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 | 99*10^189876-7 | 189878 | Robert Price | 07/2020 |
1502 | 2^630359+1788953 | 189757 | Enzo Doria | 05/2016 |
1503 | 2^630228+1871971 | 189718 | Enzo Doria | 05/2016 |
1504 | 2^630108+781 | 189682 | Lelio R Paula | 08/2013 |
1505 | 2^629870-1867811 | 189610 | Enzo Doria | 04/2016 |
1506 | (359^74189-1)/358 | 189558 | Alexander Zhirkov | 11/2017 |
1507 | 2^629326+2792929 | 189447 | Enzo Doria | 02/2016 |
1508 | 4*10^189401+13 | 189402 | Robert Price | 02/2021 |
1509 | (10^189385-61)/3 | 189385 | Serge Batalov | 12/2014 |
1510 | 2^629036+1874011 | 189359 | Enzo Doria | 06/2016 |
1511 | 2^628930+80779 | 189327 | Enzo Doria | 07/2016 |
1512 | (134*10^189309-11)/3 | 189311 | Robert Price | 01/2022 |
1513 | 2^628582+1179439 | 189223 | Enzo Doria | 06/2016 |
1514 | (44*10^188999-503)/9 | 189000 | Robert Price | 12/2018 |
1515 | (16*10^188823+167)/3 | 188824 | Robert Price | 06/2019 |
1516 | (10^188796+7)/4967/71933 | 188788 | Alfred Reich | 08/2021 |
1517 | 2^627037-2785843 | 188757 | Enzo Doria | 10/2015 |
1518 | (10^188566+7)/311640753181661 | 188552 | Alfred Reich | 04/2022 |
1519 | (16*10^188457+161)/3 | 188458 | Robert Price | 02/2019 |
1520 | L(901657) | 188436 | Renaud Lifchitz | 11/2008 |
1521 | (19*10^188375+137)/3 | 188376 | Robert Price | 03/2022 |
1522 | 2^625651+74213 | 188340 | Enzo Doria | 04/2016 |
1523 | 2^625584-460919 | 188320 | Enzo Doria | 06/2015 |
1524 | (8*10^188308-71)/9 | 188308 | Serge Batalov | 11/2022 |
1525 | (14*10^188218+139)/9 | 188219 | Robert Price | 11/2021 |
1526 | (10^188164+359)/9 | 188164 | Serge Batalov | 12/2014 |
1527 | 2^624481-113611 | 187988 | Enzo Doria | 08/2014 |
1530 | (2^624389+125582)/2 | 187960 | Stefano Morozzi | 09/2019 |
1528 | (2^624389+166982)/2 | 187960 | Stefano Morozzi | 09/2019 |
1529 | (2^624389+179886)/2 | 187960 | Stefano Morozzi | 09/2019 |
1531 | (2^624387+64466)/2 | 187959 | Stefano Morozzi | 09/2019 |
1532 | (2^624378+112990)/2 | 187957 | Stefano Morozzi | 09/2019 |
1533 | (2^624380+161986)/2 | 187957 | Stefano Morozzi | 09/2019 |
1535 | (2^624376+55762)/2 | 187956 | Stefano Morozzi | 09/2019 |
1534 | (2^624377+169506)/2 | 187956 | Stefano Morozzi | 09/2019 |
1536 | (2^624355+80178)/2 | 187950 | Stefano Morozzi | 09/2019 |
1537 | (2^624351+61350)/2 | 187949 | Stefano Morozzi | 09/2019 |
1538 | (2^624341+63462)/2 | 187946 | Stefano Morozzi | 09/2019 |
1539 | (2^624344+135990)/2 | 187946 | Stefano Morozzi | 09/2019 |
1540 | (2^624344+183898)/2 | 187946 | Stefano Morozzi | 09/2019 |
1542 | (2^624340+126982)/2 | 187945 | Stefano Morozzi | 09/2019 |
1541 | (2^624338+196110)/2 | 187945 | Stefano Morozzi | 09/2019 |
1543 | (2^624337+105162)/2 | 187944 | Stefano Morozzi | 09/2019 |
1544 | (2^624333+44594)/2 | 187943 | Stefano Morozzi | 09/2019 |
1545 | (2^624321+88742)/2 | 187940 | Stefano Morozzi | 09/2019 |
1546 | (2^624324+135178)/2 | 187940 | Stefano Morozzi | 09/2019 |
1547 | (2^624317+14186)/2 | 187938 | Stefano Morozzi | 09/2019 |
1548 | (2^624313+24450)/2 | 187937 | Stefano Morozzi | 09/2019 |
