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 | 3*10^171391+59 | 171392 | Robert Price | 08/2018 |
1502 | (13*10^171306-37)/3 | 171307 | Robert Price | 01/2019 |
1503 | 8*10^171296+87 | 171297 | Robert Price | 10/2019 |
1504 | (55^98419-1)/54 | 171284 | Paul Bourdelais | 12/2017 |
1505 | (29*10^171275+67)/3 | 171276 | Robert Price | 12/2019 |
1506 | 2^568642+1876129 | 171179 | Enzo Doria | 07/2016 |
1507 | (19*10^170970+131)/3 | 170971 | Robert Price | 06/2020 |
1508 | (46*10^170932+143)/9 | 170933 | Robert Price | 01/2019 |
1509 | (79*10^170901-1)/3 | 170903 | Robert Price | 02/2020 |
1510 | (58*10^170842+221)/9 | 170843 | Robert Price | 02/2017 |
1511 | 3*10^170800+73 | 170801 | Robert Price | 08/2018 |
1512 | 11^164009-270 | 170798 | Enzo Doria | 10/2012 |
1513 | 2*10^170767+41 | 170768 | Robert Price | 05/2018 |
1514 | 3^357706-112358 | 170670 | Enzo Doria | 07/2014 |
1515 | TheodorusPrime(170657) | 170657 | Eric W. Weisstein | 08/2013 |
1516 | 2^566871+1876163 | 170646 | Enzo Doria | 07/2016 |
1517 | (10657#+(404267#)/(10657#))/(1675379) | 170624 | Makoto Morimoto | 10/2017 |
1518 | 2^566496+7 | 170533 | Donovan Johnson | 07/2006 |
1519 | (7^201653+1)/8 | 170416 | Paul Bourdelais | 02/2010 |
1520 | 7*10^170348+33 | 170349 | Robert Price | 06/2020 |
1521 | 2^565183-352021 | 170138 | Enzo Doria | 07/2015 |
1522 | 2^565143-114457 | 170125 | Enzo Doria | 02/2015 |
1523 | 2^564976-49869 | 170075 | Enzo Doria | 10/2015 |
1524 | (7*10^169944+23)/3 | 169945 | Robert Price | 06/2020 |
1525 | 2^564526-351401 | 169940 | Enzo Doria | 07/2015 |
1526 | 4*10^169759+19 | 169760 | Robert Price | 10/2018 |
1527 | 21^128327-20^128327 | 169677 | Jean-Louis Charton | 11/2014 |
1528 | (4*10^169559+83)/3 | 169560 | Robert Price | 02/2018 |
1529 | (194*10^169461-17)/3 | 169463 | Robert Price | 09/2020 |
1530 | 2^562749+2793047 | 169405 | Enzo Doria | 02/2016 |
1531 | (154*10^169337-1)/9 | 169339 | Serge Batalov | 12/2014 |
1532 | (56*10^169311+691)/9 | 169312 | Robert Price | 05/2019 |
1533 | 2^562369-29503 | 169290 | Enzo Doria | 08/2015 |
1534 | (17*10^169283+19)/9 | 169284 | Robert Price | 03/2021 |
1535 | (22*10^169019+383)/9 | 169020 | Robert Price | 05/2018 |
1536 | 5*10^168807+87 | 168808 | Robert Price | 02/2019 |
1537 | 2^560405-39943 | 168699 | Enzo Doria | 09/2015 |
1538 | 89*10^168614-7 | 168616 | Robert Price | 04/2020 |
1539 | (23*10^168608-83)/3 | 168609 | Robert Price | 08/2019 |
1540 | (94*10^168541+11)/3 | 168543 | Robert Price | 04/2020 |
1541 | 2^559686-350471 | 168483 | Enzo Doria | 06/2015 |
1542 | 2^559672-1855889 | 168479 | Enzo Doria | 09/2015 |
1543 | (5*10^168379-473)/9 | 168379 | Robert Price | 01/2018 |
1544 | 2^559000-59939 | 168276 | Enzo Doria | 11/2015 |
1545 | (16*10^168181+41)/3 | 168182 | Robert Price | 03/2019 |
1546 | (19*10^168173+77)/3 | 168174 | Robert Price | 05/2019 |
1547 | 2^558640-114149 | 168168 | Enzo Doria | 12/2014 |
1548 | 2^558498-1849277 | 168125 | Enzo Doria | 08/2015 |
1549 | 2^558476-1850249 | 168119 | Enzo Doria | 08/2015 |
