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 | (86^103471+1)/87 | 200163 | Paul Bourdelais | 05/2018 |
1502 | (10^(2*100072+1)+36*10^100072-1)/9 | 200145 | Robert Price | 09/2023 |
1503 | 103*(10^100000+20110)^2-4707*(10^100000+20110)+50383 | 200003 | Robert Price | 05/2017 |
1504 | 103*(10^100000+33798)^2-4707*(10^100000+33798)+50383 | 200003 | Robert Price | 01/2018 |
1505 | numbpart(32235776596) | 200002 | Serge Batalov | 04/2017 |
1506 | (10^200001+149)/3 | 200001 | Serge Batalov | 12/2014 |
1507 | 10^200000+571791 | 200001 | Patrick De Geest | 08/2019 |
1508 | (3^419180-621444)/3 | 200000 | Stefano Morozzi | 06/2019 |
1509 | (3^419180-1941384)/3 | 200000 | Stefano Morozzi | 08/2019 |
1510 | 10^200000-45557 | 200000 | Patrick De Geest | 08/2019 |
1511 | (10^200000-1)/9-10^58838 | 200000 | Akihiko Yoshida | 04/2020 |
1512 | 2593604092947240127723272^8192+2593604092947240127722755^8192 | 200000 | Youcef Lemsafer | 01/2023 |
1513 | (2593604092947240127723019^8192+2593604092947240127723011^8192)/2 | 199999 | Youcef Lemsafer | 01/2023 |
1514 | (2593604092947240127723087^8192+2593604092947240127722984^8192)/147457 | 199994 | Youcef Lemsafer | 01/2023 |
1515 | (2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986 | 199989 | Youcef Lemsafer | 01/2023 |
1516 | (2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169 | 199986 | Youcef Lemsafer | 01/2023 |
1517 | 92*10^199980-9 | 199982 | Robert Price | 12/2021 |
1518 | (2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649 | 199977 | Youcef Lemsafer | 01/2023 |
1519 | (85*10^199951-139)/9 | 199952 | Robert Price | 08/2021 |
1520 | (10^199926+7)/29/373/2339 | 199919 | Alfred Reich | 08/2021 |
1521 | 23*10^199833-9 | 199835 | Robert Price | 10/2021 |
1522 | fibonacci(956176)-4 | 199829 | Jon Grantham | 08/2023 |
1523 | (299*10^199801-17)/3 | 199803 | Robert Price | 04/2020 |
1524 | 6*10^199788+77 | 199789 | Robert Price | 06/2020 |
1525 | (23*10^199615+37)/3 | 199616 | Robert Price | 02/2022 |
1526 | (17*10^199607-167)/3 | 199608 | Robert Price | 05/2022 |
1527 | 2^663020-933075 | 199589 | Paul Bourdelais | 06/2021 |
1528 | 3*2^662703-5 | 199494 | Jon Grantham | 07/2023 |
1529 | (14*10^199447+73)/3 | 199448 | Robert Price | 12/2018 |
1530 | (2^662424-15)/7 | 199409 | Stefano Morozzi | 08/2022 |
1531 | 2^662194+22189 | 199341 | Enzo Doria | 09/2023 |
1532 | 2^662103-29287 | 199313 | Enzo Doria | 08/2015 |
1533 | (2*10^199283+457)/9 | 199283 | Robert Price | 01/2018 |
1534 | (10^199248-19)/9 | 199248 | Robert Price | 01/2018 |
1535 | (83*10^199213+529)/9 | 199214 | Robert Price | 12/2021 |
1536 | (194*10^199146-17)/3 | 199148 | Robert Price | 09/2020 |
1537 | (151*10^199003-1)/3 | 199005 | Robert Price | 03/2020 |
1538 | 9*10^198946-73 | 198947 | Robert Price | 01/2021 |
1539 | 45*10^198931-7 | 198933 | Robert Price | 07/2020 |
1540 | 2^660482-2891 | 198825 | Yves Minet | 05/2016 |
1541 | 2^659589-21 | 198557 | Stefano Morozzi | 07/2022 |
1542 | 2^659583+1879223 | 198555 | Enzo Doria | 08/2016 |
1543 | (53*10^198529+1)/9 | 198530 | Serge Batalov | 07/2010 |
1544 | (49*10^198403+311)/9 | 198404 | Robert Price | 06/2019 |