1549 | (2^624309+184590)/2 | 187936 | Stefano Morozzi | 09/2019 |
1551 | (2^624307+152658)/2 | 187935 | Stefano Morozzi | 09/2019 |
1550 | (2^624307+185978)/2 | 187935 | Stefano Morozzi | 09/2019 |
1552 | (2^624303+40814)/2 | 187934 | Stefano Morozzi | 09/2019 |
1553 | (2^624304+99238)/2 | 187934 | Stefano Morozzi | 09/2019 |
1554 | 2^624077-112723 | 187866 | Enzo Doria | 07/2014 |
1555 | 2^624008+1874941 | 187846 | Enzo Doria | 06/2016 |
1556 | 2^623870+78679 | 187804 | Enzo Doria | 05/2016 |
1557 | 2^623714-114035 | 187757 | Enzo Doria | 11/2014 |
1558 | 2^623651-1834251 | 187738 | Enzo Doria | 07/2015 |
1559 | (7*10^187645+53)/3 | 187646 | Robert Price | 05/2018 |
1560 | 2^623146+1879609 | 187586 | Enzo Doria | 09/2016 |
1561 | (401*10^187512+13)/9 | 187514 | Robert Price | 09/2021 |
1562 | (5*10^187471+91)/3 | 187472 | Robert Price | 04/2018 |
1563 | 2^622500+81931 | 187392 | Enzo Doria | 08/2016 |
1564 | (13*10^187382-157)/9 | 187383 | Robert Price | 05/2021 |
1565 | 2^622300-1861739 | 187331 | Enzo Doria | 12/2015 |
1566 | (22*10^187317-91)/3 | 187318 | Robert Price | 02/2022 |
1567 | (38*10^187281+349)/9 | 187282 | Robert Price | 10/2018 |
1568 | 2^622052+76771 | 187257 | Enzo Doria | 05/2016 |
1569 | 2^622005-24091 | 187243 | Enzo Doria | 08/2013 |
1570 | 7*10^187205-57 | 187206 | Robert Price | 06/2020 |
1571 | 2^621879-351787 | 187205 | Enzo Doria | 07/2015 |
1572 | (5*10^187168-53)/3 | 187169 | Robert Price | 09/2020 |
1573 | (23*10^187164-143)/3 | 187165 | Robert Price | 12/2019 |
1574 | 2^621700+79411 | 187151 | Enzo Doria | 06/2016 |
1575 | (7*10^187101+131)/3 | 187102 | Robert Price | 06/2020 |
1576 | (2*10^187062-71)/3 | 187062 | Robert Price | 12/2017 |
1577 | 2^620929-113203 | 186919 | Enzo Doria | 07/2014 |
1578 | 10^186842+168223 | 186843 | Patrick De Geest | 07/2018 |
1579 | 10^186842-8001 | 186842 | Robert Price | 03/2018 |
1580 | 2^620347-1777 | 186744 | Lelio R Paula | 07/2013 |
1581 | (11*10^186659+133)/9 | 186660 | Robert Price | 04/2022 |
1582 | 11^179143-4170 | 186559 | Enzo Doria | 12/2012 |
1583 | (5^266863+1)/6 | 186529 | Paul Bourdelais | 07/2010 |
1584 | 2*10^186517+33 | 186518 | Robert Price | 11/2021 |
1585 | 2^619297-2792353 | 186427 | Enzo Doria | 02/2016 |
1586 | (49*10^186409+383)/9 | 186410 | Robert Price | 04/2019 |
1587 | 2^618940-460139 | 186320 | Enzo Doria | 06/2015 |
1588 | 2^618046+74179 | 186051 | Enzo Doria | 04/2016 |
1589 | 3*10^186019+11 | 186020 | Robert Price | 07/2018 |
1590 | (16*10^185978-19)/3 | 185979 | Robert Price | 02/2019 |
1591 | (22*10^185950-7)/3 | 185951 | Robert Price | 12/2022 |
1592 | 2*10^185930-3 | 185931 | Robert Price | 07/2015 |
1593 | (82^97151+1)/83 | 185928 | Paul Bourdelais | 10/2017 |
1594 | 4*10^185905+91 | 185906 | Robert Price | 08/2018 |
1595 | (34*10^185902-601)/9 | 185903 | Robert Price | 07/2022 |
1596 | (19*10^185873+131)/3 | 185874 | Robert Price | 06/2020 |
1597 | (37*10^185811+377)/9 | 185812 | Robert Price | 11/2018 |
1598 | 2^617250+9385 | 185811 | Lelio R Paula | 07/2013 |
1599 | 2^617130+9 | 185775 | Stefano Morozzi | 05/2021 |
