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
Search by form
| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 501 | 100000^100000+85707^85707 | 500001 | Henri Lifchitz | 01/2025 |
| 502 | 2^1660964-382425 | 500000 | Tony Prest / Never Odd Or Even | 05/2020 |
| 503 | 2^1660328+226951 | 499809 | Enzo Doria | 04/2025 |
| 504 | (87^257689-1)/86 | 499791 | Paul Bourdelais | 01/2021 |
| 505 | (64*10^499210+53)/9 | 499211 | Serge Batalov | 03/2015 |
| 506 | 2^1656126+223227 | 498544 | Enzo Doria | 03/2025 |
| 507 | Tau(631^32370) | 498503 | Nik Lygeros / Olivier Rozier | 05/2015 |
| 508 | 2^1653321+49217 | 497700 | Enzo Doria | 09/2025 |
| 509 | 29^339887-28^339887 | 497051 | Jean-Louis Charton | 05/2019 |
| 510 | 2^1650975+185225 | 496993 | Stefano Morozzi | 09/2024 |
| 511 | 2^1650959+198513 | 496989 | Stefano Morozzi | 09/2024 |
| 512 | 2^1650942+181575 | 496984 | Stefano Morozzi | 09/2024 |
| 513 | 2^1650905+193947 | 496972 | Stefano Morozzi | 09/2024 |
| 514 | 2^1650877+186537 | 496964 | Stefano Morozzi | 01/2025 |
| 515 | 2^1650867+192615 | 496961 | Stefano Morozzi | 09/2024 |
| 516 | 2^1650854+188973 | 496957 | Stefano Morozzi | 01/2025 |
| 517 | 2^1650837+199641 | 496952 | Stefano Morozzi | 01/2025 |
| 518 | 2^1650819+198315 | 496947 | Stefano Morozzi | 07/2024 |
| 519 | 2^1650788+185823 | 496937 | Stefano Morozzi | 09/2024 |
| 520 | 2^1650749+185235 | 496925 | Stefano Morozzi | 06/2024 |
| 521 | 2^1650695+183141 | 496909 | Stefano Morozzi | 04/2024 |
| 522 | 2^1650640+185311 | 496893 | Stefano Morozzi | 03/2024 |
| 523 | 2^1650593+187871 | 496879 | Stefano Morozzi | 03/2024 |
| 524 | 2^1650538+196863 | 496862 | Stefano Morozzi | 03/2024 |
| 525 | 2^1650484+181413 | 496846 | Stefano Morozzi | 03/2024 |
| 526 | 2^1650473+193151 | 496842 | Stefano Morozzi | 03/2024 |
| 527 | 2^1650443+193613 | 496833 | Stefano Morozzi | 01/2024 |
| 528 | 2^1650426+183543 | 496828 | Stefano Morozzi | 01/2024 |
| 529 | 2^1650388+189741 | 496817 | Stefano Morozzi | 10/2023 |
| 530 | 2^1650267+193743 | 496780 | Stefano Morozzi | 09/2023 |
| 531 | 2^1650196+191835 | 496759 | Stefano Morozzi | 07/2023 |
| 532 | 2^1650190+185733 | 496757 | Stefano Morozzi | 07/2023 |
| 533 | 2^1650141+189525 | 496742 | Stefano Morozzi | 07/2023 |
| 534 | 2^1650103+189519 | 496731 | Stefano Morozzi | 05/2023 |
| 535 | 2^1648342+215029 | 496201 | Enzo Doria | 01/2024 |
| 536 | 2^1646078+36937 | 495519 | Enzo Doria | 10/2024 |
| 537 | 2^1645332+34951 | 495295 | Enzo Doria | 12/2024 |
| 538 | (136688^96721-1)/(136688^311-1) | 495136 | Ryan Propper | 11/2023 |