1550 | (7*10^168067+71)/3 | 168068 | Robert Price | 05/2018 |
1551 | 2^558150-1852211 | 168020 | Enzo Doria | 08/2015 |
1552 | 2^558125-113661 | 168013 | Enzo Doria | 09/2014 |
1553 | 393^64747-392^64747 | 167980 | Jean-Louis Charton | 08/2012 |
1554 | (13*10^167911+179)/3 | 167912 | Robert Price | 11/2018 |
1555 | (26*10^167861-167)/3 | 167862 | Robert Price | 10/2019 |
1556 | 39^105456+2 | 167788 | Robert Price | 04/2015 |
1557 | (28^115877-1)/27 | 167691 | Paul Bourdelais | 12/2017 |
1558 | 10^167639+121911 | 167640 | Patrick De Geest | 07/2018 |
1559 | 10^167639-8001 | 167639 | Robert Price | 03/2018 |
1560 | 2^556504-462059 | 167525 | Enzo Doria | 07/2015 |
1561 | (88*10^167522-637)/9 | 167523 | Robert Price | 11/2020 |
1562 | 5*10^167510+9 | 167511 | Robert Price | 08/2015 |
1563 | 7*10^167437-93 | 167438 | Robert Price | 08/2020 |
1564 | 11^160663+6 | 167314 | Paul Bourdelais | 02/2021 |
1565 | 2^555343+1874333 | 167175 | Enzo Doria | 06/2016 |
1566 | 2^555210-461261 | 167135 | Enzo Doria | 07/2015 |
1567 | 9*10^166996+59 | 166997 | Robert Price | 01/2020 |
1568 | (68*10^166976-329)/9 | 166977 | Robert Price | 03/2021 |
1569 | 2^554372+1880527 | 166883 | Enzo Doria | 11/2016 |
1570 | 2^554299+72173 | 166861 | Enzo Doria | 04/2016 |
1571 | (185*10^166837+7)/3 | 166839 | Robert Price | 03/2020 |
1572 | 2^554037-2797063 | 166782 | Enzo Doria | 03/2016 |
1573 | (49*10^166721-139)/9 | 166722 | Robert Price | 03/2019 |
1574 | 2*10^166646+69 | 166647 | Robert Price | 06/2020 |
1575 | 2^553484-29819 | 166616 | Enzo Doria | 08/2015 |
1576 | (188*10^166611+7)/3 | 166613 | Robert Price | 03/2020 |
1577 | 2^553383-2784217 | 166585 | Enzo Doria | 10/2015 |
1578 | 2^553069+76427 | 166491 | Enzo Doria | 05/2016 |
1579 | 2*10^166458+51 | 166459 | Robert Price | 05/2018 |
1580 | 589^60089-588^60089 | 166454 | Jean-Louis Charton | 09/2012 |
1581 | 11^159756-2424 | 166369 | Mike Oakes | 06/2010 |
1582 | 2^552649-361275 | 166364 | Enzo Doria | 05/2014 |
1583 | 2^552628-113669 | 166358 | Enzo Doria | 09/2014 |
1584 | 10^166324+550603 | 166325 | Patrick De Geest | 07/2018 |
1585 | 10^166324-801 | 166324 | Robert Price | 02/2018 |
1586 | (85*10^166297-1)/3 | 166299 | Robert Price | 02/2020 |
1587 | 8*10^166227+87 | 166228 | Robert Price | 10/2019 |
1588 | 2^552137+1879397 | 166210 | Enzo Doria | 09/2016 |
1589 | (103*10^166126+11)/3 | 166128 | Robert Price | 01/2021 |
1590 | (23^121949-1)/22 | 166061 | Paul Bourdelais | 10/2017 |
1591 | 2^551542+19249 | 166031 | Payam Samidoost | 08/2002 |
1592 | 2^551535-23821 | 166029 | Enzo Doria | 08/2013 |
1593 | 2^551507-23557 | 166021 | Enzo Doria | 08/2013 |
1594 | 7*10^165916-3 | 165917 | Robert Price | 08/2015 |
1595 | (29*10^165796+67)/3 | 165797 | Robert Price | 12/2019 |
1596 | 81^86837-80^86837 | 165728 | Robert Price | 01/2015 |
1597 | (71*10^165663-539)/9 | 165664 | Robert Price | 07/2019 |
1598 | 2^550270-69551 | 165648 | Enzo Doria | 12/2015 |
1599 | (202*10^165569-13)/9 | 165571 | Robert Price | 01/2020 |
