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
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 501 | 2^1594129+22697 | 479881 | Enzo Doria | 11/2023 |
| 502 | 2^1593922+213289 | 479819 | Enzo Doria | 10/2023 |
| 503 | 2^1592677+228257 | 479444 | Enzo Doria | 11/2024 |
| 504 | 2^1592234+26809 | 479311 | Enzo Doria | 03/2024 |
| 505 | 2^1590797+34967 | 478878 | Enzo Doria | 10/2024 |
| 506 | (94^241993-1)/93 | 477482 | Paul Bourdelais | 09/2020 |
| 507 | 2^1585195+1888373 | 477192 | Enzo Doria | 08/2017 |
| 508 | 2^1585021+43427 | 477139 | Enzo Doria | 03/2025 |
| 509 | (33^313553+1)/34 | 476134 | Paul Bourdelais | 02/2021 |
| 510 | 2^1581306+220309 | 476021 | Enzo Doria | 03/2024 |
| 511 | 2^1578654+215029 | 475223 | Enzo Doria | 01/2024 |
| 512 | (84615^96721-1)/(84615^311-1) | 475056 | Ryan Propper | 11/2023 |
| 513 | 3^994536+16 | 474515 | Robert Price | 10/2020 |
| 514 | 2^1576219+233663 | 474490 | Enzo Doria | 03/2025 |
| 515 | 2^1575391+71483 | 474240 | Enzo Doria | 04/2018 |
| 516 | (2^1572882+5)/3 | 473485 | Serge Batalov | 08/2015 |
| 517 | (6^608099-1)/5 | 473193 | Paul Bourdelais | 05/2010 |
| 518 | 2^1570431+41183 | 472747 | Enzo Doria | 02/2025 |
| 519 | 2^1569708+20371 | 472530 | Enzo Doria | 09/2023 |
| 520 | 2^1569375+29153 | 472429 | Enzo Doria | 05/2024 |
| 521 | 3^989124+16 | 471933 | Robert Price | 10/2020 |
| 522 | 2^1567006+1888099 | 471716 | Enzo Doria | 05/2017 |
| 523 | 2^1563462+39919 | 470649 | Enzo Doria | 12/2024 |
| 524 | 2^1563067+1889813 | 470531 | Enzo Doria | 08/2017 |
| 525 | 2^1562428+215851 | 470338 | Enzo Doria | 02/2024 |
| 526 | 2^1557036+226321 | 468715 | Enzo Doria | 09/2024 |
| 527 | 2^1556730+222829 | 468623 | Enzo Doria | 07/2024 |
| 528 | 2^1554175+228353 | 467854 | Enzo Doria | 12/2024 |
| 529 | 2^1551415+215813 | 467023 | Enzo Doria | 02/2024 |
| 530 | 2^1551411+212933 | 467022 | Enzo Doria | 09/2023 |
| 531 | 2^1550887+36743 | 466864 | Enzo Doria | 11/2024 |
| 532 | 2^1549797+60197 | 466536 | Enzo Doria | 02/2018 |
| 533 | 2^1549030+1887619 | 466305 | Enzo Doria | 05/2017 |
| 534 | 2^1545920+41467 | 465369 | Enzo Doria | 02/2025 |
| 535 | 2^1544971+43403 | 465083 | Enzo Doria | 03/2025 |
| 536 | 416^177481-415^177481 | 464840 | Jean-Louis Charton | 12/2016 |
| 537 | 2^1541374+226729 | 464000 | Enzo Doria | 09/2024 |
| 538 | (78^245183-1)/77 | 463908 | Paul Bourdelais | 02/2021 |
| 539 | 93331^93331-90^90 | 463858 | Henri Lifchitz | 10/2024 |
| 540 | 2^1540117+31907 | 463622 | Enzo Doria | 04/2024 |
| 541 | 2^1538959-25 | 463273 | Boyan Hu | 01/2025 |
