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
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
1501 | 524309#+616367 | 227431 | Makoto Morimoto | 02/2016 |
1502 | 2^755097-114193 | 227307 | Enzo Doria | 12/2014 |
1503 | 7*10^227178+39 | 227179 | Robert Price | 01/2023 |
1504 | 9*10^227153-89 | 227154 | Robert Price | 02/2023 |
1505 | 2^754473-2791513 | 227120 | Enzo Doria | 01/2016 |
1506 | 2^754376+25 | 227090 | Stefano Morozzi | 05/2021 |
1507 | 2^754138+213289 | 227019 | Enzo Doria | 09/2023 |
1508 | 2^754038+25 | 226989 | Stefano Morozzi | 05/2021 |
1509 | 2^753263+217133 | 226755 | Enzo Doria | 12/2023 |
1510 | 7*10^226479-9 | 226480 | Robert Price | 02/2023 |
1511 | 2^751426-764321 | 226202 | Enzo Doria | 12/2013 |
1512 | (18^180181-1)/17 | 226176 | Andy Steward | 04/2007 |
1513 | 2^750740-3 | 225996 | Paul Bourdelais | 03/2012 |
1514 | 2^750725+60227 | 225991 | Enzo Doria | 02/2016 |
1515 | 2^750525-113743 | 225931 | Enzo Doria | 09/2014 |
1516 | (2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263) | 225744 | Dario Alpern | 10/2014 |
1517 | 2^749444-1861889 | 225606 | Enzo Doria | 12/2015 |
1518 | tau(311^16452) | 225560 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
1519 | 2^749096+1876861 | 225501 | Enzo Doria | 07/2016 |
1520 | 2^748895+26213 | 225440 | Enzo Doria | 12/2023 |
1521 | (519643#+43033)/(23*1871*2706283) | 225379 | Makoto Morimoto | 08/2019 |
1522 | 2^748657+79607 | 225369 | Enzo Doria | 06/2016 |
1523 | (2^746920-11)/5 | 224845 | Stefano Morozzi | 08/2022 |
1524 | 2^746653-291583 | 224765 | Enzo Doria | 07/2015 |
1525 | 2^746461-114043 | 224708 | Enzo Doria | 11/2014 |
1526 | 2^746302+25 | 224660 | Stefano Morozzi | 05/2021 |
1527 | (202*10^224545-1)/3 | 224547 | Robert Price | 06/2023 |
1528 | (19*10^224533-37)/9 | 224534 | Alfred Reich | 12/2023 |
1529 | 2^745674+213949 | 224471 | Enzo Doria | 10/2023 |
1530 | 2^745098-350471 | 224297 | Enzo Doria | 06/2015 |
1531 | 2^745039-4897 | 224280 | Yves Minet | 03/2021 |
1532 | 23*10^224232-7 | 224234 | Robert Price | 10/2022 |
1533 | (154*10^224061-1)/9 | 224063 | Serge Batalov | 12/2014 |
1534 | 2^744211-1845787 | 224030 | Enzo Doria | 07/2015 |
1535 | 2^743592-134579 | 223844 | Hans Havermann | 10/2018 |
1536 | 2^742452+3 | 223501 | Paul Bourdelais | 06/2019 |
1537 | 234178^9+9^234178 | 223463 | Anatoly F. Selevich | 07/2011 |
1538 | 2^741651-461197 | 223260 | Enzo Doria | 07/2015 |
1539 | 10^223236-1001 | 223236 | Robert Price | 10/2022 |
1540 | 2^741362-1845251 | 223173 | Enzo Doria | 07/2015 |
1541 | 3^467546-5*2^467546 | 223077 | Jon Grantham | 08/2023 |
1542 | 2^740455-1863877 | 222900 | Enzo Doria | 12/2015 |
1543 | 2^740274+217519 | 222845 | Enzo Doria | 01/2024 |
1544 | (14*10^222718-41)/9 | 222719 | Serge Batalov | 01/2023 |
1545 | 2^739636-2792219 | 222653 | Enzo Doria | 02/2016 |
1546 | 11^213654-180 | 222498 | Enzo Doria | 01/2013 |
1547 | 2^738957-1859743 | 222449 | Enzo Doria | 11/2015 |
1548 | 4*10^222253-21 | 222254 | Robert Price | 12/2022 |
1549 | 2^737825+57 | 222108 | Stefano Morozzi | 05/2021 |