1600 | 2^550000-23625 | 165567 | Enzo Doria | 08/2013 |
1601 | 2^549675-1852057 | 165469 | Enzo Doria | 08/2015 |
1602 | -tau(103^14938) | 165374 | Nik Lygeros / Olivier Rozier | 10/2013 |
1603 | (28*10^165358-1)/9 | 165359 | Serge Batalov | 10/2014 |
1604 | 2^549278+1879669 | 165350 | Enzo Doria | 09/2016 |
1605 | (7*10^165350-439)/9 | 165350 | Robert Price | 02/2018 |
1606 | 2^549252-351269 | 165342 | Enzo Doria | 06/2015 |
1607 | 67*10^165327-9 | 165329 | Robert Price | 03/2021 |
1608 | (14*10^165282+73)/3 | 165283 | Robert Price | 12/2018 |
1609 | 2^549049+2797607 | 165281 | Enzo Doria | 04/2016 |
1610 | (7*10^165239+107)/3 | 165240 | Robert Price | 02/2018 |
1611 | (44^100511-1)/43 | 165184 | Paul Bourdelais | 11/2017 |
1612 | (7*10^165134+107)/3 | 165135 | Robert Price | 02/2018 |
1613 | (23*10^165060-83)/3 | 165061 | Robert Price | 08/2019 |
1614 | (76*10^164984+77)/9 | 164985 | Robert Price | 10/2019 |
1615 | 9*10^164791-89 | 164792 | Robert Price | 04/2020 |
1616 | 2^547178-1856501 | 164717 | Enzo Doria | 10/2015 |
1617 | 11^158160-60 | 164707 | Enzo Doria | 07/2012 |
1618 | (26*10^164643-167)/3 | 164644 | Robert Price | 10/2019 |
1619 | 2^546398-59201 | 164483 | Enzo Doria | 10/2015 |
1620 | 2^546332-114893 | 164463 | Enzo Doria | 05/2015 |
1621 | 2^545958+1876189 | 164350 | Enzo Doria | 07/2016 |
1622 | 2^545878-49841 | 164326 | Enzo Doria | 10/2015 |
1623 | (10^164284+77)/3 | 164284 | Robert Price | 01/2018 |
1624 | 2^545668-4019 | 164263 | Yves Minet | 04/2017 |
1625 | 10^164216-50000000001 | 164216 | Robert Price | 12/2020 |
1626 | (13*53^238539*617^9)/10^247183 | 164151 | Hans Havermann | 07/2017 |
1627 | (16*10^164122+197)/3 | 164123 | Robert Price | 04/2019 |
1628 | 2^545185+76757 | 164118 | Enzo Doria | 05/2016 |
1629 | 2^545076-114329 | 164085 | Enzo Doria | 01/2015 |
1630 | (2*10^164043-143)/3 | 164043 | Robert Price | 03/2018 |
1631 | (29^112153+1)/30 | 164011 | Lelio R Paula | 03/2017 |
1632 | 2^544757+1874777 | 163989 | Enzo Doria | 06/2016 |
1633 | 2^544444-457199 | 163894 | Enzo Doria | 01/2015 |
1634 | 2^544264-343529 | 163840 | Enzo Doria | 07/2015 |
1635 | 7*10^163780+9 | 163781 | Robert Price | 09/2015 |
1636 | 2^543989+2793047 | 163758 | Enzo Doria | 02/2016 |
1637 | (28*10^163709+113)/3 | 163710 | Robert Price | 03/2020 |
1638 | (68*10^163521-329)/9 | 163522 | Robert Price | 03/2021 |
1639 | 2^542870-69551 | 163421 | Enzo Doria | 12/2015 |
1640 | 2^542395+72533 | 163278 | Enzo Doria | 04/2016 |
1641 | 2^542072-3683 | 163180 | Yves Minet | 03/2017 |
1642 | 2^541779-1867357 | 163092 | Enzo Doria | 04/2016 |
1643 | 8*10^162924+9 | 162925 | Robert Price | 12/2015 |
1644 | 2^540905+81557 | 162829 | Enzo Doria | 08/2016 |
1645 | 2^540628-2939 | 162746 | Yves Minet | 09/2014 |
1646 | 919^54919-918^54919 | 162743 | Jean-Louis Charton | 01/2013 |
1647 | (203*10^162689+1)/3 | 162691 | Robert Price | 03/2020 |
1648 | 3*10^162620-59 | 162621 | Robert Price | 09/2018 |
1649 | 3^340694-112960 | 162553 | Enzo Doria | 07/2014 |
1650 | 2^539807-114081 | 162499 | Enzo Doria | 12/2014 |
