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) !!!
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
1501 | 39^105456+2 | 167788 | Robert Price | 04/2015 |
1502 | (28^115877-1)/27 | 167691 | Paul Bourdelais | 12/2017 |
1503 | 10^167639+121911 | 167640 | Patrick De Geest | 07/2018 |
1504 | 10^167639-8001 | 167639 | Robert Price | 03/2018 |
1505 | 2^556504-462059 | 167525 | Enzo Doria | 07/2015 |
1506 | (88*10^167522-637)/9 | 167523 | Robert Price | 11/2020 |
1507 | 5*10^167510+9 | 167511 | Robert Price | 08/2015 |
1508 | 7*10^167437-93 | 167438 | Robert Price | 08/2020 |
1509 | 2^555343+1874333 | 167175 | Enzo Doria | 06/2016 |
1510 | 2^555210-461261 | 167135 | Enzo Doria | 07/2015 |
1511 | 9*10^166996+59 | 166997 | Robert Price | 01/2020 |
1512 | 2^554372+1880527 | 166883 | Enzo Doria | 11/2016 |
1513 | 2^554299+72173 | 166861 | Enzo Doria | 04/2016 |
1514 | (185*10^166837+7)/3 | 166839 | Robert Price | 03/2020 |
1515 | 2^554037-2797063 | 166782 | Enzo Doria | 03/2016 |
1516 | (49*10^166721-139)/9 | 166722 | Robert Price | 03/2019 |
1517 | 2*10^166646+69 | 166647 | Robert Price | 06/2020 |
1518 | 2^553484-29819 | 166616 | Enzo Doria | 08/2015 |
1519 | (188*10^166611+7)/3 | 166613 | Robert Price | 03/2020 |
1520 | 2^553383-2784217 | 166585 | Enzo Doria | 10/2015 |
1521 | 2^553069+76427 | 166491 | Enzo Doria | 05/2016 |
1522 | 2*10^166458+51 | 166459 | Robert Price | 05/2018 |
1523 | 589^60089-588^60089 | 166454 | Jean-Louis Charton | 09/2012 |
1524 | 11^159756-2424 | 166369 | Mike Oakes | 06/2010 |
1525 | 2^552649-361275 | 166364 | Enzo Doria | 05/2014 |
1526 | 2^552628-113669 | 166358 | Enzo Doria | 09/2014 |
1527 | 10^166324+550603 | 166325 | Patrick De Geest | 07/2018 |
1528 | 10^166324-801 | 166324 | Robert Price | 02/2018 |
1529 | (85*10^166297-1)/3 | 166299 | Robert Price | 02/2020 |
1530 | 8*10^166227+87 | 166228 | Robert Price | 10/2019 |
1531 | 2^552137+1879397 | 166210 | Enzo Doria | 09/2016 |
1532 | (23^121949-1)/22 | 166061 | Paul Bourdelais | 10/2017 |
1533 | 2^551542+19249 | 166031 | Payam Samidoost | 08/2002 |
1534 | 2^551535-23821 | 166029 | Enzo Doria | 08/2013 |
1535 | 2^551507-23557 | 166021 | Enzo Doria | 08/2013 |
1536 | 7*10^165916-3 | 165917 | Robert Price | 08/2015 |
1537 | (29*10^165796+67)/3 | 165797 | Robert Price | 12/2019 |
1538 | 81^86837-80^86837 | 165728 | Robert Price | 01/2015 |
1539 | (71*10^165663-539)/9 | 165664 | Robert Price | 07/2019 |
1540 | 2^550270-69551 | 165648 | Enzo Doria | 12/2015 |
1541 | (202*10^165569-13)/9 | 165571 | Robert Price | 01/2020 |
1542 | 2^550000-23625 | 165567 | Enzo Doria | 08/2013 |
1543 | 2^549675-1852057 | 165469 | Enzo Doria | 08/2015 |
1544 | -tau(103^14938) | 165374 | Nik Lygeros / Olivier Rozier | 10/2013 |
1545 | (28*10^165358-1)/9 | 165359 | Serge Batalov | 10/2014 |
1547 | 2^549278+1879669 | 165350 | Enzo Doria | 09/2016 |
1546 | (7*10^165350-439)/9 | 165350 | Robert Price | 02/2018 |
1548 | 2^549252-351269 | 165342 | Enzo Doria | 06/2015 |
1549 | (14*10^165282+73)/3 | 165283 | Robert Price | 12/2018 |
