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 ? |
| 1501 | 3^648872+16 | 309591 | Robert Price | 04/2020 |
| 1502 | (16976^73441-1)/(16976^271-1) | 309498 | Ryan Propper | 11/2023 |
| 1503 | 64221^64366+64366^64221 | 309451 | Norbert Schneider | 06/2023 |
| 1504 | (11121^76729-1)/(11121^277-1) | 309336 | Ryan Propper | 11/2023 |
| 1505 | 2^1027478+219259 | 309302 | Enzo Doria | 02/2024 |
| 1506 | 2^1026999+20513 | 309158 | Enzo Doria | 07/2023 |
| 1507 | 5^442281+2 | 309142 | Paul Bourdelais | 01/2021 |
| 1508 | 2^1026204+22741 | 308919 | Enzo Doria | 09/2023 |
| 1509 | 2^1026190+15 | 308914 | Stefano Morozzi | 10/2022 |
| 1510 | 2^1025108+20851 | 308589 | Enzo Doria | 08/2023 |
| 1511 | 2^1022860+234121 | 307912 | Enzo Doria | 03/2025 |
| 1512 | A352736(16) | 306985 | Kellen Shenton | 05/2022 |
| 1513 | 2^1019777+213947 | 306984 | Enzo Doria | 10/2023 |
| 1514 | 2^1018820+236731 | 306696 | Enzo Doria | 05/2025 |
| 1515 | (11^293831-1)/10 | 305993 | Paul Bourdelais | 03/2010 |
| 1516 | (67^167449-1)/66 | 305773 | Paul Bourdelais | 08/2020 |
| 1517 | (62^170539+1)/63 | 305671 | Paul Bourdelais | 12/2020 |
| 1518 | 2^1015321-1015321 | 305643 | Henri Lifchitz | 08/2013 |
| 1519 | (7*10^(2*152761+1)+9*10^152761-7)/9 | 305523 | Robert Price | 06/2026 |
| 1520 | 2^1014775+27113 | 305478 | Enzo Doria | 12/2023 |
| 1521 | 2^1014450+7 | 305380 | Stefano Morozzi | 10/2022 |
| 1522 | 2^1014404+46171 | 305367 | Enzo Doria | 05/2025 |
| 1523 | 2^1014336+215731 | 305346 | Enzo Doria | 12/2023 |
| 1524 | 2^1014224-2791229 | 305312 | Enzo Doria | 01/2016 |
| 1525 | (10^304986+7)/673 | 304984 | Alfred Reich | 11/2021 |
| 1526 | 65473^45250+45250^65473 | 304818 | Hans Havermann | 02/2022 |
| 1527 | 66012^41423+41423^66012 | 304794 | Hans Havermann | 03/2022 |
| 1528 | 65073^48202+48202^65073 | 304742 | Hans Havermann | 04/2022 |
| 1529 | 2^1012054+31669 | 304659 | Enzo Doria | 06/2024 |
| 1530 | 238176^19+19^238176 | 304569 | Hans Havermann | 03/2022 |
| 1531 | 73122^14615+14615^73122 | 304539 | Hans Havermann | 05/2022 |
| 1532 | 64492^52639+52639^64492 | 304487 | Hans Havermann | 03/2022 |
| 1533 | 65955^41288+41288^65955 | 304437 | Hans Havermann | 04/2022 |
| 1534 | 71729^17530+17530^71729 | 304403 | Hans Havermann | 03/2022 |
| 1535 | 70170^21733+21733^70170 | 304336 | Hans Havermann | 03/2022 |
| 1536 | 2^1010751-107709 | 304267 | Enzo Doria | 03/2014 |
| 1537 | 84473^3994+3994^84473 | 304222 | Hans Havermann | 03/2022 |
| 1538 | (2^1010623-1)/12602017578957977 | 304212 | Tony Prest / Never Odd Or Even | 02/2014 |
| 1539 | 74442^12125+12125^74442 | 303998 | Hans Havermann | 02/2022 |
| 1540 | 77842^8039+8039^77842 | 303989 | Hans Havermann | 01/2022 |
