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 | 63722^51915+51915^63722 | 300468 | Hans Havermann | 06/2021 |
| 1502 | 2^998053+1879667 | 300444 | Enzo Doria | 09/2016 |
| 1503 | 77018^7959+7959^77018 | 300437 | Hans Havermann | 07/2021 |
| 1504 | 314738^9+9^314738 | 300337 | Anatoly F. Selevich | 02/2011 |
| 1505 | 2^997689+217787 | 300335 | Enzo Doria | 01/2024 |
| 1506 | 69478^20987+20987^69478 | 300281 | Hans Havermann | 07/2021 |
| 1507 | 64088^48393+48393^64088 | 300239 | Hans Havermann | 07/2021 |
| 1508 | 2^997369+237917 | 300238 | Enzo Doria | 06/2025 |
| 1509 | 64605^44146+44146^64605 | 300084 | Hans Havermann | 08/2021 |
| 1510 | 2^996845+29027 | 300081 | Enzo Doria | 02/2024 |
| 1511 | 7^355039-6^355039 | 300043 | Jean-Louis Charton | 05/2011 |
| 1512 | 67594^27465+27465^67594 | 300035 | Hans Havermann | 06/2021 |
| 1513 | 10^300000+287389 | 300001 | Patrick De Geest | 10/2019 |
| 1514 | 10^300000-83657 | 300000 | Patrick De Geest | 10/2019 |
| 1515 | 70599^17756+17756^70599 | 300000 | Hans Havermann | 06/2021 |
| 1516 | numbpart(72526161452) | 299999 | Serge Batalov | 04/2017 |
| 1517 | 2^996182-114431 | 299881 | Enzo Doria | 02/2015 |
| 1518 | 3*2^996126+5 | 299865 | Jon Grantham | 07/2023 |
| 1519 | 2^996034-17 | 299837 | Stefano Morozzi | 07/2022 |
| 1520 | 2^995793+36587 | 299764 | Enzo Doria | 09/2024 |
| 1521 | (19*10^299640+77)/3 | 299641 | Robert Price | 03/2023 |
| 1522 | 2^995214-2788361 | 299590 | Enzo Doria | 12/2015 |
| 1523 | 2^994791-114319 | 299462 | Enzo Doria | 01/2015 |
| 1524 | 2^994490-1863791 | 299372 | Enzo Doria | 01/2016 |
| 1525 | 2^993322+1885729 | 299020 | Enzo Doria | 03/2017 |
| 1526 | 2^993227+230033 | 298992 | Enzo Doria | 12/2024 |
| 1527 | (36395^65536+36393^65536)/2 | 298913 | Kellen Shenton | 04/2022 |
| 1528 | 2^992711-2788807 | 298836 | Enzo Doria | 12/2015 |
| 1529 | 2^992525-114199 | 298780 | Enzo Doria | 12/2014 |
| 1530 | (7^353501-3^353501)/4 | 298743 | Jon Grantham | 08/2023 |
| 1531 | 2^992329+1884707 | 298721 | Enzo Doria | 02/2017 |
| 1532 | 2^992292+229801 | 298710 | Enzo Doria | 12/2024 |
| 1533 | 2^992052+215491 | 298638 | Enzo Doria | 11/2023 |
| 1534 | 2^991968-23 | 298613 | Stefano Morozzi | 07/2022 |
| 1535 | 2^991715-19 | 298536 | Stefano Morozzi | 07/2022 |
| 1536 | 2^991387+237383 | 298438 | Enzo Doria | 06/2025 |
| 1537 | (10^298414+7)/191/823/56921/1334467 | 298398 | Alfred Reich | 10/2021 |
| 1538 | 2^989562+25 | 297888 | Stefano Morozzi | 05/2021 |
| 1539 | 2^988580+214051 | 297593 | Enzo Doria | 10/2023 |
| 1540 | 2^988537+218837 | 297580 | Enzo Doria | 03/2024 |
| 1541 | (19*10^297497+77)/3 | 297498 | Robert Price | 03/2023 |
