 | 2^338314-106973 | 101843 | Stefano Morozzi | 03/2022 |
7644 | 2^338313+170411 | 101843 | Stefano Morozzi | 11/2022 |
7645 | 2^338315-88807 | 101843 | Stefano Morozzi | 12/2022 |
7646 | 2^338311-51799 | 101842 | Stefano Morozzi | 12/2021 |
7647 | 2^338309+157259 | 101842 | Stefano Morozzi | 02/2022 |
7648 | 2^338310+40903 | 101842 | Stefano Morozzi | 06/2022 |
7649 | 2^338309-168051 | 101842 | Stefano Morozzi | 02/2023 |
7650 | 2^338308-55853 | 101841 | Stefano Morozzi | 02/2022 |
7651 | 2^338307+134871 | 101841 | Stefano Morozzi | 03/2022 |
7652 | 2^338307+19689 | 101841 | Stefano Morozzi | 09/2022 |
7653 | 2^338308+66873 | 101841 | Stefano Morozzi | 09/2022 |
7654 | 2^338306+124399 | 101841 | Stefano Morozzi | 02/2023 |
7655 | 2^338306-91913 | 101841 | Stefano Morozzi | 02/2023 |
7656 | 2^338304+78757 | 101840 | Stefano Morozzi | 01/2022 |
7657 | 2^338304-5807 | 101840 | Stefano Morozzi | 02/2022 |
7658 | 2^338305+110879 | 101840 | Stefano Morozzi | 03/2022 |
7659 | 2^338304+91147 | 101840 | Stefano Morozzi | 06/2022 |
7660 | 2^338304-64475 | 101840 | Stefano Morozzi | 01/2023 |
7661 | 2^338299+85611 | 101839 | Stefano Morozzi | 03/2022 |
7662 | 2^338299-189985 | 101839 | Stefano Morozzi | 01/2023 |
7663 | 2^338298-25571 | 101838 | Stefano Morozzi | 12/2021 |
7664 | 2^338297+35547 | 101838 | Stefano Morozzi | 03/2022 |
7665 | 2^338298+111199 | 101838 | Stefano Morozzi | 03/2022 |
7666 | 2^338297+145455 | 101838 | Stefano Morozzi | 11/2022 |
7667 | 2^338297-166285 | 101838 | Stefano Morozzi | 01/2023 |
7668 | 2^338294-150711 | 101837 | Stefano Morozzi | 12/2021 |
7669 | 2^338294+177597 | 101837 | Stefano Morozzi | 12/2021 |
7670 | 2^338294-177807 | 101837 | Stefano Morozzi | 01/2022 |
7671 | 2^338295-52929 | 101837 | Stefano Morozzi | 01/2022 |
7672 | 2^338293+37407 | 101837 | Stefano Morozzi | 04/2022 |
7673 | 2^338292+40573 | 101837 | Stefano Morozzi | 06/2022 |
7674 | 2^338294+172425 | 101837 | Stefano Morozzi | 11/2022 |
7675 | 2^338293-191799 | 101837 | Stefano Morozzi | 02/2023 |
7676 | 2^338289+30957 | 101836 | Stefano Morozzi | 01/2022 |
7677 | 2^338291+131825 | 101836 | Stefano Morozzi | 02/2022 |
7678 | 2^338291+110111 | 101836 | Stefano Morozzi | 03/2022 |
7679 | 2^338290-156423 | 101836 | Stefano Morozzi | 03/2022 |
7680 | 2^338291-157845 | 101836 | Stefano Morozzi | 03/2022 |
7681 | 2^338290+69243 | 101836 | Stefano Morozzi | 09/2022 |
7682 | 2^338291-189327 | 101836 | Stefano Morozzi | 01/2023 |
7683 | 2^338291+74079 | 101836 | Stefano Morozzi | 02/2023 |
7684 | 2^338288+26623 | 101835 | Stefano Morozzi | 12/2021 |
7685 | 2^338286+33325 | 101835 | Stefano Morozzi | 02/2022 |
7686 | 2^338287+132633 | 101835 | Stefano Morozzi | 02/2022 |
7687 | 2^338287+157149 | 101835 | Stefano Morozzi | 02/2022 |
7688 | 2^338288-107193 | 101835 | Stefano Morozzi | 03/2022 |
7689 | 2^338286-83333 | 101835 | Stefano Morozzi | 04/2022 |
7690 | 2^338287+114425 | 101835 | Stefano Morozzi | 05/2022 |
7691 | 2^338288+194403 | 101835 | Stefano Morozzi | 09/2022 |
7692 | 2^338288-113177 | 101835 | Stefano Morozzi | 12/2022 |
7693 | 2^338288-65747 | 101835 | Stefano Morozzi | 01/2023 |
7694 | 2^338285+82131 | 101834 | Stefano Morozzi | 02/2022 |
7695 | 2^338284-104217 | 101834 | Stefano Morozzi | 02/2022 |
7696 | 2^338282-84533 | 101834 | Stefano Morozzi | 04/2022 |