| 539 | 2^1643411+26213 | 494717 | Enzo Doria | 03/2024 |
| 540 | 2^1642987+238853 | 494589 | Enzo Doria | 09/2025 |
| 541 | 2^1642104+227491 | 494323 | Enzo Doria | 10/2024 |
| 542 | 2^1640056+216241 | 493707 | Enzo Doria | 02/2024 |
| 543 | 2^1639019+45113 | 493394 | Enzo Doria | 05/2025 |
| 544 | 2^1636027+25763 | 492494 | Enzo Doria | 01/2024 |
| 545 | 2^1636012+238741 | 492489 | Enzo Doria | 10/2025 |
| 546 | 2^1635235+227693 | 492255 | Enzo Doria | 10/2024 |
| 547 | 2^1632498+30397 | 491431 | Enzo Doria | 08/2024 |
| 548 | 2^1631030+73519 | 490989 | Enzo Doria | 08/2023 |
| 549 | 2^1629568+237541 | 490549 | Enzo Doria | 08/2025 |
| 550 | (2^1629469-1)/644908484660139264379223 | 490496 | Gord Palameta | 11/2017 |
| 551 | 2^1627834+225529 | 490027 | Enzo Doria | 08/2024 |
| 552 | 2^1626709+30407 | 489689 | Enzo Doria | 07/2024 |
| 553 | 2^1626438+38557 | 489607 | Enzo Doria | 11/2024 |
| 554 | 2^1621040+39415 | 487982 | Enzo Doria | 11/2024 |
| 555 | 2^1619885+28229 | 487634 | Enzo Doria | 04/2024 |
| 556 | 10^487291+7 | 487292 | Alfred Reich | 06/2021 |
| 557 | 2^1617677+227927 | 486970 | Enzo Doria | 10/2024 |
| 558 | 2^1617579+1889543 | 486940 | Enzo Doria | 09/2017 |
| 559 | 97481^97481-70^70 | 486325 | Henri Lifchitz | 10/2024 |
| 560 | 2^1613665+237257 | 485762 | Enzo Doria | 07/2025 |
| 561 | 2^1613632+215011 | 485752 | Enzo Doria | 11/2023 |
| 562 | 2^1612600+27331 | 485441 | Enzo Doria | 03/2024 |
| 563 | 2^1610146+24739 | 484703 | Enzo Doria | 11/2023 |
| 564 | 2^1609360+43711 | 484466 | Enzo Doria | 03/2025 |
| 565 | L(2316773) | 484177 | Serge Batalov | 06/2017 |
| 566 | (57^275669-1)/56 | 484039 | Paul Bourdelais | 04/2021 |
| 567 | 2^1602171+40943 | 482302 | Enzo Doria | 01/2025 |
| 568 | 2^1601964+215491 | 482240 | Enzo Doria | 11/2023 |
| 569 | 10^482076+9 | 482077 | Boyan Hu | 06/2025 |
| 570 | 96672^96672-1825^1825 | 481939 | Henri Lifchitz | 12/2024 |
| 571 | 2^1600308+34051 | 481741 | Enzo Doria | 09/2024 |
| 572 | 2^1599674+43909 | 481550 | Enzo Doria | 04/2025 |
| 573 | 2^1599624+20011 | 481535 | Enzo Doria | 07/2023 |
| 574 | 2^1599281+237557 | 481432 | Enzo Doria | 08/2025 |
| 575 | 2^1599238+234559 | 481419 | Enzo Doria | 04/2025 |
| 576 | 2^1599205+27047 | 481409 | Enzo Doria | 03/2024 |
| 577 | 2^1599120-5 | 481384 | Stefano Morozzi | 12/2022 |
| 578 | 10^480684-3 | 480684 | Paul Bourdelais | 01/2021 |
| 579 | 2^1595483+184133 | 480289 | Enzo Doria | 07/2017 |
| 580 | 2^1594947+3 | 480127 | Paul Bourdelais | 07/2019 |
| 581 | 2^1594420+36781 | 479969 | Enzo Doria | 10/2024 |