| 1541 | 64209^54140+54140^64209 | 303935 | Hans Havermann | 02/2022 |
| 1542 | 2^1009577+1869587 | 303913 | Enzo Doria | 06/2016 |
| 1543 | 67389^32338+32338^67389 | 303906 | Hans Havermann | 02/2022 |
| 1544 | 8^336419-7^336419 | 303817 | Jean-Louis Charton | 01/2008 |
| 1545 | 2^1009168+15 | 303790 | Stefano Morozzi | 10/2022 |
| 1546 | 80766^5771+5771^80766 | 303782 | Hans Havermann | 01/2022 |
| 1547 | 66094^39385+39385^66094 | 303724 | Hans Havermann | 01/2022 |
| 1548 | 69147^24574+24574^69147 | 303589 | Hans Havermann | 02/2022 |
| 1549 | 78390^7459+7459^78390 | 303580 | Hans Havermann | 01/2022 |
| 1550 | 2^1008301+1869377 | 303529 | Enzo Doria | 06/2016 |
| 1551 | 65008^46615+46615^65008 | 303492 | Hans Havermann | 02/2022 |
| 1552 | (2^1007838+5)/3 | 303389 | Serge Batalov | 08/2015 |
| 1553 | 65018^46293+46293^65018 | 303343 | Hans Havermann | 01/2022 |
| 1554 | 6^389756+5 | 303290 | Paul Bourdelais | 02/2021 |
| 1555 | 71016^18649+18649^71016 | 303285 | Hans Havermann | 01/2022 |
| 1556 | 2^1007065+29231 | 303157 | Enzo Doria | 03/2024 |
| 1557 | 80160^6047+6047^80160 | 303129 | Hans Havermann | 01/2022 |
| 1558 | 67434^31237+31237^67434 | 303094 | Hans Havermann | 03/2022 |
| 1559 | 65537^42102+42102^65537 | 303063 | Hans Havermann | 02/2022 |
| 1560 | 71790^16553+16553^71790 | 302874 | Hans Havermann | 11/2021 |
| 1561 | 65208^44129+44129^65208 | 302874 | Hans Havermann | 11/2021 |
| 1562 | 84181^3960+3960^84181 | 302858 | Hans Havermann | 11/2021 |
| 1563 | (13703^73441-1)/(13703^271-1) | 302691 | Ryan Propper | 11/2023 |
| 1564 | 71956^16087+16087^71956 | 302682 | Hans Havermann | 11/2021 |
| 1565 | 2^1005326+383059 | 302634 | Enzo Doria | 12/2016 |
| 1566 | 2^1004929+1877567 | 302514 | Enzo Doria | 08/2016 |
| 1567 | 69341^22978+22978^69341 | 302418 | Hans Havermann | 12/2021 |
| 1568 | 111443^516+516^111443 | 302306 | Hans Havermann | 12/2021 |
| 1569 | 67638^29387+29387^67638 | 302218 | Hans Havermann | 11/2021 |
| 1570 | 2^1003494+1874899 | 302082 | Enzo Doria | 06/2016 |
| 1571 | 75189^10400+10400^75189 | 302037 | Hans Havermann | 12/2021 |
| 1572 | 67237^31042+31042^67237 | 302026 | Hans Havermann | 12/2021 |
| 1573 | 64540^47791+47791^64540 | 302005 | Hans Havermann | 11/2021 |
| 1574 | 2^1003046+60529 | 301947 | Enzo Doria | 04/2016 |
| 1575 | 83278^4209+4209^83278 | 301815 | Hans Havermann | 09/2021 |
| 1576 | 64431^48250+48250^64431 | 301763 | Hans Havermann | 09/2021 |
| 1577 | 67237^30714+30714^67237 | 301716 | Hans Havermann | 09/2021 |
| 1578 | 2^1002144+235861 | 301676 | Enzo Doria | 05/2025 |
| 1579 | 64641^46288+46288^64641 | 301581 | Hans Havermann | 09/2021 |
| 1580 | 71513^16482+16482^71513 | 301572 | Hans Havermann | 10/2021 |