1550 | (54^128189+1)/55 | 222073 | Paul Bourdelais | 11/2018 |
1551 | 2^737166+220099 | 221910 | Enzo Doria | 03/2024 |
1552 | (10^221654+179)/9 | 221654 | Serge Batalov | 12/2014 |
1553 | 2^736281+79817 | 221643 | Enzo Doria | 06/2016 |
1554 | 10^221631+247617 | 221632 | Patrick De Geest | 10/2013 |
1555 | 10^221631-9 | 221631 | Alexander Gramolin | 02/2011 |
1556 | 10^221628+7 | 221629 | Alfred Reich | 04/2021 |
1557 | 2^735970-1839821 | 221550 | Enzo Doria | 06/2015 |
1558 | 2^735367+60293 | 221368 | Enzo Doria | 03/2016 |
1559 | 77*10^221343+3 | 221345 | Robert Price | 11/2023 |
1560 | (202*10^221092-1)/3 | 221094 | Robert Price | 06/2023 |
1561 | (29^151153+1)/30 | 221045 | Paul Bourdelais | 09/2017 |
1562 | 2^734228+24751 | 221025 | Enzo Doria | 10/2023 |
1563 | 2^733264-2784089 | 220735 | Enzo Doria | 10/2015 |
1564 | 2^733114-24555 | 220690 | Enzo Doria | 09/2013 |
1565 | 2^731891-636259 | 220322 | Enzo Doria | 12/2013 |
1566 | 98*10^220185-9 | 220187 | Robert Price | 05/2023 |
1567 | 418319^39164+418318 | 220161 | Alfred Reich | 11/2023 |
1568 | 2^731124-25539 | 220091 | Enzo Doria | 09/2013 |
1569 | 2^730972-462029 | 220045 | Enzo Doria | 07/2015 |
1570 | 2^730833+1868627 | 220003 | Enzo Doria | 04/2016 |
1571 | 2^730645-2787133 | 219947 | Enzo Doria | 11/2015 |
1572 | 2^730547-25581 | 219917 | Enzo Doria | 09/2013 |
1573 | (113*13^197420-5)/12 | 219916 | Anonymous | 11/2022 |
1574 | (13^197420*113-5)/12 | 219916 | Eric Chen | 10/2023 |
1575 | 2^730460+82291 | 219891 | Enzo Doria | 09/2016 |
1576 | (5*10^219847-101)/3 | 219848 | Robert Price | 08/2023 |
1577 | (2^730339+1)/(3*27839062003*7943469324347) | 219831 | Gord Palameta | 12/2018 |
1578 | L(1051849) | 219824 | Renaud Lifchitz | 03/2009 |
1579 | 3*2^730149+5 | 219798 | Jon Grantham | 07/2023 |
1580 | 8*10^219740-3 | 219741 | Serge Batalov | 01/2023 |
1581 | 11^210961-240 | 219694 | Enzo Doria | 01/2013 |
1582 | (26*10^219639-77)/3 | 219640 | Robert Price | 03/2023 |
1583 | 2^729611-113437 | 219635 | Enzo Doria | 08/2014 |
1584 | 7^259710-2 | 219481 | Paul Bourdelais | 01/2021 |
1585 | F(1049897) | 219416 | Henri Lifchitz | 10/2008 |
1586 | (1488^69151-1)/1487 | 219386 | Alexander Zhirkov | 02/2023 |
1587 | 2^728604+1879321 | 219332 | Enzo Doria | 10/2016 |
1588 | 33^144412+2 | 219292 | Robert Price | 04/2015 |
1589 | 2^728277-183313 | 219234 | Hans Havermann | 10/2018 |
1590 | 2^727998-1862711 | 219150 | Enzo Doria | 12/2015 |
1591 | (29*10^219124+91)/3 | 219125 | Robert Price | 12/2022 |
1592 | 2^727729-114073 | 219069 | Enzo Doria | 12/2014 |
1593 | 2^727496-1851809 | 218999 | Enzo Doria | 08/2015 |
1594 | 2^727025+25907 | 218857 | Enzo Doria | 12/2023 |
1595 | 2^726591+2793143 | 218726 | Enzo Doria | 02/2016 |
1596 | (7*10^218644+17)/3 | 218645 | Robert Price | 06/2023 |
1597 | 2^725534-2791931 | 218408 | Enzo Doria | 02/2016 |
1598 | Phi(220531,10)/2686456812680882641 | 217774 | Makoto Kamada | 10/2020 |
1599 | 2^722184+1877821 | 217400 | Enzo Doria | 08/2016 |