1545 | 96*10^198376-7 | 198378 | Robert Price | 03/2021 |
1546 | (10^198375+7)/59/1201/87589 | 198366 | Alfred Reich | 08/2021 |
1547 | 2^658828-29819 | 198327 | Enzo Doria | 08/2015 |
1548 | 2^658776-2791229 | 198312 | Enzo Doria | 01/2016 |
1549 | (35*10^198294-377)/9 | 198295 | Robert Price | 07/2018 |
1550 | (4*10^198268+137)/3 | 198269 | Robert Price | 03/2018 |
1551 | 2^658544-1854029 | 198242 | Enzo Doria | 09/2015 |
1552 | (62*10^198229-233)/9 | 198230 | Robert Price | 02/2022 |
1553 | (26*10^198200-41)/3 | 198201 | Robert Price | 02/2022 |
1554 | (157^90239-1)/156 | 198154 | Alexander Zhirkov | 06/2016 |
1555 | 2*10^197959-37 | 197960 | Robert Price | 11/2021 |
1556 | (232*10^197897+17)/3 | 197899 | Robert Price | 04/2021 |
1557 | (4*10^197778+173)/3 | 197779 | Robert Price | 02/2018 |
1558 | 2^656763+211373 | 197706 | Enzo Doria | 08/2023 |
1559 | 78*10^197702-7 | 197704 | Robert Price | 10/2020 |
1560 | (17*10^197640-23)/3 | 197641 | Robert Price | 03/2021 |
1561 | (29*10^197629-77)/3 | 197630 | Robert Price | 02/2020 |
1562 | 2^656462+1874419 | 197615 | Enzo Doria | 06/2016 |
1563 | (89^101363+1)/90 | 197595 | Paul Bourdelais | 11/2017 |
1564 | 2^655893-344563 | 197444 | Enzo Doria | 07/2015 |
1565 | 2^655875+71333 | 197439 | Enzo Doria | 04/2016 |
1566 | 2^655845-9 | 197430 | Robert Price | 01/2017 |
1567 | (299*10^197426+1)/3 | 197428 | Robert Price | 04/2020 |
1568 | 2^655682-1849121 | 197380 | Enzo Doria | 08/2015 |
1569 | 4*10^197268-89 | 197269 | Robert Price | 11/2018 |
1570 | (11*10^197198-89)/3 | 197199 | Robert Price | 05/2021 |
1571 | 2^655045-49603 | 197189 | Enzo Doria | 10/2015 |
1572 | 2^655000-2784089 | 197175 | Enzo Doria | 10/2015 |
1573 | (18^157051-1)/17 | 197141 | Paul Bourdelais | 03/2010 |
1574 | (4*10^197061+41)/9 | 197061 | Serge Batalov | 11/2022 |
1575 | (154*10^197005+17)/9 | 197007 | Robert Price | 06/2022 |
1576 | 2^654400-39719 | 196995 | Enzo Doria | 09/2015 |
1577 | (5^281807-2^281807)/3 | 196975 | Jon Grantham | 08/2023 |
1578 | (14*10^196965-221)/9 | 196966 | Robert Price | 04/2018 |
1579 | 2^654216-459995 | 196939 | Enzo Doria | 06/2015 |
1580 | (17*10^196921+31)/3 | 196922 | Robert Price | 01/2019 |
1581 | (14*10^196885-89)/3 | 196886 | Robert Price | 05/2020 |
1582 | 3*10^196881-59 | 196882 | Robert Price | 09/2018 |
1583 | 2^653851+82295 | 196829 | Enzo Doria | 09/2016 |
1584 | (38*10^196792+691)/9 | 196793 | Robert Price | 10/2018 |
1585 | (65*10^196768+493)/9 | 196769 | Robert Price | 08/2021 |
1587 | 2^653636-29429 | 196765 | Enzo Doria | 08/2015 |
1586 | 2^653638-11 | 196765 | Stefano Morozzi | 07/2022 |
1588 | 2^653601-69673 | 196754 | Enzo Doria | 02/2016 |
1589 | (44*10^196684+1)/9 | 196685 | Serge Batalov | 07/2010 |
1590 | 2^652786-1852571 | 196509 | Enzo Doria | 08/2015 |
1591 | 2^652752-1325 | 196498 | Yves Minet | 07/2015 |
1592 | 2^652470-1859141 | 196414 | Enzo Doria | 10/2015 |
1593 | 2^652307+1877483 | 196364 | Enzo Doria | 08/2016 |
1594 | 2^652293-115273 | 196360 | Enzo Doria | 06/2015 |
1595 | (47*10^196281+403)/9 | 196282 | Robert Price | 03/2019 |
