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 ? |
1751 | 5*3^514648+2^514648 | 245551 | Jon Grantham | 08/2023 |
1752 | 88093#+(653879#)/(88093#) | 245374 | Makoto Morimoto | 11/2017 |
1753 | 2^815111-113857 | 245373 | Enzo Doria | 10/2014 |
1754 | (34555^54289-1)/(34555^233-1) | 245334 | Ryan Propper | 11/2023 |
1755 | 2^814914-4001 | 245314 | Yves Minet | 05/2017 |
1756 | 846^83761-845^83761 | 245200 | Jean-Louis Charton | 12/2012 |
1757 | 2^814356-2790449 | 245146 | Enzo Doria | 12/2015 |
1758 | 2^814276-459029 | 245122 | Enzo Doria | 04/2015 |
1759 | 2^814023+180923 | 245046 | Enzo Doria | 07/2016 |
1760 | 2^813496+216751 | 244887 | Enzo Doria | 12/2023 |
1761 | (3^513059-2^513059)/(1026119*5430216457) | 244776 | Mike Oakes | 03/2017 |
1762 | 3^513007+16 | 244767 | Robert Price | 04/2020 |
1763 | (46^147197-31^147197)/15 | 244752 | Aurel Gibier | 06/2024 |
1764 | 2^811882+27289 | 244401 | Enzo Doria | 12/2023 |
1765 | 2^811842-113675 | 244389 | Enzo Doria | 09/2014 |
1766 | 2^811132-2787929 | 244176 | Enzo Doria | 11/2015 |
1767 | 2^809746-2790971 | 243758 | Enzo Doria | 01/2016 |
1768 | (14*10^243724-197)/3 | 243725 | Robert Price | 03/2023 |
1769 | 2^808767-3295 | 243464 | Yves Minet | 12/2016 |
1770 | 2^808621-113809 | 243420 | Enzo Doria | 09/2014 |
1771 | 2^808199+29693 | 243293 | Enzo Doria | 03/2024 |
1772 | 2^807724+1879621 | 243150 | Enzo Doria | 09/2016 |
1773 | 2^807417+217787 | 243057 | Enzo Doria | 01/2024 |
1774 | (23*10^242909+91)/3 | 242910 | Robert Price | 03/2023 |
1775 | 2^806708+20371 | 242844 | Enzo Doria | 08/2023 |
1776 | 2*10^242822-91 | 242823 | Robert Price | 02/2023 |
1777 | 20^186554-3 | 242713 | Paul Bourdelais | 12/2020 |
1778 | 2^805843-113611 | 242583 | Enzo Doria | 08/2014 |
1779 | 2^805745-459763 | 242554 | Enzo Doria | 05/2015 |
1780 | 2^805353+782687 | 242436 | Enzo Doria | 11/2016 |
1781 | (19*10^242362-7)/3 | 242363 | Robert Price | 12/2023 |
1782 | 2^804895+29963 | 242298 | Enzo Doria | 03/2024 |
1783 | 2^804725+28229 | 242247 | Enzo Doria | 01/2024 |
1784 | 6^311257+5 | 242206 | Paul Bourdelais | 02/2021 |
1785 | (21^242194)%(10^242194) | 242194 | Henri Lifchitz | 06/2025 |
1786 | 2^804277-417933 | 242112 | Enzo Doria | 01/2014 |
1787 | 2^803468-269039 | 241868 | Enzo Doria | 10/2013 |
1788 | 2^803172+80851 | 241779 | Enzo Doria | 07/2016 |
1789 | 2^803011+220073 | 241731 | Enzo Doria | 03/2024 |
1790 | 3^506233-2 | 241535 | Robert Price | 11/2013 |
1791 | 2^802025-25999 | 241434 | Enzo Doria | 10/2013 |
1792 | (3^505823+3^252912+1)/7 | 241339 | Serge Batalov | 03/2014 |
1793 | 2^801575+25073 | 241299 | Enzo Doria | 11/2023 |
1794 | 2^801303+1872923 | 241217 | Enzo Doria | 05/2016 |
1795 | 2^801105+216977 | 241157 | Enzo Doria | 12/2023 |