1550 | 2^549049+2797607 | 165281 | Enzo Doria | 04/2016 |
1551 | (7*10^165239+107)/3 | 165240 | Robert Price | 02/2018 |
1552 | (44^100511-1)/43 | 165184 | Paul Bourdelais | 11/2017 |
1553 | (7*10^165134+107)/3 | 165135 | Robert Price | 02/2018 |
1554 | (23*10^165060-83)/3 | 165061 | Robert Price | 08/2019 |
1555 | (76*10^164984+77)/9 | 164985 | Robert Price | 10/2019 |
1556 | 9*10^164791-89 | 164792 | Robert Price | 04/2020 |
1557 | 2^547178-1856501 | 164717 | Enzo Doria | 10/2015 |
1558 | 11^158160-60 | 164707 | Enzo Doria | 07/2012 |
1559 | (26*10^164643-167)/3 | 164644 | Robert Price | 10/2019 |
1560 | 2^546398-59201 | 164483 | Enzo Doria | 10/2015 |
1561 | 2^546332-114893 | 164463 | Enzo Doria | 05/2015 |
1562 | 2^545958+1876189 | 164350 | Enzo Doria | 07/2016 |
1563 | 2^545878-49841 | 164326 | Enzo Doria | 10/2015 |
1564 | (10^164284+77)/3 | 164284 | Robert Price | 01/2018 |
1565 | 2^545668-4019 | 164263 | Yves Minet | 04/2017 |
1566 | 10^164216-50000000001 | 164216 | Robert Price | 12/2020 |
1567 | (13*53^238539*617^9)/10^247183 | 164151 | Hans Havermann | 07/2017 |
1568 | (16*10^164122+197)/3 | 164123 | Robert Price | 04/2019 |
1569 | 2^545185+76757 | 164118 | Enzo Doria | 05/2016 |
1570 | 2^545076-114329 | 164085 | Enzo Doria | 01/2015 |
1571 | (2*10^164043-143)/3 | 164043 | Robert Price | 03/2018 |
1572 | (29^112153+1)/30 | 164011 | Lelio R Paula | 03/2017 |
1573 | 2^544757+1874777 | 163989 | Enzo Doria | 06/2016 |
1574 | 2^544444-457199 | 163894 | Enzo Doria | 01/2015 |
1575 | 2^544264-343529 | 163840 | Enzo Doria | 07/2015 |
1576 | 7*10^163780+9 | 163781 | Robert Price | 09/2015 |
1577 | 2^543989+2793047 | 163758 | Enzo Doria | 02/2016 |
1578 | (28*10^163709+113)/3 | 163710 | Robert Price | 03/2020 |
1579 | 2^542870-69551 | 163421 | Enzo Doria | 12/2015 |
1580 | 2^542395+72533 | 163278 | Enzo Doria | 04/2016 |
1581 | 2^542072-3683 | 163180 | Yves Minet | 03/2017 |
1582 | 2^541779-1867357 | 163092 | Enzo Doria | 04/2016 |
1583 | 8*10^162924+9 | 162925 | Robert Price | 12/2015 |
1584 | 2^540905+81557 | 162829 | Enzo Doria | 08/2016 |
1585 | 2^540628-2939 | 162746 | Yves Minet | 09/2014 |
1586 | 919^54919-918^54919 | 162743 | Jean-Louis Charton | 01/2013 |
1587 | (203*10^162689+1)/3 | 162691 | Robert Price | 03/2020 |
1588 | 3*10^162620-59 | 162621 | Robert Price | 09/2018 |
1589 | 3^340694-112960 | 162553 | Enzo Doria | 07/2014 |
1590 | 2^539807-114081 | 162499 | Enzo Doria | 12/2014 |
1591 | 2^539654-114893 | 162453 | Enzo Doria | 05/2015 |
1592 | 9*10^162449-71 | 162450 | Robert Price | 11/2020 |
1593 | 2^539617-1851583 | 162441 | Enzo Doria | 08/2015 |
1594 | (91*10^162410+11)/3 | 162412 | Robert Price | 02/2020 |
1595 | 2^539346+81049 | 162360 | Enzo Doria | 07/2016 |
1596 | 2^539220-115499 | 162322 | Enzo Doria | 07/2015 |
1597 | 2^539217-113713 | 162321 | Enzo Doria | 09/2014 |
1598 | 9^170099-8^170099 | 162316 | Jean-Louis Charton | 05/2005 |
1599 | 4*10^162263-39 | 162264 | Robert Price | 09/2020 |