| 542 | 2^1537058+29839 | 462701 | Enzo Doria | 07/2024 |
| 543 | 2^1534770+20809 | 462012 | Enzo Doria | 08/2023 |
| 544 | 2^1531286+24799 | 460964 | Enzo Doria | 11/2023 |
| 545 | 2^1530725+38267 | 460795 | Enzo Doria | 10/2024 |
| 546 | 2^1530380+38011 | 460691 | Enzo Doria | 11/2024 |
| 547 | 2^1527857+225269 | 459931 | Enzo Doria | 11/2024 |
| 548 | 10^459480-11 | 459480 | Mischa Rodermond | 04/2023 |
| 549 | (5^656657-2^656657)/3 | 458984 | Jon Grantham | 08/2023 |
| 550 | 2^1522569+71657 | 458339 | Enzo Doria | 04/2018 |
| 551 | 2^1520990+35257 | 457864 | Enzo Doria | 10/2024 |
| 552 | 2^1520920+38251 | 457843 | Enzo Doria | 11/2024 |
| 553 | (55814^96721-1)/(55814^311-1) | 457634 | Ryan Propper | 11/2023 |
| 554 | 2^1518191+75353 | 457022 | Ben Maloney / Five or Bust | 01/2009 |
| 555 | 2^1512733+227027 | 455379 | Enzo Doria | 10/2024 |
| 556 | 2^1510915+223463 | 454831 | Enzo Doria | 06/2024 |
| 557 | 6^584279-5 | 454658 | Paul Bourdelais | 02/2021 |
| 558 | 2^1509037-13 | 454266 | Stefano Morozzi | 12/2022 |
| 559 | (52^264697-1)/51 | 454220 | Paul Bourdelais | 10/2021 |
| 560 | 2^1507169+29027 | 453704 | Enzo Doria | 05/2024 |
| 561 | 2^1506029+1890167 | 453360 | Enzo Doria | 02/2018 |
| 562 | 2^1504232+26101 | 452819 | Enzo Doria | 01/2024 |
| 563 | 2^1501670+41629 | 452048 | Enzo Doria | 02/2025 |
| 564 | 2^1498015+219113 | 450948 | Enzo Doria | 03/2024 |
| 565 | 2^1497532+220471 | 450803 | Enzo Doria | 04/2024 |
| 566 | 2^1497523+230873 | 450800 | Enzo Doria | 01/2025 |
| 567 | 2^1497369+216977 | 450753 | Enzo Doria | 01/2024 |
| 568 | (34^294277+1)/35 | 450678 | Paul Bourdelais | 06/2018 |
| 569 | 2^1496854+232399 | 450598 | Enzo Doria | 02/2025 |
| 570 | 2^1496449+42587 | 450477 | Enzo Doria | 02/2025 |
| 571 | 2^1495434+1890439 | 450171 | Enzo Doria | 12/2017 |
| 572 | 2^1495078+227779 | 450064 | Enzo Doria | 10/2024 |
| 573 | 2^1494634+7 | 449930 | Stefano Morozzi | 10/2022 |
| 574 | 2^1493170+784129 | 449489 | Enzo Doria | 08/2017 |
| 575 | 2^1490332-229043 | 448635 | Enzo Doria | 01/2025 |
| 576 | 2^1489873+1888277 | 448497 | Enzo Doria | 06/2017 |
| 577 | 2^1487389+32417 | 447749 | Enzo Doria | 06/2024 |
| 578 | 2^1486846+36019 | 447586 | Enzo Doria | 11/2024 |
| 579 | 2^1485471+224789 | 447172 | Enzo Doria | 09/2024 |
| 580 | 2^1485203+71663 | 447091 | Enzo Doria | 09/2023 |
| 581 | 2^1484671+1888463 | 446931 | Enzo Doria | 06/2017 |
| 582 | 2^1483112+23961 | 446462 | Enzo Doria | 12/2023 |
| 583 | 2^1482867+1886783 | 446388 | Enzo Doria | 04/2017 |