| 1542 | (2*10^297488-23)/3 | 297488 | Robert Price | 10/2022 |
| 1543 | 2^988148+48271 | 297463 | Enzo Doria | 07/2025 |
| 1544 | 2^987033+46427 | 297127 | Enzo Doria | 05/2025 |
| 1545 | (2^986191+1)/3 | 296873 | Vincent Diepeveen | 06/2008 |
| 1546 | 2^985217-114553 | 296580 | Enzo Doria | 03/2015 |
| 1547 | (76^157649-1)/75 | 296507 | Paul Bourdelais | 07/2019 |
| 1548 | 2^984650+21529 | 296410 | Enzo Doria | 08/2023 |
| 1549 | 2^984131-1828009 | 296253 | Enzo Doria | 01/2015 |
| 1550 | 2^983620+60451 | 296100 | Phil Moore | 03/2008 |
| 1551 | 2^982721-2683 | 295829 | Yves Minet | 02/2016 |
| 1552 | (23*10^295581+7)/3 | 295582 | Robert Price | 05/2023 |
| 1553 | 2^981298-2788421 | 295401 | Enzo Doria | 12/2015 |
| 1554 | 2^981163-2790967 | 295360 | Enzo Doria | 12/2015 |
| 1555 | 2^981016-15 | 295316 | Stefano Morozzi | 07/2022 |
| 1556 | 8*10^295160-13 | 295161 | Robert Price | 08/2023 |
| 1557 | 2^979594+1865839 | 294888 | Enzo Doria | 02/2016 |
| 1558 | 2^979502+221029 | 294860 | Enzo Doria | 03/2024 |
| 1559 | 2*10^294527-91 | 294528 | Robert Price | 02/2023 |
| 1560 | (49363^63001-1)/(49363^251-1) | 294511 | Ryan Propper | 11/2023 |
| 1561 | 10^294475+49 | 294476 | Robert Price | 02/2023 |
| 1562 | 2^977896+234601 | 294377 | Enzo Doria | 04/2025 |
| 1563 | (11*10^294308+91)/3 | 294309 | Robert Price | 03/2023 |
| 1564 | 2^976760+1885021 | 294035 | Enzo Doria | 02/2017 |
| 1565 | 3*2^976518+5 | 293962 | Jon Grantham | 07/2023 |
| 1566 | 2^975798+218599 | 293745 | Enzo Doria | 01/2024 |
| 1567 | 2^974441+1878407 | 293336 | Enzo Doria | 08/2016 |
| 1568 | 2^974180+1876831 | 293258 | Enzo Doria | 07/2016 |
| 1569 | 2^974170+453319 | 293255 | Enzo Doria | 01/2017 |
| 1570 | (211^126023-1)/210 | 292911 | Anonymous | 05/2024 |
| 1571 | 2^972744-114419 | 292826 | Enzo Doria | 03/2015 |
| 1572 | 11^281143+6 | 292781 | Paul Bourdelais | 03/2021 |
| 1573 | (4*10^292619-91)/3 | 292620 | Robert Price | 12/2022 |
| 1574 | E(69468)/13247122135 | 292549 | Sergey Batalov | 10/2023 |
| 1575 | CopelandErdos(292447) | 292447 | Mark Rodenkirch | 12/2015 |
| 1576 | 3*10^292344-97 | 292345 | Robert Price | 01/2023 |
| 1577 | 2^970911+1873373 | 292274 | Enzo Doria | 07/2016 |
| 1578 | 2^970670+383059 | 292201 | Enzo Doria | 12/2016 |
| 1579 | 2^970141-100363 | 292042 | Enzo Doria | 02/2014 |
| 1580 | 2^969945+1874717 | 291983 | Enzo Doria | 06/2016 |
| 1581 | 2^969384+1880701 | 291814 | Enzo Doria | 10/2016 |
| 1582 | (13*10^291721-43)/3 | 291722 | Robert Price | 08/2023 |
| 1583 | (3^611333-2^611333)/(99035947*87109884549431) | 291659 | Mike Oakes | 02/2017 |