| 1581 | 72017^15396+15396^72017 | 301565 | Hans Havermann | 09/2021 |
| 1582 | 65534^39927+39927^65534 | 301540 | Hans Havermann | 10/2021 |
| 1583 | (23^221411-1)/22 | 301501 | Paul Bourdelais | 08/2020 |
| 1584 | 63169^59152+59152^63169 | 301441 | Hans Havermann | 09/2021 |
| 1585 | 75055^10348+10348^75055 | 301336 | Hans Havermann | 09/2021 |
| 1586 | 2^1000647+1881353 | 301225 | Enzo Doria | 11/2016 |
| 1587 | 83686^3961+3961^83686 | 301086 | Hans Havermann | 10/2021 |
| 1588 | 68529^24742+24742^68529 | 301078 | Hans Havermann | 09/2021 |
| 1589 | 65207^41416+41416^65207 | 301072 | Hans Havermann | 10/2021 |
| 1591 | 2^1000000+821751 | 301030 | Tony Prest / Never Odd Or Even | 10/2015 |
| 1590 | 2^999999+77151 | 301030 | Norman Luhn | 09/2023 |
| 1592 | 90762^2071+2071^90762 | 300984 | Hans Havermann | 06/2021 |
| 1593 | 63909^51142+51142^63909 | 300934 | Hans Havermann | 08/2021 |
| 1594 | 2^999646+1874029 | 300924 | Enzo Doria | 06/2016 |
| 1595 | 66280^34607+34607^66280 | 300856 | Hans Havermann | 06/2021 |
| 1596 | 65534^38925+38925^65534 | 300817 | Hans Havermann | 07/2021 |
| 1597 | 63296^56517+56517^63296 | 300794 | Hans Havermann | 06/2021 |
| 1598 | 110610^523+523^110610 | 300694 | Hans Havermann | 06/2021 |
| 1599 | 66428^33609+33609^66428 | 300684 | Hans Havermann | 06/2021 |
| 1600 | 74247^11210+11210^74247 | 300672 | Hans Havermann | 06/2021 |
| 1601 | (59^169777-1)/58 | 300649 | Paul Bourdelais | 08/2020 |
| 1602 | 10^300476+3 | 300477 | Ed Trice | 10/2012 |
| 1603 | 10^300476-530913 | 300476 | Patrick De Geest | 03/2016 |
| 1604 | 66703^31960+31960^66703 | 300471 | Hans Havermann | 06/2021 |
| 1605 | 63722^51915+51915^63722 | 300468 | Hans Havermann | 06/2021 |
| 1606 | 2^998053+1879667 | 300444 | Enzo Doria | 09/2016 |
| 1607 | 77018^7959+7959^77018 | 300437 | Hans Havermann | 07/2021 |
| 1608 | 314738^9+9^314738 | 300337 | Anatoly F. Selevich | 02/2011 |
| 1609 | 2^997689+217787 | 300335 | Enzo Doria | 01/2024 |
| 1610 | 69478^20987+20987^69478 | 300281 | Hans Havermann | 07/2021 |
| 1611 | 64088^48393+48393^64088 | 300239 | Hans Havermann | 07/2021 |
| 1612 | 2^997369+237917 | 300238 | Enzo Doria | 06/2025 |
| 1613 | 64605^44146+44146^64605 | 300084 | Hans Havermann | 08/2021 |
| 1614 | 2^996845+29027 | 300081 | Enzo Doria | 02/2024 |
| 1615 | 7^355039-6^355039 | 300043 | Jean-Louis Charton | 05/2011 |
| 1616 | 67594^27465+27465^67594 | 300035 | Hans Havermann | 06/2021 |
| 1617 | 10^300000+287389 | 300001 | Patrick De Geest | 10/2019 |
| 1618 | 10^300000-83657 | 300000 | Patrick De Geest | 10/2019 |
| 1619 | 70599^17756+17756^70599 | 300000 | Hans Havermann | 06/2021 |
| 1620 | numbpart(72526161452) | 299999 | Serge Batalov | 04/2017 |