| 584 | 2^1482148+284011 | 446172 | Enzo Doria | 04/2017 |
| 585 | 2^1481363+215843 | 445935 | Enzo Doria | 12/2023 |
| 586 | 2^1480415+217643 | 445650 | Enzo Doria | 02/2024 |
| 587 | 2^1480400+225013 | 445645 | Enzo Doria | 10/2024 |
| 588 | 2^1479356+1888291 | 445331 | Enzo Doria | 06/2017 |
| 589 | (157742^85849-1)/(157742^293-1) | 444716 | Ryan Propper | 11/2023 |
| 590 | 2^1476810+23299 | 444565 | Enzo Doria | 12/2023 |
| 591 | 2^1474222+38569 | 443786 | Enzo Doria | 11/2024 |
| 592 | 2^1474189+36557 | 443776 | Enzo Doria | 11/2024 |
| 593 | 2^1473184+212671 | 443473 | Enzo Doria | 09/2023 |
| 594 | 2^1472225+37997 | 443184 | Enzo Doria | 10/2024 |
| 595 | 2^1466432+20371 | 441441 | Enzo Doria | 08/2023 |
| 596 | 14^384558+3 | 440753 | Paul Bourdelais | 01/2021 |
| 597 | 2^1463913+219047 | 440682 | Enzo Doria | 04/2024 |
| 598 | 2^1461244+784531 | 439879 | Enzo Doria | 10/2017 |
| 599 | 2^1461058+34429 | 439823 | Enzo Doria | 08/2024 |
| 600 | 2^1460142+233959 | 439547 | Enzo Doria | 03/2025 |
| 601 | 2^1459599+215813 | 439384 | Enzo Doria | 01/2024 |
| 602 | 2^1457449+25757 | 438736 | Enzo Doria | 12/2023 |
| 603 | 2^1457045+231317 | 438615 | Enzo Doria | 01/2025 |
| 604 | 3^919094+5*2^919094 | 438520 | Jon Grantham | 08/2023 |
| 605 | 2^1456277+28229 | 438384 | Enzo Doria | 03/2024 |
| 606 | 2^1455129+218027 | 438038 | Enzo Doria | 01/2024 |
| 607 | 2^1454061+216977 | 437716 | Enzo Doria | 01/2024 |
| 608 | 2^1453419+26783 | 437523 | Enzo Doria | 01/2024 |
| 609 | (67^239053+1)/68 | 436527 | Paul Bourdelais | 09/2021 |
| 610 | 2^1448714+231559 | 436107 | Enzo Doria | 02/2025 |
| 611 | 2^1448122+74209 | 435929 | Enzo Doria | 08/2023 |
| 612 | 2^1446449+221087 | 435425 | Enzo Doria | 05/2024 |
| 613 | 2^1446263+74333 | 435369 | Enzo Doria | 08/2023 |
| 614 | 2^1444386+221029 | 434804 | Enzo Doria | 03/2024 |
| 615 | (80^228419+1)/81 | 434701 | Paul Bourdelais | 02/2021 |
| 616 | 2^1443089+60227 | 434414 | Enzo Doria | 10/2017 |
| 617 | (21^328129-1)/20 | 433858 | Paul Bourdelais | 06/2014 |
| 618 | (35^280979+1)/36 | 433850 | Paul Bourdelais | 09/2021 |
| 619 | 2^1438663+214175 | 433081 | Enzo Doria | 11/2023 |
| 620 | 2^1434519+215813 | 431834 | Enzo Doria | 01/2024 |
| 621 | 2^1434400+3 | 431798 | Paul Bourdelais | 06/2019 |
| 622 | 2^1434298+31669 | 431767 | Enzo Doria | 08/2024 |
| 623 | 2^1434097+215207 | 431707 | Enzo Doria | 11/2023 |
| 624 | 2^1433033+212987 | 431386 | Enzo Doria | 10/2023 |
| 625 | 2^1432308+1888801 | 431168 | Enzo Doria | 10/2017 |