| 582 | 2^1594135+225893 | 479883 | Enzo Doria | 10/2024 |
| 583 | 2^1594129+22697 | 479881 | Enzo Doria | 11/2023 |
| 584 | 2^1593922+213289 | 479819 | Enzo Doria | 10/2023 |
| 585 | 2^1592677+228257 | 479444 | Enzo Doria | 11/2024 |
| 586 | 2^1592625+234041 | 479428 | Enzo Doria | 04/2025 |
| 587 | 2^1592234+26809 | 479311 | Enzo Doria | 03/2024 |
| 588 | 2^1590797+34967 | 478878 | Enzo Doria | 10/2024 |
| 589 | (94^241993-1)/93 | 477482 | Paul Bourdelais | 09/2020 |
| 590 | 2^1585195+1888373 | 477192 | Enzo Doria | 08/2017 |
| 591 | 2^1585021+43427 | 477139 | Enzo Doria | 03/2025 |
| 592 | (33^313553+1)/34 | 476134 | Paul Bourdelais | 02/2021 |
| 593 | 2^1581306+220309 | 476021 | Enzo Doria | 03/2024 |
| 594 | 2^1579739+50783 | 475549 | Enzo Doria | 10/2025 |
| 595 | 2^1578654+215029 | 475223 | Enzo Doria | 01/2024 |
| 596 | (84615^96721-1)/(84615^311-1) | 475056 | Ryan Propper | 11/2023 |
| 597 | 3^994536+16 | 474515 | Robert Price | 10/2020 |
| 598 | 2^1576219+233663 | 474490 | Enzo Doria | 03/2025 |
| 599 | 2^1575391+71483 | 474240 | Enzo Doria | 04/2018 |
| 600 | (2^1572882+5)/3 | 473485 | Serge Batalov | 08/2015 |
| 601 | 2^1572882+50239 | 473485 | Enzo Doria | 09/2025 |
| 602 | 2^1572813+240791 | 473464 | Enzo Doria | 11/2025 |
| 603 | 2^1572728+45421 | 473439 | Enzo Doria | 07/2025 |
| 604 | (6^608099-1)/5 | 473193 | Paul Bourdelais | 05/2010 |
| 605 | 2^1570431+41183 | 472747 | Enzo Doria | 02/2025 |
| 606 | 2^1569708+20371 | 472530 | Enzo Doria | 09/2023 |
| 607 | 2^1569375+29153 | 472429 | Enzo Doria | 05/2024 |
| 608 | 3^989124+16 | 471933 | Robert Price | 10/2020 |
| 609 | 2^1567006+1888099 | 471716 | Enzo Doria | 05/2017 |
| 610 | -E(107194)/47 | 471629 | Serge Batalov | 07/2025 |
| 611 | 2^1564510+45709 | 470965 | Enzo Doria | 06/2025 |
| 612 | 2^1563462+39919 | 470649 | Enzo Doria | 12/2024 |
| 613 | 2^1563067+1889813 | 470531 | Enzo Doria | 08/2017 |
| 614 | 2^1562428+215851 | 470338 | Enzo Doria | 02/2024 |
| 615 | 2^1557036+226321 | 468715 | Enzo Doria | 09/2024 |
| 616 | 2^1556730+222829 | 468623 | Enzo Doria | 07/2024 |
| 617 | 2^1554175+228353 | 467854 | Enzo Doria | 12/2024 |
| 618 | 2^1551415+215813 | 467023 | Enzo Doria | 02/2024 |
| 619 | 2^1551411+212933 | 467022 | Enzo Doria | 09/2023 |
| 620 | 2^1550887+36743 | 466864 | Enzo Doria | 11/2024 |
| 621 | 2^1549797+60197 | 466536 | Enzo Doria | 02/2018 |
| 622 | 2^1549030+1887619 | 466305 | Enzo Doria | 05/2017 |
| 623 | 2^1545920+41467 | 465369 | Enzo Doria | 02/2025 |
| 624 | 2^1544971+43403 | 465083 | Enzo Doria | 03/2025 |