1600 | 39^116749+2 | 185756 | Robert Price | 04/2015 |
1601 | 2^616924-39719 | 185713 | Enzo Doria | 09/2015 |
1602 | 2^616712+1867621 | 185649 | Enzo Doria | 04/2016 |
1603 | (3^388897+2^388897)/5 | 185551 | Jean-Louis Charton | 09/2011 |
1604 | 8*10^185529-67 | 185530 | Robert Price | 08/2019 |
1605 | 4*10^185355+9 | 185356 | Robert Price | 05/2015 |
1606 | (16*10^185347+89)/3 | 185348 | Robert Price | 03/2021 |
1607 | 2^615622+76639 | 185321 | Enzo Doria | 05/2016 |
1608 | 2^615591+1879223 | 185312 | Enzo Doria | 08/2016 |
1609 | 2^615503+1876643 | 185285 | Enzo Doria | 07/2016 |
1610 | 5^265007-4^265007 | 185232 | Jean-Louis Charton | 02/2013 |
1612 | (4*10^185221-91)/3 | 185222 | Robert Price | 03/2018 |
1611 | (7*10^185221+131)/3 | 185222 | Robert Price | 06/2020 |
1613 | (62*10^185216-413)/9 | 185217 | Robert Price | 09/2021 |
1614 | (232*10^185180+17)/3 | 185182 | Robert Price | 04/2021 |
1615 | 56*10^185139-3 | 185141 | Robert Price | 03/2020 |
1616 | (28*10^185105+47)/3 | 185106 | Robert Price | 02/2021 |
1617 | 2^614783-2790097 | 185069 | Enzo Doria | 12/2015 |
1618 | 2^614745-29323 | 185057 | Enzo Doria | 07/2015 |
1619 | (((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840 | 185052 | Serge Batalov | 07/2013 |
1620 | (49*10^184993-67)/9 | 184994 | Robert Price | 03/2019 |
1621 | (5*10^184954-191)/3 | 184955 | Robert Price | 05/2021 |
1622 | (14*10^184950+211)/9 | 184951 | Robert Price | 04/2018 |
1623 | 2^614315+81353 | 184928 | Enzo Doria | 08/2016 |
1624 | 2^614294-1849961 | 184921 | Enzo Doria | 08/2015 |
1625 | 2^614266+1877809 | 184913 | Enzo Doria | 08/2016 |
1626 | (185*10^184878-11)/3 | 184880 | Robert Price | 10/2020 |
1627 | 91*10^184867-9 | 184869 | Robert Price | 06/2021 |
1628 | (85*10^184768+77)/9 | 184769 | Robert Price | 07/2022 |
1629 | 2^613715-1860727 | 184747 | Enzo Doria | 11/2015 |
1630 | (4*10^184730+89)/3 | 184731 | Robert Price | 08/2021 |
1631 | 2*10^184723+41 | 184724 | Robert Price | 05/2018 |
1632 | (49*10^184703+293)/9 | 184704 | Robert Price | 03/2021 |
1633 | 2^613487-349987 | 184678 | Enzo Doria | 07/2015 |
1634 | (95^93377+1)/96 | 184672 | Paul Bourdelais | 11/2017 |
1635 | 14^161089-161089^14 | 184629 | Serge Batalov | 05/2016 |
1636 | 2^613033-114621 | 184542 | Enzo Doria | 05/2015 |
1637 | (9^193247+1)/10 | 184404 | Paul Bourdelais | 02/2010 |
1638 | 2^612341-1604809 | 184334 | Enzo Doria | 05/2015 |
1639 | (11*10^184308-161)/3 | 184309 | Robert Price | 11/2021 |
1640 | (2^611999-1)/18464214225958267477777390354183 | 184199 | Dario Alpern | 06/2017 |
1641 | (14*10^184150+37)/3 | 184151 | Robert Price | 12/2018 |
1642 | 2^611731-4837 | 184150 | Yves Minet | 08/2018 |
1643 | 3*10^184124-7 | 184125 | Robert Price | 08/2015 |
1644 | 2^611628-24537 | 184119 | Enzo Doria | 08/2013 |
1645 | 3*10^184110+13 | 184111 | Robert Price | 07/2018 |
1646 | (194*10^184093+1)/3 | 184095 | Robert Price | 01/2022 |
1647 | 2^611460+71881 | 184068 | Enzo Doria | 04/2016 |
1648 | 4*10^184004-63 | 184005 | Robert Price | 10/2018 |
1649 | 2^610982-1867301 | 183924 | Enzo Doria | 03/2016 |