7697 | 2^338283+67545 | 101834 | Stefano Morozzi | 09/2022 |
7698 | 2^338283-65439 | 101834 | Stefano Morozzi | 01/2023 |
7707 | 2^338280-19745 | 101833 | Enzo Doria | 06/2013 |
7699 | 2^338279-125947 | 101833 | Stefano Morozzi | 12/2021 |
7700 | 2^338280-50343 | 101833 | Stefano Morozzi | 12/2021 |
7701 | 2^338279+133331 | 101833 | Stefano Morozzi | 02/2022 |
7702 | 2^338281-54561 | 101833 | Stefano Morozzi | 02/2022 |
7703 | 2^338280+192063 | 101833 | Stefano Morozzi | 09/2022 |
7704 | 2^338281+18971 | 101833 | Stefano Morozzi | 09/2022 |
7705 | 2^338281-186711 | 101833 | Stefano Morozzi | 12/2022 |
7706 | 2^338281-91273 | 101833 | Stefano Morozzi | 01/2023 |
7708 | 2^338278+188215 | 101832 | Stefano Morozzi | 05/2022 |
7709 | 2^338273+181101 | 101831 | Stefano Morozzi | 01/2022 |
7710 | 2^338275+32909 | 101831 | Stefano Morozzi | 02/2022 |
7711 | 2^338272+166431 | 101831 | Stefano Morozzi | 06/2022 |
7712 | 2^338272+22011 | 101831 | Stefano Morozzi | 11/2022 |
7713 | 2^338275+148271 | 101831 | Stefano Morozzi | 11/2022 |
7714 | 2^338270-135725 | 101830 | Stefano Morozzi | 06/2022 |
7715 | 2^338269-136951 | 101830 | Stefano Morozzi | 12/2022 |
7716 | 2^338270-192701 | 101830 | Stefano Morozzi | 02/2023 |
7717 | 2^338271-42831 | 101830 | Stefano Morozzi | 02/2023 |
7718 | 2^338266+110665 | 101829 | Stefano Morozzi | 03/2022 |
7719 | 2^338267+110481 | 101829 | Stefano Morozzi | 03/2022 |
7720 | 2^338267-166035 | 101829 | Stefano Morozzi | 01/2023 |
7721 | 2^338265-154893 | 101828 | Stefano Morozzi | 02/2022 |
7722 | 2^338264+163611 | 101828 | Stefano Morozzi | 05/2022 |
7723 | 2^338263-62767 | 101828 | Stefano Morozzi | 12/2022 |
7724 | 2^338261-188119 | 101827 | Stefano Morozzi | 12/2022 |
7725 | 2^338259-40327 | 101827 | Stefano Morozzi | 01/2023 |
7726 | 2^338256+5223 | 101826 | Stefano Morozzi | 01/2022 |
7727 | 2^338257+178425 | 101826 | Stefano Morozzi | 01/2022 |
7728 | 2^338256-180569 | 101826 | Stefano Morozzi | 02/2022 |
7729 | 2^338257-5965 | 101826 | Stefano Morozzi | 02/2022 |
7730 | 2^338258-9225 | 101826 | Stefano Morozzi | 04/2022 |
7731 | 2^338255-127021 | 101825 | Stefano Morozzi | 12/2021 |
7732 | 2^338253+159005 | 101825 | Stefano Morozzi | 03/2022 |
7733 | 2^338253+64817 | 101825 | Stefano Morozzi | 05/2022 |
7734 | 2^338254-85403 | 101825 | Stefano Morozzi | 06/2022 |
7735 | 2^338254+142947 | 101825 | Stefano Morozzi | 09/2022 |
7736 | 2^338253+121095 | 101825 | Stefano Morozzi | 11/2022 |
7737 | 2^338254+196725 | 101825 | Stefano Morozzi | 11/2022 |
7738 | 2^338254-91007 | 101825 | Stefano Morozzi | 01/2023 |
7739 | 2^338251+78975 | 101824 | Stefano Morozzi | 01/2022 |
7740 | 2^338252-178709 | 101824 | Stefano Morozzi | 01/2022 |
7741 | 2^338252+129703 | 101824 | Stefano Morozzi | 01/2022 |
7742 | 2^338252+132285 | 101824 | Stefano Morozzi | 02/2022 |
7743 | 2^338251-33381 | 101824 | Stefano Morozzi | 04/2022 |
7744 | 2^338252-13805 | 101824 | Stefano Morozzi | 12/2022 |
7745 | 2^338245-134755 | 101822 | Stefano Morozzi | 04/2022 |
7746 | 2^338244-59219 | 101822 | Stefano Morozzi | 04/2022 |
7747 | 2^338244-64703 | 101822 | Stefano Morozzi | 01/2023 |
7748 | 2^338241+1391 | 101821 | Stefano Morozzi | 12/2021 |
7749 | 2^338242+151195 | 101821 | Stefano Morozzi | 12/2021 |
7750 | 2^338240-152495 | 101821 | Stefano Morozzi | 12/2021 |