1600 | (109*10^217360-1)/9 | 217362 | Serge Batalov | 12/2014 |
1601 | 2^721721-4453 | 217260 | Yves Minet | 03/2021 |
1602 | 10^216950+49 | 216951 | Robert Price | 02/2023 |
1603 | 281*499979#/46410-2702372 | 216849 | Robert Smith | 08/2016 |
1604 | 281*499979#/46410+2400766 | 216849 | Robert Smith | 08/2016 |
1605 | tau(311^15786) | 216429 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
1606 | 2^718756-114107 | 216368 | Enzo Doria | 12/2014 |
1607 | 2^717672+121 | 216041 | Stefano Morozzi | 05/2021 |
1608 | 2^717305+80327 | 215931 | Enzo Doria | 07/2016 |
1609 | 2^717069-59773 | 215860 | Enzo Doria | 10/2015 |
1610 | 10^215802+33 | 215803 | Robert Price | 08/2023 |
1611 | 30^146021-29^146021 | 215691 | Jean-Louis Charton | 09/2018 |
1612 | 277^88301-276^88301 | 215674 | Jean-Louis Charton | 06/2012 |
1613 | 2^716428+215011 | 215667 | Enzo Doria | 11/2023 |
1614 | (13*10^215592-43)/3 | 215593 | Robert Price | 08/2023 |
1615 | 227^91413-40 | 215372 | Enzo Doria | 04/2015 |
1616 | (2^715008-21)/5 | 215239 | Stefano Morozzi | 08/2022 |
1617 | 2^714717+782897 | 215152 | Enzo Doria | 11/2016 |
1618 | tau(373^15186) | 214796 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
1619 | 2^713241+1879157 | 214707 | Enzo Doria | 08/2016 |
1620 | (23*10^214633+91)/3 | 214634 | Robert Price | 03/2023 |
1621 | 11^206081-10^206081 | 214612 | Jean-Louis Charton | 10/2011 |
1622 | 2^712801-69553 | 214575 | Enzo Doria | 01/2016 |
1623 | 2^712603-25357 | 214515 | Enzo Doria | 09/2013 |
1624 | 2^711721-1846723 | 214250 | Enzo Doria | 07/2015 |
1625 | 2^710730-396765 | 213952 | Enzo Doria | 09/2013 |
1626 | (19*10^213934-37)/9 | 213935 | Alfred Reich | 12/2023 |
1627 | (19*10^213730-37)/9 | 213731 | Alfred Reich | 12/2023 |
1628 | (713^74897-1)/712 | 213685 | Jinyuan Wang | 08/2023 |
1629 | 2^709773+25907 | 213663 | Enzo Doria | 12/2023 |
1630 | 2^708468-114329 | 213271 | Enzo Doria | 02/2015 |
1631 | 2^708293+27557 | 213218 | Enzo Doria | 01/2024 |
1632 | 2^707277+28997 | 212912 | Enzo Doria | 02/2024 |
1633 | (163*10^212779-1)/9 | 212781 | Serge Batalov | 12/2014 |
1634 | 2^706838-69041 | 212780 | Enzo Doria | 11/2015 |
1635 | 2^705653+25907 | 212423 | Enzo Doria | 12/2023 |
1636 | 22*10^212339+7 | 212341 | Robert Price | 10/2022 |
1637 | 2^704577-113871 | 212099 | Enzo Doria | 10/2014 |
1638 | (2^704548-19)/3 | 212090 | Stefano Morozzi | 08/2022 |
1639 | 2^704110-2792441 | 211959 | Enzo Doria | 02/2016 |
1640 | 2^704084+28531 | 211951 | Enzo Doria | 02/2024 |
1641 | 2^703943-1862947 | 211908 | Enzo Doria | 12/2015 |
1642 | (60^119083+1)/61 | 211746 | Paul Bourdelais | 10/2018 |
1643 | (184*10^211682-1)/3 | 211684 | Robert Price | 12/2022 |
1644 | (10^211610-91)/9 | 211610 | Serge Batalov | 12/2014 |
1645 | 227^89797+2 | 211565 | Lelio R Paula | 08/2012 |
1646 | 2^702194-3 | 211382 | Paul Bourdelais | 03/2012 |
1647 | 2^702064+1874911 | 211343 | Enzo Doria | 07/2016 |
1648 | 2^701968-113873 | 211314 | Enzo Doria | 10/2014 |
1649 | (14*10^211262-41)/9 | 211263 | Serge Batalov | 01/2023 |
1650 | 2^701713-113779 | 211237 | Enzo Doria | 09/2014 |