1650 | 3*10^183872-49 | 183873 | Robert Price | 07/2018 |
1651 | 2^610597+1178897 | 183809 | Enzo Doria | 05/2016 |
1652 | (8*10^183773-269)/9 | 183773 | Robert Price | 09/2021 |
1653 | (65*10^183768-29)/9 | 183769 | Robert Price | 01/2021 |
1654 | (17*10^183764+31)/3 | 183765 | Robert Price | 01/2019 |
1655 | (28*10^183760-1)/9 | 183761 | Serge Batalov | 10/2014 |
1656 | 2^610401+1277 | 183750 | Lelio R Paula | 07/2013 |
1657 | 2^610356-1849019 | 183736 | Enzo Doria | 08/2015 |
1658 | (63^102103+1)/64 | 183717 | Paul Bourdelais | 10/2017 |
1659 | 23*10^183710-7 | 183712 | Robert Price | 02/2020 |
1660 | (2^610289+1)/(3*528882550291) | 183704 | Gord Palameta | 08/2018 |
1661 | (4*10^183659+149)/9 | 183659 | Robert Price | 04/2018 |
1662 | (4*10^183657+41)/9 | 183657 | Serge Batalov | 11/2022 |
1663 | 7*10^183596+39 | 183597 | Robert Price | 01/2023 |
1664 | 2^609846-1834251 | 183582 | Enzo Doria | 07/2015 |
1665 | 10^183546+1547323 | 183547 | Patrick De Geest | 02/2021 |
1667 | 10^183546-800000001 | 183546 | Robert Price | 09/2020 |
1666 | 10^183546-584297 | 183546 | Patrick De Geest | 02/2021 |
1668 | 7*10^183511+39 | 183512 | Robert Price | 01/2023 |
1669 | (23*10^183477-71)/3 | 183478 | Robert Price | 07/2020 |
1670 | 11^176176-240 | 183469 | Enzo Doria | 11/2012 |
1671 | (41^113749+1)/42 | 183451 | Paul Bourdelais | 11/2017 |
1672 | 6*10^183429+53 | 183430 | Robert Price | 05/2020 |
1673 | (28*10^183403+191)/3 | 183404 | Robert Price | 02/2020 |
1674 | (101^91463+1)/102 | 183320 | Paul Bourdelais | 11/2017 |
1675 | 2^608965-113989 | 183317 | Enzo Doria | 10/2014 |
1676 | A005165(43592) | 183312 | Serge Batalov | 07/2017 |
1677 | (61*10^183294+119)/9 | 183295 | Robert Price | 05/2019 |
1678 | 2^608814-461261 | 183272 | Enzo Doria | 06/2015 |
1679 | (163*10^183227-1)/9 | 183229 | Serge Batalov | 12/2014 |
1680 | 2^608541-608541^2 | 183190 | Henri Lifchitz | 02/2018 |
1681 | 2^608293+143807 | 183115 | Enzo Doria | 10/2016 |
1682 | 2^608164-462419 | 183076 | Enzo Doria | 08/2015 |
1683 | 2^607950-1862303 | 183012 | Enzo Doria | 12/2015 |
1684 | (46*10^182896+683)/9 | 182897 | Robert Price | 03/2019 |
1685 | (2*10^182787+73)/3 | 182787 | Robert Price | 09/2020 |
1686 | 2^607101+1871987 | 182756 | Enzo Doria | 05/2016 |
1687 | 2^606869-69175 | 182686 | Enzo Doria | 11/2015 |
1688 | 8*10^182671+71 | 182672 | Robert Price | 05/2022 |
1689 | (23*10^182666-71)/3 | 182667 | Robert Price | 07/2020 |
1690 | 3*10^182614-11 | 182615 | Robert Price | 07/2018 |
1691 | 2^606560-357 | 182593 | Enzo Doria | 05/2014 |
1692 | 66*10^182420+7 | 182422 | Robert Price | 07/2020 |
1693 | 2^605687+1866983 | 182330 | Enzo Doria | 03/2016 |
1694 | 2^605655-114445 | 182321 | Enzo Doria | 02/2015 |
1695 | 94*10^182291-3 | 182293 | Robert Price | 05/2020 |
1696 | (20^140053+1)/21 | 182212 | Paul Bourdelais | 04/2010 |
1697 | (14*10^182177-221)/9 | 182178 | Robert Price | 04/2018 |
1698 | 2^605174-112751 | 182176 | Enzo Doria | 06/2014 |
1699 | 2^604761+1874507 | 182052 | Enzo Doria | 06/2016 |
1700 | 2^604705+1871957 | 182035 | Enzo Doria | 05/2016 |