| 625 | 416^177481-415^177481 | 464840 | Jean-Louis Charton | 12/2016 |
| 626 | 2^1541374+226729 | 464000 | Enzo Doria | 09/2024 |
| 627 | (78^245183-1)/77 | 463908 | Paul Bourdelais | 02/2021 |
| 628 | 93331^93331-90^90 | 463858 | Henri Lifchitz | 10/2024 |
| 629 | 2^1540755+236603 | 463814 | Enzo Doria | 08/2025 |
| 630 | 2^1540117+31907 | 463622 | Enzo Doria | 04/2024 |
| 631 | 2^1538959-25 | 463273 | Boyan Hu | 01/2025 |
| 632 | 2^1537058+29839 | 462701 | Enzo Doria | 07/2024 |
| 633 | 2^1534770+20809 | 462012 | Enzo Doria | 08/2023 |
| 634 | 2^1531286+24799 | 460964 | Enzo Doria | 11/2023 |
| 635 | 2^1530725+38267 | 460795 | Enzo Doria | 10/2024 |
| 636 | 2^1530380+38011 | 460691 | Enzo Doria | 11/2024 |
| 637 | 2^1527857+225269 | 459931 | Enzo Doria | 11/2024 |
| 638 | 2^1527070+47659 | 459694 | Enzo Doria | 07/2025 |
| 639 | 10^459480-11 | 459480 | Mischa Rodermond | 04/2023 |
| 640 | 2^1526274+44629 | 459455 | Enzo Doria | 05/2025 |
| 641 | (5^656657-2^656657)/3 | 458984 | Jon Grantham | 08/2023 |
| 642 | 2^1522569+71657 | 458339 | Enzo Doria | 04/2018 |
| 643 | 2^1520990+35257 | 457864 | Enzo Doria | 10/2024 |
| 644 | 2^1520920+38251 | 457843 | Enzo Doria | 11/2024 |
| 645 | (55814^96721-1)/(55814^311-1) | 457634 | Ryan Propper | 11/2023 |
| 646 | 2^1518191+75353 | 457022 | Ben Maloney / Five or Bust | 01/2009 |
| 647 | 2^1513244+44641 | 455532 | Enzo Doria | 04/2025 |
| 648 | 2^1512733+227027 | 455379 | Enzo Doria | 10/2024 |
| 649 | 2^1510915+223463 | 454831 | Enzo Doria | 06/2024 |
| 650 | 6^584279-5 | 454658 | Paul Bourdelais | 02/2021 |
| 651 | 2^1509037-13 | 454266 | Stefano Morozzi | 12/2022 |
| 652 | (52^264697-1)/51 | 454220 | Paul Bourdelais | 10/2021 |
| 653 | 2^1507169+29027 | 453704 | Enzo Doria | 05/2024 |
| 654 | 2^1506029+1890167 | 453360 | Enzo Doria | 02/2018 |
| 655 | 2^1504232+26101 | 452819 | Enzo Doria | 01/2024 |
| 656 | -E(103274)/8318971 | 452706 | Serge Batalov | 07/2025 |
| 657 | 2^1502037+51287 | 452159 | Enzo Doria | 11/2025 |
| 658 | 2^1501670+41629 | 452048 | Enzo Doria | 02/2025 |
| 659 | 2^1498015+219113 | 450948 | Enzo Doria | 03/2024 |
| 660 | 2^1497532+220471 | 450803 | Enzo Doria | 04/2024 |
| 661 | 2^1497523+230873 | 450800 | Enzo Doria | 01/2025 |
| 662 | 2^1497466+241489 | 450783 | Enzo Doria | 10/2025 |
| 663 | 2^1497369+216977 | 450753 | Enzo Doria | 01/2024 |
| 664 | (34^294277+1)/35 | 450678 | Paul Bourdelais | 06/2018 |
| 665 | 2^1496854+232399 | 450598 | Enzo Doria | 02/2025 |
| 666 | 2^1496449+42587 | 450477 | Enzo Doria | 02/2025 |