1651 | 2^701616-216803 | 211208 | Enzo Doria | 01/2024 |
1652 | 2^701449-25201 | 211158 | Enzo Doria | 09/2013 |
1653 | 2^701403-2786977 | 211144 | Enzo Doria | 11/2015 |
1654 | 2^701189-25423 | 211079 | Enzo Doria | 09/2013 |
1655 | 2^701162-459161 | 211071 | Enzo Doria | 05/2015 |
1656 | 2^700793+219407 | 210960 | Enzo Doria | 03/2024 |
1657 | (24^152783-1)/23 | 210872 | Paul Bourdelais | 04/2018 |
1658 | 2^700400+9385 | 210842 | Lelio R Paula | 01/2014 |
1659 | 2^700304-17 | 210813 | Stefano Morozzi | 07/2022 |
1660 | 2^700131+1874693 | 210761 | Enzo Doria | 06/2016 |
1661 | (2^700095+225414)/2 | 210750 | Stefano Morozzi | 04/2020 |
1662 | (2^700090+278254)/2 | 210748 | Stefano Morozzi | 04/2020 |
1663 | (2^700075+303666)/2 | 210744 | Stefano Morozzi | 04/2020 |
1664 | (2^700073+75882)/2 | 210743 | Stefano Morozzi | 04/2020 |
1665 | (2^700074+328890)/2 | 210743 | Stefano Morozzi | 04/2020 |
1666 | (2^700052+79162)/2 | 210737 | Stefano Morozzi | 04/2020 |
1667 | (2^700052+304458)/2 | 210737 | Stefano Morozzi | 04/2020 |
1668 | (2^700048+376578)/2 | 210736 | Stefano Morozzi | 04/2020 |
1669 | 11^202357-1140 | 210734 | Enzo Doria | 12/2012 |
1670 | (2^700021+25874)/2 | 210728 | Stefano Morozzi | 04/2020 |
1671 | (2^700018+377518)/2 | 210727 | Stefano Morozzi | 04/2020 |
1672 | 2^699999+300729 | 210721 | Norman Luhn | 09/2023 |
1673 | (238*10^210712-1)/3 | 210714 | Robert Price | 09/2023 |
1674 | 2^699740+25 | 210643 | Stefano Morozzi | 05/2021 |
1675 | (23*10^210525-143)/3 | 210526 | Robert Price | 12/2023 |
1676 | 2^698929-2788423 | 210399 | Enzo Doria | 11/2015 |
1677 | (5^300893+4^300893)/9 | 210315 | Jean-Louis Charton | 11/2011 |
1678 | 2^698316+1878601 | 210215 | Enzo Doria | 08/2016 |
1679 | 34*10^210097-9 | 210099 | Robert Price | 05/2023 |
1680 | (19*10^210011-49)/3 | 210012 | Robert Price | 06/2023 |
1681 | 6*10^209846-91 | 209847 | Robert Price | 05/2023 |
1682 | 2^697036+1878751 | 209829 | Enzo Doria | 08/2016 |
1683 | 2^696813+28607 | 209762 | Enzo Doria | 02/2024 |
1684 | (238*10^209715-1)/3 | 209717 | Robert Price | 09/2023 |
1685 | 6^269407+5 | 209640 | Paul Bourdelais | 02/2021 |
1686 | (2^696343-1)/11141489/36009913139329 | 209600 | Tony Prest / Never Odd Or Even | 02/2014 |
1687 | 2^696254-115151 | 209594 | Enzo Doria | 06/2015 |
1688 | (35^135623+1)/36 | 209410 | Paul Bourdelais | 07/2018 |
1689 | 7*10^209161+39 | 209162 | Robert Price | 01/2023 |
1690 | 2^694633+1887257 | 209106 | Enzo Doria | 05/2017 |
1691 | fibonacci(999790)-4 | 208944 | Jon Grantham | 08/2023 |
1692 | 2^693959+180923 | 208903 | Enzo Doria | 07/2016 |
1693 | (2^693747-11)/3 | 208839 | Stefano Morozzi | 08/2022 |
1694 | 2^693462-1847561 | 208753 | Enzo Doria | 07/2015 |
1695 | 2^690890-59981 | 207979 | Enzo Doria | 11/2015 |
1696 | (38^131591+1)/39 | 207884 | Paul Bourdelais | 07/2018 |
1697 | 3*2^690484+5 | 207857 | Jon Grantham | 07/2023 |
1698 | 2^690163+1877063 | 207760 | Enzo Doria | 07/2016 |
1699 | 7^245608-2 | 207563 | Paul Bourdelais | 01/2021 |