| 1584 | 10^(2*145126+1)-2*10^145126-1 | 290253 | Robert Price | 03/2025 |
| 1585 | 3*2^963892+5 | 290161 | Jon Grantham | 07/2023 |
| 1586 | (151*10^289877-1)/3 | 289879 | Robert Price | 07/2023 |
| 1587 | 2^962194+60139 | 289650 | Enzo Doria | 02/2016 |
| 1588 | 2^961409+44267 | 289413 | Enzo Doria | 04/2025 |
| 1589 | 2^959307-1861507 | 288781 | Enzo Doria | 11/2015 |
| 1590 | (17*10^288692+31)/3 | 288693 | Robert Price | 04/2023 |
| 1591 | 14^251797-3 | 288592 | Paul Bourdelais | 12/2020 |
| 1592 | (8745^73441-1)/(8745^271-1) | 288419 | Ryan Propper | 11/2023 |
| 1593 | (2*10^288371-23)/3 | 288371 | Robert Price | 10/2022 |
| 1594 | (31*10^288238-1)/3 | 288240 | Robert Price | 02/2023 |
| 1595 | (7^341063-2^341063)/5 | 288231 | Jon Grantham | 08/2023 |
| 1596 | 2^957372+283531 | 288198 | Enzo Doria | 02/2017 |
| 1597 | 2^957192-1864049 | 288144 | Enzo Doria | 01/2016 |
| 1598 | (95774^58081-1)/(95774^241-1) | 288116 | Ryan Propper | 11/2023 |
| 1599 | 2^956446+1875199 | 287919 | Enzo Doria | 06/2016 |
| 1600 | 2^956283+219143 | 287870 | Enzo Doria | 02/2024 |
| 1601 | 7*10^287854+39 | 287855 | Robert Price | 01/2023 |
| 1602 | 2^956082+28309 | 287810 | Enzo Doria | 02/2024 |
| 1603 | (17^233689+1)/18 | 287542 | Paul Bourdelais | 09/2013 |
| 1604 | 2^955178+1883587 | 287538 | Enzo Doria | 12/2016 |
| 1605 | 2^954127-954127^2 | 287221 | Henri Lifchitz | 01/2021 |
| 1606 | 2^954001+1875257 | 287183 | Enzo Doria | 07/2016 |
| 1607 | 2*10^287175-49 | 287176 | Robert Price | 05/2023 |
| 1608 | (22*10^287085-19)/3 | 287086 | Robert Price | 07/2023 |
| 1609 | 2^953667+38573 | 287083 | Enzo Doria | 11/2024 |
| 1610 | 2^953488+22411 | 287029 | Enzo Doria | 09/2023 |
| 1611 | (23891^65536+1)/2 | 286932 | Serge Batalov | 03/2018 |
| 1612 | 5*3^601336-2^601336 | 286911 | Jon Grantham | 08/2023 |
| 1613 | 2^952268+1878601 | 286662 | Enzo Doria | 09/2016 |
| 1614 | 2^950801+81557 | 286220 | Enzo Doria | 08/2016 |
| 1615 | 2^949403+217523 | 285799 | Enzo Doria | 01/2024 |
| 1616 | 22845^65536+22844^65536 | 285658 | Kellen Shenton | 03/2021 |
| 1617 | (19*10^285615+53)/9 | 285616 | Rytis Slatkevicius | 12/2024 |
| 1618 | (11*2^948635-13)/15 | 285568 | Renaud Lifchitz | 11/2011 |
| 1619 | (54^164839+1)/55 | 285565 | Paul Bourdelais | 07/2019 |
| 1620 | 2^948510+782569 | 285530 | Enzo Doria | 10/2016 |
| 1621 | 2^948374-114137 | 285490 | Enzo Doria | 01/2015 |
| 1622 | 2^947739+1872923 | 285298 | Enzo Doria | 06/2016 |
| 1623 | 2^946274+218407 | 284857 | Enzo Doria | 03/2024 |
| 1624 | 7*10^284751+9 | 284752 | Robert Price | 04/2023 |
| 1625 | 2^944561-21 | 284342 | Stefano Morozzi | 07/2022 |
| 1626 | (4*10^284330-31)/9 | 284330 | Serge Batalov | 11/2022 |