| 667 | 2^1495434+1890439 | 450171 | Enzo Doria | 12/2017 |
| 668 | 2^1495078+227779 | 450064 | Enzo Doria | 10/2024 |
| 669 | 2^1494634+7 | 449930 | Stefano Morozzi | 10/2022 |
| 670 | 2^1494534+48319 | 449900 | Enzo Doria | 09/2025 |
| 671 | 2^1493170+784129 | 449489 | Enzo Doria | 08/2017 |
| 672 | 2^1490332-229043 | 448635 | Enzo Doria | 01/2025 |
| 673 | 2^1489873+1888277 | 448497 | Enzo Doria | 06/2017 |
| 674 | 2^1487389+32417 | 447749 | Enzo Doria | 06/2024 |
| 675 | 2^1486846+36019 | 447586 | Enzo Doria | 11/2024 |
| 676 | 2^1485471+224789 | 447172 | Enzo Doria | 09/2024 |
| 677 | 2^1485203+71663 | 447091 | Enzo Doria | 09/2023 |
| 678 | 2^1484671+1888463 | 446931 | Enzo Doria | 06/2017 |
| 679 | 2^1483112+23961 | 446462 | Enzo Doria | 12/2023 |
| 680 | 2^1482867+1886783 | 446388 | Enzo Doria | 04/2017 |
| 681 | 2^1482148+284011 | 446172 | Enzo Doria | 04/2017 |
| 682 | 2^1481363+215843 | 445935 | Enzo Doria | 12/2023 |
| 683 | 2^1480415+217643 | 445650 | Enzo Doria | 02/2024 |
| 684 | 2^1480400+225013 | 445645 | Enzo Doria | 10/2024 |
| 685 | 2^1479356+1888291 | 445331 | Enzo Doria | 06/2017 |
| 686 | (157742^85849-1)/(157742^293-1) | 444716 | Ryan Propper | 11/2023 |
| 687 | 2^1477225+50147 | 444690 | Enzo Doria | 09/2025 |
| 688 | 2^1476810+23299 | 444565 | Enzo Doria | 12/2023 |
| 689 | 2^1475372+236521 | 444132 | Enzo Doria | 07/2025 |
| 690 | 2^1474222+38569 | 443786 | Enzo Doria | 11/2024 |
| 691 | 2^1474189+36557 | 443776 | Enzo Doria | 11/2024 |
| 692 | 2^1473184+212671 | 443473 | Enzo Doria | 09/2023 |
| 693 | 2^1472225+37997 | 443184 | Enzo Doria | 10/2024 |
| 694 | 2^1471949+241577 | 443101 | Enzo Doria | 10/2025 |
| 695 | 2^1467760+235441 | 441840 | Enzo Doria | 05/2025 |
| 696 | 2^1466458+235399 | 441448 | Enzo Doria | 06/2025 |
| 697 | 2^1466432+20371 | 441441 | Enzo Doria | 08/2023 |
| 698 | 14^384558+3 | 440753 | Paul Bourdelais | 01/2021 |
| 699 | 2^1463913+219047 | 440682 | Enzo Doria | 04/2024 |
| 700 | 2^1461244+784531 | 439879 | Enzo Doria | 10/2017 |
| 701 | 2^1461058+34429 | 439823 | Enzo Doria | 08/2024 |
| 702 | 2^1460142+233959 | 439547 | Enzo Doria | 03/2025 |
| 703 | 2^1459599+215813 | 439384 | Enzo Doria | 01/2024 |
| 704 | 2^1457449+25757 | 438736 | Enzo Doria | 12/2023 |
| 705 | 2^1457045+231317 | 438615 | Enzo Doria | 01/2025 |
| 706 | 2^1457005+46301 | 438603 | Enzo Doria | 10/2025 |
| 707 | 3^919094+5*2^919094 | 438520 | Jon Grantham | 08/2023 |
| 708 | 2^1456277+28229 | 438384 | Enzo Doria | 03/2024 |
| 709 | 2^1455129+218027 | 438038 | Enzo Doria | 01/2024 |