1600 | (115*10^162153-1)/3 | 162155 | Serge Batalov | 12/2014 |
1601 | (10^162138+11)/3 | 162138 | Serge Batalov | 07/2015 |
1602 | 2^538473-112723 | 162097 | Enzo Doria | 06/2014 |
1603 | 2^538157+79337 | 162002 | Enzo Doria | 06/2016 |
1604 | 2^538136-114749 | 161996 | Enzo Doria | 05/2015 |
1605 | 2^538104+1531 | 161986 | Lelio R Paula | 01/2013 |
1606 | (9*29^110727-1199)/14 | 161927 | Curtis Bright | 05/2015 |
1607 | 2^537815-22737 | 161899 | Enzo Doria | 07/2013 |
1608 | 2^537804-39839 | 161896 | Enzo Doria | 09/2015 |
1609 | (754*10^161816-7)/9 | 161818 | Robert Price | 05/2020 |
1610 | 2^537458-59201 | 161791 | Enzo Doria | 10/2015 |
1611 | 2*10^161766+51 | 161767 | Robert Price | 05/2018 |
1612 | (7*10^161760+131)/3 | 161761 | Robert Price | 06/2020 |
1613 | 2^537209-49849 | 161717 | Enzo Doria | 10/2015 |
1614 | (58*10^161691+329)/9 | 161692 | Robert Price | 05/2019 |
1615 | 2^536937+1879397 | 161635 | Enzo Doria | 09/2016 |
1616 | 34*10^161593-9 | 161595 | Robert Price | 06/2020 |
1617 | (31*10^161582-1)/3 | 161584 | Robert Price | 02/2020 |
1618 | 2^536569-22881 | 161524 | Enzo Doria | 07/2013 |
1619 | 10^161253+573493 | 161254 | Patrick De Geest | 07/2018 |
1620 | 10^161253-8001 | 161253 | Robert Price | 03/2018 |
1621 | 97*10^161247-3 | 161249 | Robert Price | 05/2020 |
1622 | 7*10^161192-9 | 161193 | Robert Price | 10/2015 |
1623 | 2^535269-113803 | 161133 | Enzo Doria | 09/2014 |
1624 | 2^535205-23295 | 161113 | Enzo Doria | 08/2013 |
1625 | (89^82609+1)/90 | 161036 | Paul Bourdelais | 10/2017 |
1626 | 2^534359-23229 | 160859 | Enzo Doria | 08/2013 |
1627 | 8*10^160782+53 | 160783 | Robert Price | 08/2020 |
1628 | 67^88037-66^88037 | 160763 | Robert Price | 10/2013 |
1629 | (88*10^160761-637)/9 | 160762 | Robert Price | 11/2020 |
1630 | 2^533948-1852559 | 160735 | Enzo Doria | 08/2015 |
1631 | 2^533665-23335 | 160650 | Enzo Doria | 08/2013 |
1632 | (19*10^160619+77)/3 | 160620 | Robert Price | 05/2019 |
1633 | 3^336353-2^336353 | 160482 | Mike Oakes | 10/2007 |
1634 | (91*10^160249+11)/3 | 160251 | Robert Price | 02/2020 |
1635 | 2^532253+1868417 | 160225 | Enzo Doria | 04/2016 |
1636 | 2^532108-291989 | 160181 | Enzo Doria | 07/2015 |
1637 | (26*10^160166-131)/3 | 160167 | Robert Price | 10/2019 |
1638 | (17*10^160143+67)/3 | 160144 | Robert Price | 01/2019 |
1639 | (19*10^159921-49)/3 | 159922 | Robert Price | 05/2019 |
1640 | 2^531110-1853771 | 159881 | Enzo Doria | 09/2015 |
1641 | (275^65536+53^65536)/2 | 159864 | Kellen Shenton | 11/2020 |
1642 | 2^530992-1845299 | 159845 | Enzo Doria | 07/2015 |
1643 | (136*10^159736-1)/9 | 159738 | Serge Batalov | 12/2014 |
1644 | 2^530417-113833 | 159672 | Enzo Doria | 09/2014 |
1645 | 2^530406-69701 | 159669 | Enzo Doria | 02/2016 |
1646 | 5*10^159656+41 | 159657 | Robert Price | 03/2019 |
1647 | 7^188858-188858^7 | 159604 | Norbert Schneider | 05/2018 |
1648 | (24^115597-1)/23 | 159547 | Paul Bourdelais | 09/2017 |
1649 | (17*10^159438-377)/9 | 159439 | Robert Price | 03/2018 |
1650 | (203*10^159381+1)/3 | 159383 | Robert Price | 03/2020 |