| 1627 | (32*10^283826-23)/9 | 283827 | Serge Batalov | 01/2023 |
| 1628 | 2^942533+82067 | 283731 | Enzo Doria | 09/2016 |
| 1629 | 2^941469+39 | 283411 | Jon Grantham | 08/2023 |
| 1630 | (10^283342-31)/3 | 283342 | Robert Price | 03/2023 |
| 1631 | 2^940950+1874989 | 283255 | Enzo Doria | 06/2016 |
| 1632 | 2^940426-2786141 | 283097 | Enzo Doria | 11/2015 |
| 1633 | 2^940155+226973 | 283015 | Enzo Doria | 09/2024 |
| 1634 | (2*10^282948-11)/9 | 282948 | Serge Batalov | 11/2022 |
| 1635 | 2^939881-114115 | 282933 | Enzo Doria | 12/2014 |
| 1636 | (14*10^282673-143)/3 | 282674 | Robert Price | 05/2023 |
| 1637 | 10^282493+632551 | 282494 | Patrick De Geest | 02/2017 |
| 1639 | 10^282493-9^282493 | 282493 | Jean-Louis Charton | 03/2007 |
| 1638 | 10^282493-132327 | 282493 | Patrick De Geest | 02/2017 |
| 1640 | 3^591827-2^591827 | 282374 | Mike Oakes | 08/2009 |
| 1641 | Tau(509^18946) | 282048 | Nik Lygeros / Olivier Rozier | 05/2015 |
| 1642 | 2^936716-1835519 | 281980 | Enzo Doria | 04/2015 |
| 1643 | 2^936588+79411 | 281942 | Enzo Doria | 06/2016 |
| 1644 | 2^936047+1877423 | 281779 | Enzo Doria | 08/2016 |
| 1645 | 2^935713+1869377 | 281678 | Enzo Doria | 05/2016 |
| 1646 | 2^933082+1877059 | 280886 | Enzo Doria | 08/2016 |
| 1647 | (5*10^280710+1)/3 | 280711 | Serge Batalov | 10/2014 |
| 1648 | 2^932443+225893 | 280694 | Enzo Doria | 08/2024 |
| 1649 | 2^932064+26521 | 280580 | Enzo Doria | 12/2023 |
| 1650 | 2^931976+25 | 280553 | Stefano Morozzi | 05/2021 |
| 1651 | (42^172663+1)/43 | 280274 | Paul Bourdelais | 07/2019 |
| 1652 | (10^279978+11)/3 | 279978 | Serge Batalov | 07/2015 |
| 1653 | 2^929524-1864829 | 279815 | Enzo Doria | 01/2016 |
| 1654 | 2^929329+22697 | 279756 | Enzo Doria | 09/2023 |
| 1655 | 2^929152+60181 | 279703 | Enzo Doria | 02/2016 |
| 1656 | 2^928621-2787883 | 279543 | Enzo Doria | 11/2015 |
| 1657 | (2^927763+lucasV(-1,2,927763)+1)/2 | 279285 | Mike Oakes | 04/2017 |
| 1658 | 3*10^279271+77 | 279272 | Robert Price | 06/2024 |
| 1659 | 2^927429+1882277 | 279184 | Enzo Doria | 12/2016 |
| 1660 | 2^926766-11 | 278985 | Stefano Morozzi | 07/2022 |
| 1661 | (71^150697-1)/70 | 278978 | Paul Bourdelais | 07/2019 |
| 1662 | (33^183661-1)/32 | 278891 | Paul Bourdelais | 12/2018 |
| 1663 | (5347*26^197061-297)/25 | 278839 | Eric Chen | 12/2025 |
| 1664 | (166*10^278633-7)/3 | 278635 | Robert Price | 02/2023 |
| 1665 | (2^925391+lucasV(-1,2,925391)+1)/2 | 278571 | Mike Oakes | 03/2017 |
| 1666 | 2^925330-1301 | 278553 | Yves Minet | 06/2015 |
| 1667 | (299*10^278546+1)/3 | 278548 | Robert Price | 01/2023 |
| 1668 | 2^925299+216053 | 278543 | Enzo Doria | 11/2023 |