| 710 | 2^1454061+216977 | 437716 | Enzo Doria | 01/2024 |
| 711 | 2^1453419+26783 | 437523 | Enzo Doria | 01/2024 |
| 712 | (67^239053+1)/68 | 436527 | Paul Bourdelais | 09/2021 |
| 713 | 2^1448714+231559 | 436107 | Enzo Doria | 02/2025 |
| 714 | 2^1448122+74209 | 435929 | Enzo Doria | 08/2023 |
| 715 | 2^1448111+49853 | 435925 | Enzo Doria | 09/2025 |
| 716 | 2^1446449+221087 | 435425 | Enzo Doria | 05/2024 |
| 717 | 2^1446263+74333 | 435369 | Enzo Doria | 08/2023 |
| 718 | 2^1445551+47333 | 435155 | Enzo Doria | 08/2025 |
| 719 | 2^1444386+221029 | 434804 | Enzo Doria | 03/2024 |
| 720 | (80^228419+1)/81 | 434701 | Paul Bourdelais | 02/2021 |
| 721 | 2^1443089+60227 | 434414 | Enzo Doria | 10/2017 |
| 722 | (21^328129-1)/20 | 433858 | Paul Bourdelais | 06/2014 |
| 723 | (35^280979+1)/36 | 433850 | Paul Bourdelais | 09/2021 |
| 724 | 2^1438663+214175 | 433081 | Enzo Doria | 11/2023 |
| 725 | 2^1436073+241547 | 432302 | Enzo Doria | 10/2025 |
| 726 | 2^1434519+215813 | 431834 | Enzo Doria | 01/2024 |
| 727 | 2^1434400+3 | 431798 | Paul Bourdelais | 06/2019 |
| 728 | 2^1434298+31669 | 431767 | Enzo Doria | 08/2024 |
| 729 | 2^1434097+215207 | 431707 | Enzo Doria | 11/2023 |
| 730 | 2^1433033+212987 | 431386 | Enzo Doria | 10/2023 |
| 731 | 2^1432308+1888801 | 431168 | Enzo Doria | 10/2017 |
| 732 | (2^1430131+1)/(3*356468732537*36519993971459) | 430487 | Gord Palameta | 12/2018 |
| 733 | 2^1429978+233839 | 430467 | Enzo Doria | 04/2025 |
| 734 | (7^508867-2^508867)/5 | 430042 | Jon Grantham | 08/2023 |
| 735 | 2^1428489+25097 | 430019 | Enzo Doria | 11/2023 |
| 736 | 2^1425595+237413 | 429147 | Enzo Doria | 07/2025 |
| 737 | 2^1425483+1886813 | 429114 | Enzo Doria | 04/2017 |
| 738 | (63^238481+1)/64 | 429107 | Paul Bourdelais | 12/2020 |
| 739 | (((91969+1)/2)^91969+((91969-1)/2)^91969)/(91969^2) | 428807 | Henri Lifchitz | 11/2025 |
| 740 | (17^348259+1)/18 | 428514 | Paul Bourdelais | 05/2014 |
| 741 | 2^1422688+24391 | 428272 | Enzo Doria | 12/2023 |
| 742 | 2^1422654+226249 | 428262 | Enzo Doria | 09/2024 |
| 743 | 2^1421514+2351163 | 427919 | Enzo Doria | 05/2025 |
| 744 | (10^427912+89)/9 | 427912 | Serge Batalov | 12/2014 |
| 745 | 2^1421311+40613 | 427858 | Enzo Doria | 01/2025 |
| 746 | 2^1421089+1890167 | 427791 | Enzo Doria | 09/2017 |
| 747 | 2^1420902+221149 | 427735 | Enzo Doria | 05/2024 |
| 748 | 2^1418388+25771 | 426978 | Enzo Doria | 12/2023 |
| 749 | 2^1416724+214981 | 426477 | Enzo Doria | 11/2023 |
| 750 | (96228^85849-1)/(96228^293-1) | 426352 | Ryan Propper | 11/2023 |