| 1621 | 2^996182-114431 | 299881 | Enzo Doria | 02/2015 |
| 1622 | 3*2^996126+5 | 299865 | Jon Grantham | 07/2023 |
| 1623 | 2^996034-17 | 299837 | Stefano Morozzi | 07/2022 |
| 1624 | 2^995793+36587 | 299764 | Enzo Doria | 09/2024 |
| 1625 | (19*10^299640+77)/3 | 299641 | Robert Price | 03/2023 |
| 1626 | 2^995214-2788361 | 299590 | Enzo Doria | 12/2015 |
| 1627 | 2^994791-114319 | 299462 | Enzo Doria | 01/2015 |
| 1628 | 2^994490-1863791 | 299372 | Enzo Doria | 01/2016 |
| 1629 | (10^(2*149610+1)+27*10^149610-1)/9 | 299221 | Robert Price | 06/2026 |
| 1630 | 2^993322+1885729 | 299020 | Enzo Doria | 03/2017 |
| 1631 | 2^993227+230033 | 298992 | Enzo Doria | 12/2024 |
| 1632 | (36395^65536+36393^65536)/2 | 298913 | Kellen Shenton | 04/2022 |
| 1633 | 2^992711-2788807 | 298836 | Enzo Doria | 12/2015 |
| 1634 | 2^992525-114199 | 298780 | Enzo Doria | 12/2014 |
| 1635 | (7^353501-3^353501)/4 | 298743 | Jon Grantham | 08/2023 |
| 1636 | 2^992329+1884707 | 298721 | Enzo Doria | 02/2017 |
| 1637 | 2^992292+229801 | 298710 | Enzo Doria | 12/2024 |
| 1638 | 2^992052+215491 | 298638 | Enzo Doria | 11/2023 |
| 1639 | 2^991968-23 | 298613 | Stefano Morozzi | 07/2022 |
| 1640 | 2^991715-19 | 298536 | Stefano Morozzi | 07/2022 |
| 1641 | 2^991387+237383 | 298438 | Enzo Doria | 06/2025 |
| 1642 | (10^298414+7)/191/823/56921/1334467 | 298398 | Alfred Reich | 10/2021 |
| 1643 | 2^989562+25 | 297888 | Stefano Morozzi | 05/2021 |
| 1644 | 2^988580+214051 | 297593 | Enzo Doria | 10/2023 |
| 1645 | 2^988537+218837 | 297580 | Enzo Doria | 03/2024 |
| 1646 | (19*10^297497+77)/3 | 297498 | Robert Price | 03/2023 |
| 1647 | (2*10^297488-23)/3 | 297488 | Robert Price | 10/2022 |
| 1648 | 2^988148+48271 | 297463 | Enzo Doria | 07/2025 |
| 1649 | 2^987033+46427 | 297127 | Enzo Doria | 05/2025 |
| 1650 | (2^986191+1)/3 | 296873 | Vincent Diepeveen | 06/2008 |
| 1651 | 2^985217-114553 | 296580 | Enzo Doria | 03/2015 |
| 1652 | (76^157649-1)/75 | 296507 | Paul Bourdelais | 07/2019 |
| 1653 | 2^984650+21529 | 296410 | Enzo Doria | 08/2023 |
| 1654 | 2^984131-1828009 | 296253 | Enzo Doria | 01/2015 |
| 1655 | 2^983620+60451 | 296100 | Phil Moore | 03/2008 |
| 1656 | 2^982721-2683 | 295829 | Yves Minet | 02/2016 |
| 1657 | (23*10^295581+7)/3 | 295582 | Robert Price | 05/2023 |
| 1658 | 2^981298-2788421 | 295401 | Enzo Doria | 12/2015 |
| 1659 | 2^981163-2790967 | 295360 | Enzo Doria | 12/2015 |
| 1660 | 2^981016-15 | 295316 | Stefano Morozzi | 07/2022 |
| 1661 | 8*10^295160-13 | 295161 | Robert Price | 08/2023 |
| 1662 | 2^979594+1865839 | 294888 | Enzo Doria | 02/2016 |
| 1663 | 2^979502+221029 | 294860 | Enzo Doria | 03/2024 |
| 1664 | 2*10^294527-91 | 294528 | Robert Price | 02/2023 |