1651 | 2^539654-114893 | 162453 | Enzo Doria | 05/2015 |
1652 | 9*10^162449-71 | 162450 | Robert Price | 11/2020 |
1653 | 2^539617-1851583 | 162441 | Enzo Doria | 08/2015 |
1654 | (91*10^162410+11)/3 | 162412 | Robert Price | 02/2020 |
1655 | 2^539346+81049 | 162360 | Enzo Doria | 07/2016 |
1656 | 2^539220-115499 | 162322 | Enzo Doria | 07/2015 |
1657 | 2^539217-113713 | 162321 | Enzo Doria | 09/2014 |
1658 | 9^170099-8^170099 | 162316 | Jean-Louis Charton | 05/2005 |
1659 | 4*10^162263-39 | 162264 | Robert Price | 09/2020 |
1660 | (115*10^162153-1)/3 | 162155 | Serge Batalov | 12/2014 |
1661 | (10^162138+11)/3 | 162138 | Serge Batalov | 07/2015 |
1662 | 2^538473-112723 | 162097 | Enzo Doria | 06/2014 |
1663 | 2^538157+79337 | 162002 | Enzo Doria | 06/2016 |
1664 | 2^538136-114749 | 161996 | Enzo Doria | 05/2015 |
1665 | 2^538104+1531 | 161986 | Lelio R Paula | 01/2013 |
1666 | (9*29^110727-1199)/14 | 161927 | Curtis Bright | 05/2015 |
1667 | 2^537815-22737 | 161899 | Enzo Doria | 07/2013 |
1668 | 2^537804-39839 | 161896 | Enzo Doria | 09/2015 |
1669 | (754*10^161816-7)/9 | 161818 | Robert Price | 05/2020 |
1670 | 2^537458-59201 | 161791 | Enzo Doria | 10/2015 |
1671 | 2*10^161766+51 | 161767 | Robert Price | 05/2018 |
1672 | (7*10^161760+131)/3 | 161761 | Robert Price | 06/2020 |
1673 | 2^537209-49849 | 161717 | Enzo Doria | 10/2015 |
1674 | (58*10^161691+329)/9 | 161692 | Robert Price | 05/2019 |
1675 | 2^536937+1879397 | 161635 | Enzo Doria | 09/2016 |
1676 | 34*10^161593-9 | 161595 | Robert Price | 06/2020 |
1677 | (31*10^161582-1)/3 | 161584 | Robert Price | 02/2020 |
1678 | 2^536569-22881 | 161524 | Enzo Doria | 07/2013 |
1679 | 10^161253+573493 | 161254 | Patrick De Geest | 07/2018 |
1680 | 10^161253-8001 | 161253 | Robert Price | 03/2018 |
1681 | 97*10^161247-3 | 161249 | Robert Price | 05/2020 |
1682 | 7*10^161192-9 | 161193 | Robert Price | 10/2015 |
1683 | 2^535269-113803 | 161133 | Enzo Doria | 09/2014 |
1684 | 2^535205-23295 | 161113 | Enzo Doria | 08/2013 |
1685 | (89^82609+1)/90 | 161036 | Paul Bourdelais | 10/2017 |
1686 | 2^534359-23229 | 160859 | Enzo Doria | 08/2013 |
1687 | 8*10^160782+53 | 160783 | Robert Price | 08/2020 |
1688 | 67^88037-66^88037 | 160763 | Robert Price | 10/2013 |
1689 | (88*10^160761-637)/9 | 160762 | Robert Price | 11/2020 |
1690 | 2^533948-1852559 | 160735 | Enzo Doria | 08/2015 |
1691 | 2^533665-23335 | 160650 | Enzo Doria | 08/2013 |
1692 | (19*10^160619+77)/3 | 160620 | Robert Price | 05/2019 |
1693 | 3^336353-2^336353 | 160482 | Mike Oakes | 10/2007 |
1694 | (91*10^160249+11)/3 | 160251 | Robert Price | 02/2020 |
1695 | 2^532253+1868417 | 160225 | Enzo Doria | 04/2016 |
1696 | 2^532108-291989 | 160181 | Enzo Doria | 07/2015 |
1697 | (28*10^160171-79)/3 | 160172 | Robert Price | 02/2021 |
1698 | (26*10^160166-131)/3 | 160167 | Robert Price | 10/2019 |
1699 | (17*10^160143+67)/3 | 160144 | Robert Price | 01/2019 |
1700 | (19*10^159921-49)/3 | 159922 | Robert Price | 05/2019 |