1596 | (7*10^196125-31)/3 | 196126 | Robert Price | 12/2021 |
1597 | 33^129128+129128^33 | 196083 | Norbert Schneider | 06/2022 |
1598 | 6*10^196070+73 | 196071 | Robert Price | 04/2019 |
1599 | 2^651218-1868201 | 196037 | Enzo Doria | 04/2016 |
1600 | 2^651047-49687 | 195985 | Enzo Doria | 10/2015 |
1601 | 10^195968-700001 | 195968 | Robert Price | 08/2021 |
1602 | fibonacci(937485)+3 | 195923 | Jon Grantham | 08/2023 |
1603 | (29*10^195875-197)/3 | 195876 | Robert Price | 08/2021 |
1604 | (25*10^195808-97)/9 | 195809 | Robert Price | 01/2022 |
1605 | 2^650285-2785333 | 195756 | Enzo Doria | 10/2015 |
1606 | (10^195732+7)/18089/49605893 | 195721 | Alfred Reich | 08/2021 |
1607 | (69^106397-1)/68 | 195647 | Paul Bourdelais | 10/2017 |
1608 | 2^649811+1877573 | 195613 | Enzo Doria | 08/2016 |
1609 | 2^649662-170531 | 195568 | Hans Havermann | 10/2018 |
1610 | 2^649586+182839 | 195545 | Enzo Doria | 11/2016 |
1611 | 2^649537-1867363 | 195531 | Enzo Doria | 04/2016 |
1612 | 2^649536-1861499 | 195530 | Enzo Doria | 12/2015 |
1613 | (103*10^195478-1)/3 | 195480 | Serge Batalov | 12/2014 |
1614 | 2^649102-59351 | 195400 | Enzo Doria | 10/2015 |
1615 | (2*10^195399+529)/9 | 195399 | Robert Price | 01/2018 |
1616 | (202*10^195383-13)/9 | 195385 | Robert Price | 01/2020 |
1617 | 2^648988+1178971 | 195365 | Enzo Doria | 06/2016 |
1618 | 2^648975-114319 | 195361 | Enzo Doria | 02/2015 |
1619 | (11*10^195350-137)/9 | 195351 | Robert Price | 01/2018 |
1620 | 2^648619-24835 | 195254 | Enzo Doria | 09/2013 |
1621 | 5*10^195250-21 | 195251 | Robert Price | 12/2021 |
1622 | (14*10^195234-83)/3 | 195235 | Robert Price | 12/2018 |
1623 | 5*10^195221+81 | 195222 | Robert Price | 03/2019 |
1624 | 10^195143-5001 | 195143 | Robert Price | 12/2021 |
1625 | 2^648190-24737 | 195125 | Enzo Doria | 09/2013 |
1626 | (57^111119+1)/58 | 195110 | Paul Bourdelais | 10/2017 |
1627 | (29*10^195098-197)/3 | 195099 | Robert Price | 08/2021 |
1628 | 10^195060+89701 | 195061 | Patrick De Geest | 02/2021 |
1630 | 10^195060-40000000001 | 195060 | Robert Price | 09/2020 |
1629 | 10^195060-110337 | 195060 | Patrick De Geest | 02/2021 |
1631 | 56*10^195032-3 | 195034 | Robert Price | 03/2020 |
1632 | 11^187185-90 | 194934 | Enzo Doria | 09/2012 |
1633 | (86*10^194818-437)/9 | 194819 | Robert Price | 03/2021 |
1634 | 2^647068+77281 | 194787 | Enzo Doria | 05/2016 |
1635 | 2*10^194716-93 | 194717 | Robert Price | 12/2021 |
1636 | 15^165559-14^165559 | 194713 | Jean-Louis Charton | 03/2011 |
1637 | F(931517) | 194676 | Henri Lifchitz | 09/2008 |
1638 | 4*10^194668+49 | 194669 | Robert Price | 01/2019 |
1639 | 2^646589+1179407 | 194643 | Enzo Doria | 06/2016 |
1640 | 2^646289-114621 | 194553 | Enzo Doria | 05/2015 |
1641 | 2^646236-39659 | 194537 | Enzo Doria | 09/2015 |
1642 | (16*10^194536+53)/3 | 194537 | Robert Price | 03/2019 |
1643 | 2^646161-59833 | 194514 | Enzo Doria | 11/2015 |
1644 | (17*10^194502+31)/3 | 194503 | Robert Price | 01/2019 |
1645 | (19*10^194428+287)/9 | 194429 | Robert Price | 10/2021 |
1646 | 2*10^194413+3 | 194414 | Robert Price | 07/2015 |
1647 | 2^645360-1848599 | 194273 | Enzo Doria | 08/2015 |