1700 | (67*10^207556+23)/9 | 207557 | Serge Batalov | 01/2023 |
1701 | 2^689286-29381 | 207496 | Enzo Doria | 08/2015 |
1702 | 2^689122-114521 | 207447 | Enzo Doria | 04/2015 |
1703 | 9*10^207254-89 | 207255 | Robert Price | 02/2023 |
1704 | 2^688373+6077 | 207221 | Enzo Doria | 02/2016 |
1705 | 2^688201+1875527 | 207170 | Enzo Doria | 07/2016 |
1706 | (42^127609+1)/43 | 207140 | Paul Bourdelais | 07/2018 |
1707 | 2^687938+213589 | 207090 | Enzo Doria | 10/2023 |
1708 | 2^687619+81563 | 206994 | Enzo Doria | 08/2016 |
1709 | 3*10^206927+37 | 206928 | Robert Price | 08/2023 |
1710 | 2^687383+21803 | 206923 | Enzo Doria | 09/2023 |
1711 | 2^686572-1845299 | 206679 | Enzo Doria | 07/2015 |
1712 | (21^156217-1)/20 | 206552 | Paul Bourdelais | 04/2010 |
1713 | (2^685739+1)/(3*87774593) | 206420 | Gord Palameta | 08/2018 |
1714 | 2^685578+3 | 206380 | Paul Bourdelais | 04/2012 |
1715 | 2^685078+218599 | 206230 | Enzo Doria | 01/2024 |
1716 | 2^684836-49349 | 206157 | Enzo Doria | 10/2015 |
1717 | (73^110603-1)/72 | 206088 | Paul Bourdelais | 06/2018 |
1718 | 2^684163-2790967 | 205954 | Enzo Doria | 12/2015 |
1719 | 326^81943-325^81943 | 205941 | Jean-Louis Charton | 07/2012 |
1720 | (2^684127-1)/23765203727 | 205933 | Jens K. Andersen | 04/2009 |
1721 | (68*10^205510+13)/9 | 205511 | Serge Batalov | 01/2023 |
1722 | 4^341233-3^341233 | 205443 | Jean-Louis Charton | 01/2006 |
1723 | 2^682414+215029 | 205428 | Enzo Doria | 11/2023 |
1724 | (963^68821-1)/962 | 205334 | Jinyuan Wang | 01/2024 |
1725 | (43*10^205183-421)/9 | 205184 | Robert Price | 10/2023 |
1726 | 2^681545+467 | 205166 | Lelio R Paula | 11/2013 |
1727 | 2^681306+81049 | 205094 | Enzo Doria | 07/2016 |
1728 | 2^680697+1877057 | 204911 | Enzo Doria | 07/2016 |
1729 | 2^680415+71783 | 204826 | Enzo Doria | 04/2016 |
1730 | 10^204764-8001 | 204764 | Robert Price | 03/2023 |
1731 | (26*10^204730-77)/3 | 204731 | Robert Price | 03/2023 |
1732 | 2^679860-459995 | 204659 | Enzo Doria | 06/2015 |
1733 | 2^679593+1879547 | 204578 | Enzo Doria | 09/2016 |
1734 | 2^678899+220073 | 204369 | Enzo Doria | 03/2024 |
1735 | 2^678753+21677 | 204326 | Enzo Doria | 08/2023 |
1736 | 2^678651+1875023 | 204295 | Enzo Doria | 07/2016 |
1737 | 2^678561+678561 | 204268 | Henri Lifchitz | 05/2006 |
1738 | 5*3^427884+2^427884 | 204154 | Jon Grantham | 08/2023 |
1739 | 2^678101-114043 | 204129 | Enzo Doria | 11/2014 |
1740 | 2^678028+1875631 | 204107 | Enzo Doria | 06/2016 |
1741 | 2^677721+28607 | 204015 | Enzo Doria | 01/2024 |
1742 | (19*10^203798-7)/3 | 203799 | Robert Price | 12/2023 |
1743 | 2^676992-59783 | 203795 | Enzo Doria | 10/2015 |
1744 | 2^676972+1866871 | 203789 | Enzo Doria | 03/2016 |
1745 | 2^676815+22583 | 203742 | Enzo Doria | 09/2023 |
1746 | 2^676761-9 | 203726 | Robert Price | 01/2017 |
1747 | 2^676592-23 | 203675 | Stefano Morozzi | 07/2022 |
1748 | 2^676563-2792407 | 203666 | Enzo Doria | 02/2016 |
1749 | 2^676306-114713 | 203589 | Enzo Doria | 04/2015 |
1750 | (2^675977-1)/(1686378749257*7171117283326998925471) | 203456 | Dario Alpern | 07/2015 |