| 626 | (2^1430131+1)/(3*356468732537*36519993971459) | 430487 | Gord Palameta | 12/2018 |
| 627 | (7^508867-2^508867)/5 | 430042 | Jon Grantham | 08/2023 |
| 628 | 2^1428489+25097 | 430019 | Enzo Doria | 11/2023 |
| 629 | 2^1425483+1886813 | 429114 | Enzo Doria | 04/2017 |
| 630 | (63^238481+1)/64 | 429107 | Paul Bourdelais | 12/2020 |
| 631 | (17^348259+1)/18 | 428514 | Paul Bourdelais | 05/2014 |
| 632 | 2^1422688+24391 | 428272 | Enzo Doria | 12/2023 |
| 633 | 2^1422654+226249 | 428262 | Enzo Doria | 09/2024 |
| 634 | (10^427912+89)/9 | 427912 | Serge Batalov | 12/2014 |
| 635 | 2^1421311+40613 | 427858 | Enzo Doria | 01/2025 |
| 636 | 2^1421089+1890167 | 427791 | Enzo Doria | 09/2017 |
| 637 | 2^1420902+221149 | 427735 | Enzo Doria | 05/2024 |
| 638 | 2^1418388+25771 | 426978 | Enzo Doria | 12/2023 |
| 639 | 2^1416724+214981 | 426477 | Enzo Doria | 11/2023 |
| 640 | (96228^85849-1)/(96228^293-1) | 426352 | Ryan Propper | 11/2023 |
| 641 | 2^1414012+36991 | 425661 | Enzo Doria | 09/2024 |
| 642 | 2^1413721+225269 | 425573 | Enzo Doria | 10/2024 |
| 643 | 20^326600+3 | 424917 | Paul Bourdelais | 01/2021 |
| 644 | 2^1411443+228023 | 424887 | Enzo Doria | 11/2024 |
| 645 | (10^424861-7)/3 | 424861 | Leonid Durman | 01/2012 |
| 646 | 10^424821-11 | 424821 | Mischa Rodermond | 04/2023 |
| 647 | (2^1411200+13)/7 | 424813 | Stefano Morozzi | 09/2022 |
| 648 | 2^1411117+35927 | 424789 | Enzo Doria | 09/2024 |
| 649 | 2^1410894+219859 | 424722 | Enzo Doria | 03/2024 |
| 650 | 2^1410310+30409 | 424546 | Enzo Doria | 05/2024 |
| 651 | 2^1410233+218447 | 424523 | Enzo Doria | 03/2024 |
| 652 | 2^1408457+232007 | 423988 | Enzo Doria | 02/2025 |
| 653 | 2^1405715-1405715^2 | 423163 | Henri Lifchitz | 03/2025 |
| 654 | 1+3^605376+5^605376 | 423140 | Jon Grantham | 08/2023 |
| 655 | 2^1405367+213413 | 423058 | Enzo Doria | 10/2023 |
| 656 | 2^1404213+184217 | 422711 | Enzo Doria | 09/2017 |
| 657 | 2^1403156+40921 | 422393 | Enzo Doria | 02/2025 |
| 658 | 2^1401872+1884385 | 422006 | Enzo Doria | 04/2017 |
| 659 | 2^1401257+6077 | 421821 | Enzo Doria | 09/2017 |
| 660 | 138^196873-137^196873 | 421285 | Jean-Louis Charton | 12/2009 |
| 661 | 2^1398726+7 | 421059 | Stefano Morozzi | 10/2022 |
| 662 | 2^1398269+131595 | 420921 | Makoto Morimoto | 10/2013 |
| 663 | 2^1398238+227119 | 420912 | Enzo Doria | 10/2024 |
| 664 | 2^1398062+40639 | 420859 | Enzo Doria | 01/2025 |
| 665 | 2^1398016+229357 | 420845 | Enzo Doria | 02/2025 |
| 666 | 2^1397089-1397089 | 420566 | Henri Lifchitz | 10/2024 |
| 667 | 2^1397071+684443 | 420561 | Enzo Doria | 07/2017 |