| 1665 | (49363^63001-1)/(49363^251-1) | 294511 | Ryan Propper | 11/2023 |
| 1666 | 10^294475+49 | 294476 | Robert Price | 02/2023 |
| 1667 | 2^977896+234601 | 294377 | Enzo Doria | 04/2025 |
| 1668 | (11*10^294308+91)/3 | 294309 | Robert Price | 03/2023 |
| 1669 | 2^976760+1885021 | 294035 | Enzo Doria | 02/2017 |
| 1670 | 3*2^976518+5 | 293962 | Jon Grantham | 07/2023 |
| 1671 | 2^975798+218599 | 293745 | Enzo Doria | 01/2024 |
| 1672 | 2^974441+1878407 | 293336 | Enzo Doria | 08/2016 |
| 1673 | 2^974180+1876831 | 293258 | Enzo Doria | 07/2016 |
| 1674 | 2^974170+453319 | 293255 | Enzo Doria | 01/2017 |
| 1675 | (211^126023-1)/210 | 292911 | Anonymous | 05/2024 |
| 1676 | 2^972744-114419 | 292826 | Enzo Doria | 03/2015 |
| 1677 | 11^281143+6 | 292781 | Paul Bourdelais | 03/2021 |
| 1678 | (4*10^292619-91)/3 | 292620 | Robert Price | 12/2022 |
| 1679 | E(69468)/13247122135 | 292549 | Sergey Batalov | 10/2023 |
| 1680 | CopelandErdos(292447) | 292447 | Mark Rodenkirch | 12/2015 |
| 1681 | 3*10^292344-97 | 292345 | Robert Price | 01/2023 |
| 1682 | 2^970911+1873373 | 292274 | Enzo Doria | 07/2016 |
| 1683 | 2^970670+383059 | 292201 | Enzo Doria | 12/2016 |
| 1684 | 2^970141-100363 | 292042 | Enzo Doria | 02/2014 |
| 1685 | 2^969945+1874717 | 291983 | Enzo Doria | 06/2016 |
| 1686 | 2^969384+1880701 | 291814 | Enzo Doria | 10/2016 |
| 1687 | (13*10^291721-43)/3 | 291722 | Robert Price | 08/2023 |
| 1688 | (3^611333-2^611333)/(99035947*87109884549431) | 291659 | Mike Oakes | 02/2017 |
| 1689 | 128^138108+127 | 291023 | Alfred Reich | 06/2026 |
| 1690 | 10^(2*145126+1)-2*10^145126-1 | 290253 | Robert Price | 03/2025 |
| 1691 | 3*2^963892+5 | 290161 | Jon Grantham | 07/2023 |
| 1692 | (151*10^289877-1)/3 | 289879 | Robert Price | 07/2023 |
| 1693 | 2^962194+60139 | 289650 | Enzo Doria | 02/2016 |
| 1694 | 2^961409+44267 | 289413 | Enzo Doria | 04/2025 |
| 1695 | 2^959307-1861507 | 288781 | Enzo Doria | 11/2015 |
| 1696 | (17*10^288692+31)/3 | 288693 | Robert Price | 04/2023 |
| 1697 | 14^251797-3 | 288592 | Paul Bourdelais | 12/2020 |
| 1698 | (8745^73441-1)/(8745^271-1) | 288419 | Ryan Propper | 11/2023 |
| 1699 | (2*10^288371-23)/3 | 288371 | Robert Price | 10/2022 |
| 1700 | (31*10^288238-1)/3 | 288240 | Robert Price | 02/2023 |
| 1701 | (7^341063-2^341063)/5 | 288231 | Jon Grantham | 08/2023 |
| 1702 | 2^957372+283531 | 288198 | Enzo Doria | 02/2017 |
| 1703 | 2^957192-1864049 | 288144 | Enzo Doria | 01/2016 |
| 1704 | (95774^58081-1)/(95774^241-1) | 288116 | Ryan Propper | 11/2023 |
| 1705 | 2^956446+1875199 | 287919 | Enzo Doria | 06/2016 |
| 1706 | 2^956283+219143 | 287870 | Enzo Doria | 02/2024 |
| 1707 | 7*10^287854+39 | 287855 | Robert Price | 01/2023 |