1651 | 89*10^159258-9 | 159260 | Robert Price | 05/2020 |
1652 | 2^528944-461315 | 159229 | Enzo Doria | 07/2015 |
1653 | (13*10^159147+161)/3 | 159148 | Robert Price | 11/2018 |
1654 | 2^528620-113879 | 159131 | Enzo Doria | 10/2014 |
1655 | 2^528000-23307 | 158944 | Enzo Doria | 08/2013 |
1656 | (29*10^158909+61)/9 | 158910 | Robert Price | 08/2018 |
1657 | 2^527817+1876817 | 158889 | Enzo Doria | 07/2016 |
1658 | 2^527774-49451 | 158876 | Enzo Doria | 10/2015 |
1659 | 2^527745-291553 | 158868 | Enzo Doria | 07/2015 |
1660 | (91*10^158862+11)/3 | 158864 | Robert Price | 02/2020 |
1661 | 2^527644-1856999 | 158837 | Enzo Doria | 10/2015 |
1662 | (37200^37199-37198^37199)/(2^37199) | 158822 | Henri Lifchitz | 06/2013 |
1663 | 2^527573-1863253 | 158816 | Enzo Doria | 12/2015 |
1664 | 2^527553-23401 | 158810 | Enzo Doria | 08/2013 |
1665 | 10^158755-50001 | 158755 | Robert Price | 08/2020 |
1666 | 11^152420-210 | 158730 | Enzo Doria | 09/2012 |
1667 | (13*10^158694+401)/9 | 158695 | Robert Price | 01/2018 |
1668 | 2^527052-69059 | 158659 | Enzo Doria | 11/2015 |
1669 | 2^526849-113233 | 158598 | Enzo Doria | 07/2014 |
1670 | (2^526763-lucasV(1,2,526763)+1)/2 | 158572 | Mike Oakes | 11/2016 |
1671 | (299*10^158544-17)/3 | 158546 | Robert Price | 04/2020 |
1672 | 2^526658-3551 | 158540 | Yves Minet | 03/2017 |
1673 | 7*10^158465-11 | 158466 | Robert Price | 06/2019 |
1674 | 2^526375-23115 | 158455 | Enzo Doria | 08/2013 |
1675 | (77*10^158407-293)/9 | 158408 | Robert Price | 09/2019 |
1676 | 2^526028-112793 | 158351 | Enzo Doria | 07/2014 |
1677 | (229*10^158339-1)/3 | 158341 | Robert Price | 07/2020 |
1678 | 2^525690-9221 | 158249 | Lelio R Paula | 01/2013 |
1679 | 2*10^158242-7 | 158243 | Robert Price | 10/2015 |
1680 | 2^525667-525667^2 | 158242 | Henri Lifchitz | 12/2017 |
1681 | 2^525186-1857431 | 158097 | Enzo Doria | 10/2015 |
1682 | 2^524515-23245 | 157895 | Enzo Doria | 08/2013 |
1683 | 2^524499-109087 | 157890 | Enzo Doria | 04/2014 |
1684 | 2^18067*(2^506221+1)-1 | 157827 | Makoto Morimoto | 05/2014 |
1686 | 2^524288+189093 | 157827 | Makoto Morimoto | 01/2016 |
1685 | 2^524288-164073 | 157827 | Matthias Baur | 03/2020 |
1687 | (2^(2^19)-9333)/(19*23*463*1213*31973) | 157814 | Makoto Morimoto | 09/2017 |
1688 | (10^157792+359)/9 | 157792 | Serge Batalov | 12/2014 |
1689 | 2^523924+1876591 | 157717 | Enzo Doria | 07/2016 |
1690 | (17*10^157705+67)/3 | 157706 | Robert Price | 01/2019 |
1691 | (46^94841+1)/47 | 157696 | Robert Price | 01/2014 |
1692 | 2^523774+77839 | 157672 | Enzo Doria | 05/2016 |
1693 | 2^523587+2799143 | 157616 | Enzo Doria | 04/2016 |
1694 | 2^523371+1872113 | 157551 | Enzo Doria | 05/2016 |
1695 | (8*10^157368+49)/3 | 157369 | Robert Price | 05/2020 |
1696 | (82*10^157319+449)/9 | 157320 | Robert Price | 11/2019 |
1697 | 2^522535-351457 | 157299 | Enzo Doria | 07/2015 |
1698 | 2^522226+2799079 | 157206 | Enzo Doria | 04/2016 |
1699 | 2^522134-1849451 | 157178 | Enzo Doria | 08/2015 |
1700 | 9*10^157152+71 | 157153 | Robert Price | 08/2020 |