| 668 | 953^141023-952^141023 | 420121 | Jean-Louis Charton | 10/2016 |
| 669 | 2^1393111+1867211 | 419369 | Enzo Doria | 09/2023 |
| 670 | 2^1392384+44371 | 419150 | Enzo Doria | 03/2025 |
| 671 | 2^1391771+36623 | 418965 | Enzo Doria | 09/2024 |
| 672 | (3^877843-1)/2 | 418838 | Paul Bourdelais | 07/2010 |
| 673 | 2^1389628+28651 | 418320 | Enzo Doria | 03/2024 |
| 674 | 2^1386321+60299 | 417325 | Enzo Doria | 02/2018 |
| 675 | 2^1386320+184531 | 417324 | Enzo Doria | 09/2017 |
| 676 | 2^1382074+1883587 | 416046 | Enzo Doria | 01/2017 |
| 677 | 2^1380651+215843 | 415618 | Enzo Doria | 12/2023 |
| 678 | 2^1380634+40639 | 415613 | Enzo Doria | 01/2025 |
| 679 | 2^1379907+1885223 | 415394 | Enzo Doria | 03/2017 |
| 680 | 2^1379111+29693 | 415154 | Enzo Doria | 05/2024 |
| 681 | 2^1376707+25763 | 414431 | Enzo Doria | 12/2023 |
| 682 | 2^1375751+24443 | 414143 | Enzo Doria | 12/2023 |
| 683 | 2^1375574+1886719 | 414090 | Enzo Doria | 04/2017 |
| 684 | 2^1373958+42649 | 413603 | Enzo Doria | 02/2025 |
| 685 | 2^1373111+1884833 | 413348 | Enzo Doria | 02/2017 |
| 686 | 2^1372996+15 | 413313 | Stefano Morozzi | 10/2022 |
| 687 | 2^1372515+32393 | 413169 | Enzo Doria | 05/2024 |
| 688 | 2^1372092+228751 | 413041 | Enzo Doria | 11/2024 |
| 689 | 2^1370877+38747 | 412676 | Enzo Doria | 11/2024 |
| 690 | 2^1369291+40943 | 412198 | Enzo Doria | 02/2025 |
| 691 | 2^1369207+36833 | 412173 | Enzo Doria | 10/2024 |
| 692 | 2^1369171+216593 | 412162 | Enzo Doria | 01/2024 |
| 693 | 2^1368632+1889731 | 412000 | Enzo Doria | 10/2017 |
| 694 | (65245^85849-1)/(65245^293-1) | 411914 | Ryan Propper | 11/2023 |
| 695 | (89*10^411590+1)/9 | 411591 | Serge Batalov | 09/2014 |
| 696 | F(1968721) | 411439 | Henri Lifchitz | 11/2009 |
| 697 | 2^1366066+683749 | 411227 | Enzo Doria | 02/2017 |
| 698 | 2^1365324+233341 | 411004 | Enzo Doria | 03/2025 |
| 699 | 2^1365077+228257 | 410930 | Enzo Doria | 11/2024 |
| 700 | 2^1364401+217727 | 410726 | Enzo Doria | 02/2024 |
| 701 | 2^1364303+219533 | 410697 | Enzo Doria | 03/2024 |
| 702 | 2^1363434+27589 | 410435 | Enzo Doria | 02/2024 |
| 703 | 2^1363068+222631 | 410325 | Enzo Doria | 06/2024 |
| 704 | 2^1359550+25819 | 409266 | Enzo Doria | 12/2023 |
| 705 | 2^1357392+224401 | 408616 | Enzo Doria | 06/2024 |
| 706 | 2^1355826+15 | 408145 | Stefano Morozzi | 10/2022 |
| 707 | 2^1355790+1888939 | 408134 | Enzo Doria | 07/2017 |
| 708 | 2^1355635+1884203 | 408087 | Enzo Doria | 01/2017 |
| 709 | (22071^94249-1)/(22071^307-1) | 408068 | Ryan Propper | 11/2023 |