| 1708 | 2^956082+28309 | 287810 | Enzo Doria | 02/2024 |
| 1709 | (17^233689+1)/18 | 287542 | Paul Bourdelais | 09/2013 |
| 1710 | 2^955178+1883587 | 287538 | Enzo Doria | 12/2016 |
| 1711 | 2^954127-954127^2 | 287221 | Henri Lifchitz | 01/2021 |
| 1712 | 2^954001+1875257 | 287183 | Enzo Doria | 07/2016 |
| 1713 | 2*10^287175-49 | 287176 | Robert Price | 05/2023 |
| 1714 | (22*10^287085-19)/3 | 287086 | Robert Price | 07/2023 |
| 1715 | 2^953667+38573 | 287083 | Enzo Doria | 11/2024 |
| 1716 | 2^953488+22411 | 287029 | Enzo Doria | 09/2023 |
| 1717 | (23891^65536+1)/2 | 286932 | Serge Batalov | 03/2018 |
| 1718 | 5*3^601336-2^601336 | 286911 | Jon Grantham | 08/2023 |
| 1719 | 2^952268+1878601 | 286662 | Enzo Doria | 09/2016 |
| 1720 | 2^950801+81557 | 286220 | Enzo Doria | 08/2016 |
| 1721 | 2^949403+217523 | 285799 | Enzo Doria | 01/2024 |
| 1722 | 22845^65536+22844^65536 | 285658 | Kellen Shenton | 03/2021 |
| 1723 | (19*10^285615+53)/9 | 285616 | Rytis Slatkevicius | 12/2024 |
| 1724 | (11*2^948635-13)/15 | 285568 | Renaud Lifchitz | 11/2011 |
| 1725 | (54^164839+1)/55 | 285565 | Paul Bourdelais | 07/2019 |
| 1726 | 2^948510+782569 | 285530 | Enzo Doria | 10/2016 |
| 1727 | 2^948374-114137 | 285490 | Enzo Doria | 01/2015 |
| 1728 | 2^947739+1872923 | 285298 | Enzo Doria | 06/2016 |
| 1729 | 2^946274+218407 | 284857 | Enzo Doria | 03/2024 |
| 1730 | 7*10^284751+9 | 284752 | Robert Price | 04/2023 |
| 1731 | 2^944561-21 | 284342 | Stefano Morozzi | 07/2022 |
| 1732 | (4*10^284330-31)/9 | 284330 | Serge Batalov | 11/2022 |
| 1733 | (32*10^283826-23)/9 | 283827 | Serge Batalov | 01/2023 |
| 1734 | 2^942533+82067 | 283731 | Enzo Doria | 09/2016 |
| 1735 | 2^941469+39 | 283411 | Jon Grantham | 08/2023 |
| 1736 | (10^283342-31)/3 | 283342 | Robert Price | 03/2023 |
| 1737 | 2^940950+1874989 | 283255 | Enzo Doria | 06/2016 |
| 1738 | 2^940426-2786141 | 283097 | Enzo Doria | 11/2015 |
| 1739 | 2^940155+226973 | 283015 | Enzo Doria | 09/2024 |
| 1740 | (2*10^282948-11)/9 | 282948 | Serge Batalov | 11/2022 |
| 1741 | 2^939881-114115 | 282933 | Enzo Doria | 12/2014 |
| 1742 | (14*10^282673-143)/3 | 282674 | Robert Price | 05/2023 |
| 1743 | 10^282493+632551 | 282494 | Patrick De Geest | 02/2017 |
| 1745 | 10^282493-9^282493 | 282493 | Jean-Louis Charton | 03/2007 |
| 1744 | 10^282493-132327 | 282493 | Patrick De Geest | 02/2017 |
| 1746 | 3^591827-2^591827 | 282374 | Mike Oakes | 08/2009 |
| 1747 | Tau(509^18946) | 282048 | Nik Lygeros / Olivier Rozier | 05/2015 |
| 1748 | Sm(58628)/47409417156 | 282023 | Youcef Lemsafer | 06/2026 |
| 1749 | 2^936716-1835519 | 281980 | Enzo Doria | 04/2015 |
| 1750 | 2^936588+79411 | 281942 | Enzo Doria | 06/2016 |