1701 | 4*10^157150+93 | 157151 | Robert Price | 08/2018 |
1702 | 2^521401-29593 | 156958 | Enzo Doria | 08/2015 |
1703 | 7*10^156956+87 | 156957 | Robert Price | 07/2019 |
1704 | 2^521348-23397 | 156942 | Enzo Doria | 08/2013 |
1705 | (98^78797+1)/99 | 156901 | Paul Bourdelais | 12/2017 |
1706 | 65^86522+64 | 156857 | Lelio R Paula | 04/2016 |
1707 | 8^173687-7^173687 | 156855 | Jean-Louis Charton | 09/2004 |
1708 | 2^520977-1858183 | 156830 | Enzo Doria | 10/2015 |
1709 | (8*10^156718-101)/3 | 156719 | Robert Price | 08/2018 |
1710 | 2^520314-1849481 | 156631 | Enzo Doria | 08/2015 |
1711 | (13*10^156522+89)/3 | 156523 | Robert Price | 09/2018 |
1712 | (2^(6*86654+1)-5)/3 | 156513 | Kevin Acres | 12/2013 |
1713 | 3*10^156435-97 | 156436 | Robert Price | 07/2018 |
1714 | (8*10^156371-77)/3 | 156372 | Robert Price | 07/2018 |
1715 | 53^90679-52^90679 | 156356 | Robert Price | 01/2013 |
1716 | 2^519106-59141 | 156267 | Enzo Doria | 10/2015 |
1717 | 2^519053+6077 | 156251 | Enzo Doria | 02/2016 |
1718 | 2^518968-1860989 | 156225 | Enzo Doria | 11/2015 |
1719 | (25*10^156221-7)/9 | 156222 | Robert Price | 05/2018 |
1720 | 2^518931-2782297 | 156214 | Enzo Doria | 09/2015 |
1721 | 2^518608-2939 | 156117 | Yves Minet | 09/2014 |
1722 | 10*27^109005+697 | 156027 | Curtis Bright | 05/2015 |
1723 | 2^517967-113485 | 155924 | Enzo Doria | 08/2014 |
1724 | (103*10^155904+17)/3 | 155906 | Robert Price | 08/2020 |
1725 | 4*10^155853-39 | 155854 | Robert Price | 09/2020 |
1726 | 2^517698+4429 | 155843 | Lelio R Paula | 01/2013 |
1727 | 2^517543-113257 | 155796 | Enzo Doria | 07/2014 |
1728 | (14*10^155740-143)/3 | 155741 | Robert Price | 11/2018 |
1729 | 31^104309-30^104309 | 155563 | Henri Lifchitz | 08/2013 |
1730 | 2^516742-39851 | 155555 | Enzo Doria | 09/2015 |
1731 | (19*10^155504+131)/3 | 155505 | Robert Price | 06/2020 |
1732 | 7*10^155496+61 | 155497 | Robert Price | 08/2019 |
1733 | 2^516440+1878421 | 155464 | Enzo Doria | 08/2016 |
1734 | 2^515863-1867237 | 155291 | Enzo Doria | 03/2016 |
1735 | 2^515786-461861 | 155268 | Enzo Doria | 07/2015 |
1736 | 2^515644-113247 | 155225 | Enzo Doria | 07/2014 |
1737 | (7*10^155203+107)/3 | 155204 | Robert Price | 02/2018 |
1738 | 10^155163-40001 | 155163 | Robert Price | 01/2021 |
1739 | (17*10^155133-89)/9 | 155134 | Robert Price | 07/2018 |
1740 | 2^515227-114997 | 155099 | Enzo Doria | 06/2015 |
1742 | EPrime(155025) | 155025 | Eric W. Weisstein | 10/2010 |
1741 | (14*10^155024-221)/9 | 155025 | Robert Price | 04/2018 |
1743 | (4*10^155022+173)/3 | 155023 | Robert Price | 02/2018 |
1744 | (266*10^154897+1)/3 | 154899 | Robert Price | 04/2020 |
1745 | (115*10^154869-1)/3 | 154871 | Serge Batalov | 12/2014 |
1746 | (86*10^154853-221)/9 | 154854 | Robert Price | 09/2019 |
1747 | 2^514361+78167 | 154839 | Enzo Doria | 05/2016 |
1748 | 2^514281-115033 | 154815 | Enzo Doria | 06/2015 |
1749 | 2^514194-3311 | 154788 | Yves Minet | 12/2014 |
1750 | (14*10^154773+37)/3 | 154774 | Robert Price | 12/2018 |