| 1670 | (21^210599+1)/22 | 278457 | Paul Bourdelais | 08/2013 |
| 1669 | (79^146749-1)/6395645198026062186 | 278457 | Paul Vanderveen | 06/2025 |
| 1671 | (266*10^278325+1)/3 | 278327 | Robert Price | 01/2023 |
| 1672 | 2^923261-69175 | 277930 | Enzo Doria | 11/2015 |
| 1673 | 757^96487-756^96487 | 277796 | Jean-Louis Charton | 12/2012 |
| 1674 | 2^922301+57 | 277641 | Stefano Morozzi | 05/2021 |
| 1675 | 7*10^277478-39 | 277479 | Robert Price | 07/2023 |
| 1676 | ((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2 | 277369 | Serge Batalov | 07/2016 |
| 1677 | (5^396413-1)/4 | 277081 | Paul Bourdelais | 06/2010 |
| 1678 | 2^920318+2792299 | 277044 | Enzo Doria | 02/2016 |
| 1679 | (16*10^276537-31)/3 | 276538 | Robert Price | 03/2023 |
| 1680 | 2^918596-2786939 | 276525 | Enzo Doria | 11/2015 |
| 1681 | 2^917910+28369 | 276319 | Enzo Doria | 01/2024 |
| 1682 | 2^917328+228571 | 276144 | Enzo Doria | 11/2024 |
| 1683 | (6737^72361-1)/(6737^269-1) | 276002 | Ryan Propper | 11/2023 |
| 1684 | 2^916639+60563 | 275936 | Enzo Doria | 04/2016 |
| 1685 | (2*10^275922+1)/3 | 275922 | Serge Batalov | 11/2022 |
| 1686 | 2^916385-2786383 | 275860 | Enzo Doria | 11/2015 |
| 1687 | 2^915928+82081 | 275722 | Enzo Doria | 09/2016 |
| 1688 | (4*10^275671+11)/3 | 275672 | Tyler Busby | 02/2023 |
| 1689 | 2^915576-114137 | 275616 | Enzo Doria | 01/2015 |
| 1690 | 2^914828+1876741 | 275391 | Enzo Doria | 07/2016 |
| 1691 | 2^914757-2203 | 275370 | Yves Minet | 12/2015 |
| 1692 | 7*10^275157-27 | 275158 | Robert Price | 11/2022 |
| 1693 | 2^912744+20011 | 274764 | Enzo Doria | 06/2023 |
| 1694 | 2^911900+1871245 | 274510 | Enzo Doria | 05/2016 |
| 1695 | (16*10^274251-91)/3 | 274252 | Robert Price | 11/2022 |
| 1696 | 2^910999+9 | 274239 | Stefano Morozzi | 05/2021 |
| 1697 | (2^910869-7)/5 | 274199 | Stefano Morozzi | 08/2022 |
| 1698 | 2^910490+283429 | 274085 | Enzo Doria | 01/2017 |
| 1699 | 7*10^273983+39 | 273984 | Robert Price | 01/2023 |
| 1700 | 2^909988-1862249 | 273934 | Enzo Doria | 12/2015 |
| 1701 | 2^909901+378567 | 273908 | Boyan Hu | 08/2024 |
| 1702 | 2^909297+1879157 | 273726 | Enzo Doria | 08/2016 |
| 1703 | 2^909257-1864423 | 273714 | Enzo Doria | 01/2016 |
| 1704 | 2^909254+31309 | 273713 | Enzo Doria | 03/2024 |
| 1705 | 2^908739-7 | 273558 | Stefano Morozzi | 07/2022 |
| 1706 | 2^908579-1861747 | 273510 | Enzo Doria | 12/2015 |
| 1707 | 3*2^908005-5 | 273338 | Jon Grantham | 07/2023 |
| 1708 | 2^907635-2791597 | 273226 | Enzo Doria | 01/2016 |
| 1709 | 2^907059+211193 | 273052 | Enzo Doria | 08/2023 |
| 1710 | (53^158341+1)/54 | 273022 | Paul Bourdelais | 07/2019 |