1701 | (14*10^182000+229)/9 | 182001 | Robert Price | 03/2018 |
1702 | (10^181996+41)/3 | 181996 | Robert Price | 12/2017 |
1703 | (17*10^181979+91)/9 | 181980 | Robert Price | 02/2022 |
1704 | (5*10^181950-101)/3 | 181951 | Robert Price | 04/2018 |
1705 | 2^603915+75233 | 181797 | Enzo Doria | 04/2016 |
1706 | 39470^39537+39537^39470 | 181723 | Norbert Schneider | 12/2022 |
1707 | (10^181710+7)/563747/2019847 | 181698 | Alfred Reich | 08/2021 |
1708 | 7*10^181594-57 | 181595 | Robert Price | 06/2020 |
1709 | 8*10^181580+29 | 181581 | Robert Price | 11/2021 |
1710 | (83*10^181544+61)/9 | 181545 | Serge Batalov | 01/2023 |
1711 | (2*10^181457+7)/9 | 181457 | Rytis Slatkevicius | 01/2023 |
1712 | 3*10^181445+23 | 181446 | Robert Price | 03/2022 |
1713 | (194*10^181369-11)/3 | 181371 | Robert Price | 09/2020 |
1714 | 11^174145-360 | 181354 | Enzo Doria | 10/2012 |
1715 | 2^602351-396765 | 181326 | Enzo Doria | 08/2013 |
1716 | 6*10^181306+17 | 181307 | Robert Price | 04/2019 |
1717 | (286*10^181220-1)/3 | 181222 | Robert Price | 11/2020 |
1718 | 2^601957-113833 | 181208 | Enzo Doria | 09/2014 |
1719 | 66^99581-65^99581 | 181193 | Robert Price | 09/2013 |
1720 | 10^181182+383973 | 181183 | Patrick De Geest | 04/2016 |
1721 | 10^181182-21 | 181182 | Serge Batalov | 12/2014 |
1722 | (797*10^181171-41)/9 | 181173 | Robert Price | 04/2022 |
1723 | (5*10^181127-29)/3 | 181128 | Robert Price | 03/2018 |
1724 | 2^601521-29143 | 181076 | Enzo Doria | 07/2015 |
1725 | 2^601442-2797811 | 181053 | Enzo Doria | 04/2016 |
1726 | 44*10^181029+3 | 181031 | Robert Price | 04/2020 |
1727 | 5*10^180992-9 | 180993 | Robert Price | 05/2015 |
1728 | 10^180979+79477 | 180980 | Patrick De Geest | 04/2016 |
1729 | 10^180979+107739 | 180980 | Patrick De Geest | 04/2016 |
1730 | 10^180979-11 | 180979 | Serge Batalov | 12/2014 |
1731 | 2^601023-113851 | 180926 | Enzo Doria | 10/2014 |
1732 | (23*10^180862-143)/3 | 180863 | Robert Price | 12/2019 |
1733 | 3*10^180852+29 | 180853 | Robert Price | 05/2018 |
1734 | (277*10^180782-7)/9 | 180784 | Robert Price | 02/2022 |
1735 | (8*10^180725-629)/9 | 180725 | Robert Price | 01/2022 |
1736 | (79*10^180710-1)/3 | 180712 | Robert Price | 02/2020 |
1737 | 2^600300-1852559 | 180709 | Enzo Doria | 08/2015 |
1738 | (2*10^180706-77)/3 | 180706 | Robert Price | 02/2021 |
1739 | (10^180689+71)/9 | 180689 | Serge Batalov | 07/2015 |
1740 | 2^600209+76487 | 180681 | Enzo Doria | 05/2016 |
1741 | (8*10^180536-269)/9 | 180536 | Robert Price | 09/2021 |
1742 | 2^599702-369885 | 180529 | Enzo Doria | 11/2013 |
1743 | Tau(643^11688) | 180524 | Nik Lygeros / Olivier Rozier | 05/2015 |
1744 | (2951*29^123418-3)/4 | 180490 | Curtis Bright | 05/2015 |
1745 | (29*10^180432-17)/3 | 180433 | Robert Price | 09/2019 |
1746 | 4*10^180360+93 | 180361 | Robert Price | 08/2018 |
1747 | 2^598942+80779 | 180300 | Enzo Doria | 07/2016 |
1748 | (38*10^180296+403)/9 | 180297 | Robert Price | 10/2018 |
1749 | (85*10^180241+77)/9 | 180242 | Robert Price | 07/2022 |
1750 | 2^598591-1844797 | 180194 | Enzo Doria | 06/2015 |