| 710 | 2^1355083+221603 | 407921 | Enzo Doria | 05/2024 |
| 711 | 2^1351989+36587 | 406990 | Enzo Doria | 09/2024 |
| 712 | 2^1351675+231083 | 406895 | Enzo Doria | 02/2025 |
| 713 | 2^1349535+218783 | 406251 | Enzo Doria | 03/2024 |
| 714 | (55766^85849-1)/(55766^293-1) | 406081 | Ryan Propper | 11/2023 |
| 715 | 2^1348956+24241 | 406077 | Enzo Doria | 11/2023 |
| 716 | (88^208739+1)/89 | 405888 | Paul Bourdelais | 12/2020 |
| 717 | (2^1347781-2^673891+1)/5 | 405722 | Borys Jaworski | 10/2008 |
| 718 | 2^1347744-3 | 405712 | Paul Bourdelais | 07/2019 |
| 719 | 2^1347546+39133 | 405652 | Enzo Doria | 12/2024 |
| 720 | 2^1346431+691203 | 405317 | Boyan Hu | 09/2024 |
| 721 | 82358^82358+2025^2025 | 404848 | Henri Lifchitz | 01/2025 |
| 722 | 9*10^404644-11 | 404645 | Mischa Rodermond | 04/2023 |
| 723 | 1215^131072+242^131072 | 404302 | Kellen Shenton | 08/2022 |
| 724 | 2^1341908+212911 | 403955 | Enzo Doria | 09/2023 |
| 725 | 2^1341625+226187 | 403870 | Enzo Doria | 09/2024 |
| 726 | 1196^131072+595^131072 | 403405 | Kellen Shenton | 08/2022 |
| 727 | 2^1339302+29389 | 403171 | Enzo Doria | 04/2024 |
| 728 | 2^1335130+31669 | 401915 | Enzo Doria | 07/2024 |
| 729 | 2^1330388+38527 | 400487 | Enzo Doria | 11/2024 |
| 730 | 2^1330371+28313 | 400482 | Enzo Doria | 03/2024 |
| 731 | 10^400000+1415223 | 400001 | Patrick De Geest | 10/2020 |
| 732 | 10^400000-339233 | 400000 | Patrick De Geest | 10/2020 |
| 733 | 2^1323373+27317 | 398375 | Enzo Doria | 01/2024 |
| 734 | Tau(863^24630) | 397727 | Nik Lygeros / Olivier Rozier | 01/2016 |
| 735 | 2^1320423+24293 | 397487 | Enzo Doria | 11/2023 |
| 736 | 2^1320057+211517 | 397377 | Enzo Doria | 08/2023 |
| 737 | 2^1319770+1884949 | 397291 | Enzo Doria | 06/2017 |
| 738 | 2^1319616+30091 | 397244 | Enzo Doria | 04/2024 |
| 739 | 2^1317657+31367 | 396655 | Enzo Doria | 04/2024 |
| 740 | 2^1316848+43021 | 396411 | Enzo Doria | 02/2025 |
| 741 | 2^1315753+226187 | 396082 | Enzo Doria | 09/2024 |
| 742 | 2^1314741+219257 | 395777 | Enzo Doria | 03/2024 |
| 743 | 2^1313062+1888849 | 395272 | Enzo Doria | 08/2017 |
| 744 | (1073516^81920+1)/(1073516^16384+1) | 395236 | Serge Batalov | 01/2017 |
| 745 | 2^1312349+221177 | 395057 | Enzo Doria | 04/2024 |
| 746 | (1059995^81920+1)/(1059995^16384+1) | 394875 | Serge Batalov | 01/2017 |
| 747 | 2^1311618+783529 | 394837 | Enzo Doria | 01/2017 |
| 748 | 2^1310192+232531 | 394408 | Enzo Doria | 03/2025 |
| 749 | 2^1308992+28111 | 394046 | Enzo Doria | 02/2024 |
| 750 | 2^1308000+1883521 | 393748 | Enzo Doria | 02/2017 |