1648 | 22470^44641+44641^22470 | 194260 | Norbert Schneider | 08/2023 |
1649 | (112*10^194150-1)/3 | 194152 | Serge Batalov | 12/2014 |
1650 | 2*10^193981-43 | 193982 | Robert Price | 04/2018 |
1651 | 2^644382+75169 | 193979 | Enzo Doria | 04/2016 |
1652 | 2^644304-1861409 | 193955 | Enzo Doria | 11/2015 |
1653 | (29*10^193950-23)/3 | 193951 | Robert Price | 03/2022 |
1654 | 5*10^193907-9 | 193908 | Robert Price | 05/2015 |
1655 | 2^644043+1876703 | 193877 | Enzo Doria | 07/2016 |
1656 | 2*10^193841-63 | 193842 | Robert Price | 01/2022 |
1657 | 2^643735+1879733 | 193784 | Enzo Doria | 09/2016 |
1658 | (5^277183+1)/6 | 193742 | Paul Bourdelais | 07/2010 |
1659 | 9*10^193712+71 | 193713 | Robert Price | 08/2020 |
1660 | 2^643216-286565 | 193628 | Enzo Doria | 07/2015 |
1661 | 10^193566+1126339 | 193567 | Patrick De Geest | 09/2022 |
1663 | 10^193566-10000000001 | 193566 | Robert Price | 04/2021 |
1662 | 10^193566-454041 | 193566 | Patrick De Geest | 08/2021 |
1664 | 2^642888-24965 | 193529 | Enzo Doria | 09/2013 |
1665 | 2^642448-114825 | 193397 | Enzo Doria | 05/2015 |
1666 | 2^642437-1856623 | 193393 | Enzo Doria | 10/2015 |
1667 | 2^642039-59797 | 193273 | Enzo Doria | 11/2015 |
1668 | 2^641987+39 | 193258 | Jon Grantham | 08/2023 |
1669 | 10^193230+513861 | 193231 | Patrick De Geest | 07/2018 |
1670 | 10^193230-8001 | 193230 | Robert Price | 03/2018 |
1671 | (62*10^193225-233)/9 | 193226 | Robert Price | 02/2022 |
1672 | 2^641692-286349 | 193169 | Enzo Doria | 07/2015 |
1673 | 2^641690-24737 | 193168 | Enzo Doria | 09/2013 |
1674 | 22268^44421+44421^22268 | 193129 | Norbert Schneider | 06/2023 |
1675 | 2^641514+1876549 | 193115 | Enzo Doria | 07/2016 |
1676 | 2^640888-2785619 | 192927 | Enzo Doria | 10/2015 |
1677 | 2^640874-2783741 | 192923 | Enzo Doria | 09/2015 |
1678 | 10^192922+192207 | 192923 | Patrick De Geest | 08/2021 |
1679 | 10^192922-7001 | 192922 | Robert Price | 04/2021 |
1680 | 2^640854+25 | 192917 | Stefano Morozzi | 05/2021 |
1681 | 34*10^192868-9 | 192870 | Robert Price | 06/2020 |
1682 | (46*10^192841+683)/9 | 192842 | Robert Price | 03/2019 |
1683 | 2^640181+467 | 192714 | Lelio R Paula | 08/2013 |
1684 | 2^639536-1850249 | 192520 | Enzo Doria | 08/2015 |
1685 | 40714<>40712<>...<>1086421357911<>...<>40711<>40713 | 192464 | Hans Havermann | 12/2019 |
1686 | 5*10^192422-43 | 192423 | Robert Price | 01/2019 |
1687 | 2^639110-2792441 | 192392 | Enzo Doria | 02/2016 |
1688 | 2^638955-29827 | 192345 | Enzo Doria | 08/2015 |
1689 | 2^638713-2784223 | 192272 | Enzo Doria | 10/2015 |
1690 | (10^192216+7)/149 | 192214 | Alfred Reich | 07/2021 |
1691 | 2^638490-113507 | 192205 | Enzo Doria | 08/2014 |
1692 | 2^638189-39943 | 192115 | Enzo Doria | 09/2015 |
1693 | 2^638110+1877119 | 192091 | Enzo Doria | 07/2016 |
1694 | 2^638066-2785211 | 192078 | Enzo Doria | 10/2015 |
1695 | (35*10^191973-341)/9 | 191974 | Robert Price | 08/2021 |
1696 | (112*10^191900+17)/3 | 191902 | Robert Price | 03/2020 |
1697 | 2^637475-115309 | 191900 | Enzo Doria | 07/2015 |
1698 | (68*10^191754-113)/9 | 191755 | Robert Price | 03/2021 |