1701 | 2^531110-1853771 | 159881 | Enzo Doria | 09/2015 |
1702 | (275^65536+53^65536)/2 | 159864 | Kellen Shenton | 11/2020 |
1703 | 2^530992-1845299 | 159845 | Enzo Doria | 07/2015 |
1704 | (136*10^159736-1)/9 | 159738 | Serge Batalov | 12/2014 |
1705 | 2^530417-113833 | 159672 | Enzo Doria | 09/2014 |
1706 | 2^530406-69701 | 159669 | Enzo Doria | 02/2016 |
1707 | 5*10^159656+41 | 159657 | Robert Price | 03/2019 |
1708 | 7^188858-188858^7 | 159604 | Norbert Schneider | 05/2018 |
1709 | (24^115597-1)/23 | 159547 | Paul Bourdelais | 09/2017 |
1710 | (17*10^159438-377)/9 | 159439 | Robert Price | 03/2018 |
1711 | (203*10^159381+1)/3 | 159383 | Robert Price | 03/2020 |
1712 | 89*10^159258-9 | 159260 | Robert Price | 05/2020 |
1713 | 2^528944-461315 | 159229 | Enzo Doria | 07/2015 |
1714 | (13*10^159147+161)/3 | 159148 | Robert Price | 11/2018 |
1715 | 2^528620-113879 | 159131 | Enzo Doria | 10/2014 |
1716 | 2^528000-23307 | 158944 | Enzo Doria | 08/2013 |
1717 | (29*10^158909+61)/9 | 158910 | Robert Price | 08/2018 |
1718 | 2^527817+1876817 | 158889 | Enzo Doria | 07/2016 |
1719 | 2^527774-49451 | 158876 | Enzo Doria | 10/2015 |
1720 | 2^527745-291553 | 158868 | Enzo Doria | 07/2015 |
1721 | (91*10^158862+11)/3 | 158864 | Robert Price | 02/2020 |
1722 | 2^527644-1856999 | 158837 | Enzo Doria | 10/2015 |
1723 | (37200^37199-37198^37199)/(2^37199) | 158822 | Henri Lifchitz | 06/2013 |
1724 | 2^527573-1863253 | 158816 | Enzo Doria | 12/2015 |
1725 | 2^527553-23401 | 158810 | Enzo Doria | 08/2013 |
1726 | 10^158755-50001 | 158755 | Robert Price | 08/2020 |
1727 | 11^152420-210 | 158730 | Enzo Doria | 09/2012 |
1728 | (13*10^158694+401)/9 | 158695 | Robert Price | 01/2018 |
1729 | 2^527052-69059 | 158659 | Enzo Doria | 11/2015 |
1730 | 2^526849-113233 | 158598 | Enzo Doria | 07/2014 |
1731 | (2^526763-lucasV(1,2,526763)+1)/2 | 158572 | Mike Oakes | 11/2016 |
1732 | (299*10^158544-17)/3 | 158546 | Robert Price | 04/2020 |
1733 | 2^526658-3551 | 158540 | Yves Minet | 03/2017 |
1734 | 7*10^158465-11 | 158466 | Robert Price | 06/2019 |
1735 | 2^526375-23115 | 158455 | Enzo Doria | 08/2013 |
1736 | (77*10^158407-293)/9 | 158408 | Robert Price | 09/2019 |
1737 | 2^526028-112793 | 158351 | Enzo Doria | 07/2014 |
1738 | (229*10^158339-1)/3 | 158341 | Robert Price | 07/2020 |
1739 | 2^525690-9221 | 158249 | Lelio R Paula | 01/2013 |
1740 | 2*10^158242-7 | 158243 | Robert Price | 10/2015 |
1741 | 2^525667-525667^2 | 158242 | Henri Lifchitz | 12/2017 |
1742 | 2^525186-1857431 | 158097 | Enzo Doria | 10/2015 |
1743 | 2^524515-23245 | 157895 | Enzo Doria | 08/2013 |
1744 | 2^524499-109087 | 157890 | Enzo Doria | 04/2014 |
1745 | 2^18067*(2^506221+1)-1 | 157827 | Makoto Morimoto | 05/2014 |
1747 | 2^524288+189093 | 157827 | Makoto Morimoto | 01/2016 |
1746 | 2^524288-164073 | 157827 | Matthias Baur | 03/2020 |
1748 | (2^(2^19)-9333)/(19*23*463*1213*31973) | 157814 | Makoto Morimoto | 09/2017 |
1749 | (10^157792+359)/9 | 157792 | Serge Batalov | 12/2014 |
1750 | 2^523924+1876591 | 157717 | Enzo Doria | 07/2016 |