| 1711 | 2^906594-113201 | 272912 | Enzo Doria | 08/2014 |
| 1712 | 9*10^272800+91 | 272801 | Robert Price | 05/2023 |
| 1713 | 2*10^272710-49 | 272711 | Robert Price | 05/2023 |
| 1714 | 2*10^272403-91 | 272404 | Robert Price | 02/2023 |
| 1715 | 2^904773+1872167 | 272364 | Enzo Doria | 06/2016 |
| 1716 | 6^349903+5 | 272278 | Paul Bourdelais | 02/2021 |
| 1717 | 2^904149-1862473 | 272176 | Enzo Doria | 12/2015 |
| 1718 | 2^902926+227839 | 271808 | Enzo Doria | 10/2024 |
| 1719 | (7*10^271757-61)/9 | 271757 | Erik Branger | 03/2012 |
| 1720 | 2^902497+1880117 | 271679 | Enzo Doria | 09/2016 |
| 1721 | 2^901858+77689 | 271487 | Enzo Doria | 06/2016 |
| 1722 | 2^901372+1875301 | 271341 | Enzo Doria | 06/2016 |
| 1723 | 2^901146+219049 | 271272 | Enzo Doria | 02/2024 |
| 1724 | (8*10^271039-77)/3 | 271040 | Robert Price | 04/2023 |
| 1725 | 2^899999+1144031 | 270927 | Norman Luhn | 09/2023 |
| 1726 | 2*10^270802-91 | 270803 | Robert Price | 02/2023 |
| 1727 | 23*10^270799-7 | 270801 | Robert Price | 10/2022 |
| 1728 | 2^899121-115033 | 270663 | Enzo Doria | 07/2015 |
| 1729 | 2^898900+883021 | 270596 | Enzo Doria | 12/2016 |
| 1730 | 2^898762-251511 | 270555 | Enzo Doria | 12/2013 |
| 1731 | 2^898589+47 | 270503 | Lelio R Paula | 03/2016 |
| 1732 | (939628*10^270345-93962791)/9 | 270351 | Danilo Nitsche | 03/2026 |
| 1733 | 1447184*10^270344-14471839 | 270351 | Danilo Nitsche | 03/2026 |
| 1734 | 269048*10^270344-2690479 | 270350 | Danilo Nitsche | 02/2026 |
| 1735 | 172249*10^270344-1722489 | 270350 | Danilo Nitsche | 02/2026 |
| 1736 | (288964*10^270345-28896397)/3 | 270350 | Danilo Nitsche | 02/2026 |
| 1737 | 661681*10^270344-6616809 | 270350 | Danilo Nitsche | 02/2026 |
| 1738 | 184489*10^270344-1844889 | 270350 | Danilo Nitsche | 02/2026 |
| 1739 | 58552*10^270345-5855199 | 270350 | Danilo Nitsche | 02/2026 |
| 1740 | (245662*10^270345-24566197)/3 | 270350 | Danilo Nitsche | 02/2026 |
| 1741 | 371745*10^270344-3717449 | 270350 | Danilo Nitsche | 02/2026 |
| 1742 | (1366645*10^270344-13666441)/9 | 270350 | Danilo Nitsche | 03/2026 |
| 1743 | (1648732*10^270344-16487317)/3 | 270350 | Danilo Nitsche | 03/2026 |
| 1744 | (1386601*10^270344-13866001)/9 | 270350 | Danilo Nitsche | 03/2026 |
| 1745 | (1631944*10^270344-16319431)/9 | 270350 | Danilo Nitsche | 03/2026 |
| 1746 | 922284*10^270344-9222839 | 270350 | Danilo Nitsche | 03/2026 |
| 1747 | 992761*10^270344-9927609 | 270350 | Danilo Nitsche | 03/2026 |
| 1748 | 187322*10^270343-187321 | 270349 | Danilo Nitsche | 09/2013 |
| 1749 | 48358*10^270343-48357 | 270348 | Danilo Nitsche | 09/2013 |
| 1750 | (10^270343-1)/9 | 270343 | Maksym Voznyy | 07/2007 |