1699 | 2^636930-11 | 191736 | Stefano Morozzi | 07/2022 |
1700 | (47*10^191732+259)/9 | 191733 | Robert Price | 03/2022 |
1701 | 2^636661+1876577 | 191655 | Enzo Doria | 07/2016 |
1702 | (9^200807-2^200807)/7 | 191618 | Jon Grantham | 07/2023 |
1703 | (34^125101-1)/33 | 191589 | Paul Bourdelais | 11/2017 |
1704 | fibonacci(916540)-2 | 191546 | Jon Grantham | 08/2023 |
1705 | 2^636177-1855123 | 191509 | Enzo Doria | 09/2015 |
1706 | 2^636158-113627 | 191503 | Enzo Doria | 08/2014 |
1707 | (37*25^136966+63)/4 | 191472 | Curtis Bright | 05/2015 |
1708 | 2^636035+79823 | 191466 | Enzo Doria | 06/2016 |
1709 | 2^636011-1860847 | 191459 | Enzo Doria | 11/2015 |
1710 | 2^635926-1860611 | 191433 | Enzo Doria | 11/2015 |
1711 | 3*2^635755+5 | 191382 | Jon Grantham | 07/2023 |
1712 | 3*10^191152-7 | 191153 | Robert Price | 08/2015 |
1713 | 2^634883-1865677 | 191119 | Enzo Doria | 02/2016 |
1714 | 2^634801+1871957 | 191095 | Enzo Doria | 05/2016 |
1715 | (77*10^191080+157)/9 | 191081 | Robert Price | 05/2022 |
1716 | (35*10^191073+1)/9 | 191074 | Serge Batalov | 07/2010 |
1717 | 9*10^191018-41 | 191019 | Robert Price | 08/2020 |
1718 | 2^634470-59861 | 190995 | Enzo Doria | 11/2015 |
1719 | 2^634368-29519 | 190964 | Enzo Doria | 08/2015 |
1720 | (19*10^190935+11)/3 | 190936 | Robert Price | 07/2023 |
1721 | 2^634188-350609 | 190910 | Enzo Doria | 06/2015 |
1722 | (65*10^190899+493)/9 | 190900 | Robert Price | 08/2021 |
1723 | (62*10^190795-413)/9 | 190796 | Robert Price | 09/2021 |
1724 | (26*10^190789-131)/3 | 190790 | Robert Price | 10/2019 |
1725 | (13*10^190732-61)/3 | 190733 | Robert Price | 11/2018 |
1726 | 3*2^633524+5 | 190711 | Jon Grantham | 07/2023 |
1727 | (7*10^190683+143)/3 | 190684 | Robert Price | 03/2018 |
1728 | 2^633088-113879 | 190579 | Enzo Doria | 10/2014 |
1729 | 2^633064+1874911 | 190572 | Enzo Doria | 06/2016 |
1730 | 5*3^399402+2^399402 | 190564 | Jon Grantham | 08/2023 |
1731 | (43*10^190547+83)/9 | 190548 | Robert Price | 11/2018 |
1732 | 99*10^190543+7 | 190545 | Robert Price | 05/2021 |
1733 | (299*10^190533+1)/3 | 190535 | Robert Price | 04/2020 |
1734 | (1744*10^190519-1747)/3 | 190522 | Robert Price | 12/2020 |
1735 | 2^632815-15 | 190497 | Stefano Morozzi | 07/2022 |
1736 | 2^632795-351205 | 190491 | Enzo Doria | 06/2015 |
1737 | 41171^41272+41272^41171 | 190454 | Norbert Schneider | 05/2023 |
1738 | (16*10^190420-19)/3 | 190421 | Robert Price | 02/2019 |
1739 | (43*10^190351+101)/9 | 190352 | Robert Price | 11/2018 |
1740 | 2^632156+78391 | 190298 | Enzo Doria | 06/2016 |
1741 | 97*10^190295-3 | 190297 | Robert Price | 05/2020 |
1742 | 2^632082-1851971 | 190276 | Enzo Doria | 08/2015 |
1743 | 2^632020+1880311 | 190257 | Enzo Doria | 09/2016 |
1744 | (5*10^190242-77)/9 | 190242 | Robert Price | 04/2021 |
1745 | 7*10^190210+13 | 190211 | Robert Price | 03/2021 |
1746 | 2^631637-462373 | 190142 | Enzo Doria | 08/2015 |
1747 | 2*10^190126-21 | 190127 | Robert Price | 09/2020 |
1748 | (28*10^190105+191)/3 | 190106 | Robert Price | 02/2020 |
1749 | 2*10^190093+33 | 190094 | Robert Price | 11/2021 |
1750 | (68*10^190053-113)/9 | 190054 | Robert Price | 03/2021 |