1796 | (23*10^241048-143)/3 | 241049 | Robert Price | 12/2023 |
1797 | 2^800579-1862947 | 240999 | Enzo Doria | 12/2015 |
1798 | 2^799999+16205 | 240824 | Norman Luhn | 09/2023 |
1799 | 3^504206+2 | 240568 | Luke W. Richards | 03/2018 |
1800 | 2^798973-26283 | 240515 | Enzo Doria | 10/2013 |
1801 | 2^798671-69487 | 240424 | Enzo Doria | 12/2015 |
1802 | 2^797220+79831 | 239988 | Enzo Doria | 06/2016 |
1803 | 2^796910-26001 | 239894 | Enzo Doria | 10/2013 |
1804 | (97^120721-1)/811245216 | 239837 | Paul Vanderveen | 06/2025 |
1805 | 2^796598+653119 | 239800 | Enzo Doria | 12/2016 |
1806 | 2^796432-1859729 | 239750 | Enzo Doria | 11/2015 |
1807 | 2^796002-1852211 | 239621 | Enzo Doria | 08/2015 |
1808 | 2^795884+214081 | 239585 | Enzo Doria | 10/2023 |
1809 | 2^795709+75767 | 239533 | Enzo Doria | 04/2016 |
1810 | 2^795708+81721 | 239532 | Enzo Doria | 08/2016 |
1811 | 2^795468-2786249 | 239460 | Enzo Doria | 10/2015 |
1812 | 2^795442+80779 | 239452 | Enzo Doria | 07/2016 |
1813 | 2^795075-1852057 | 239342 | Enzo Doria | 08/2015 |
1814 | (86^123677+1)/87 | 239252 | Paul Bourdelais | 01/2019 |
1815 | 2^794043+1875023 | 239031 | Enzo Doria | 06/2016 |
1816 | 2^793347-69577 | 238822 | Enzo Doria | 01/2016 |
1817 | 5*2^793288+3 | 238805 | Jon Grantham | 07/2023 |
1818 | 2^792988-344429 | 238714 | Enzo Doria | 08/2015 |
1819 | 2^792700-2786369 | 238627 | Enzo Doria | 11/2015 |
1820 | 2^792663-1844797 | 238616 | Enzo Doria | 06/2015 |
1821 | 2^792605-291943 | 238598 | Enzo Doria | 07/2015 |
1822 | 2^792366+218599 | 238526 | Enzo Doria | 01/2024 |
1823 | (2^792061-2^396031+1)/5 | 238434 | Thomas Ritschel | 03/2014 |
1824 | 2^791321+30077 | 238212 | Enzo Doria | 03/2024 |
1825 | 4*10^238163+21 | 238164 | Robert Price | 12/2022 |
1826 | (26*10^238157-77)/3 | 238158 | Robert Price | 03/2023 |
1827 | 10^237670+9 | 237671 | Robert Price | 08/2023 |
1828 | 2^789373+1869377 | 237625 | Enzo Doria | 05/2016 |
1829 | ((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961 | 237544 | Serge Batalov | 04/2015 |
1830 | Phi(1187740M,10) | 237544 | Anonymous | 03/2025 |
1831 | 2^789033+218537 | 237523 | Enzo Doria | 01/2024 |
1832 | 2^788942+1866409 | 237496 | Enzo Doria | 02/2016 |
1833 | 2^788844-114329 | 237466 | Enzo Doria | 01/2015 |
1834 | 2^788705-1859713 | 237424 | Enzo Doria | 11/2015 |
1835 | 2^788325+224789 | 237310 | Enzo Doria | 07/2024 |
1836 | 15^201475+14 | 236953 | Alfred Reich | 10/2023 |
1837 | 2^786663+219173 | 236810 | Enzo Doria | 02/2024 |
1838 | 2^786180+1871971 | 236664 | Enzo Doria | 05/2016 |
1839 | 11^227092-90 | 236492 | Enzo Doria | 11/2012 |
1840 | 2^785260+1866361 | 236387 | Enzo Doria | 02/2016 |
1841 | 2^785220+1880611 | 236375 | Enzo Doria | 10/2016 |
1842 | (2^784689-15)/7 | 236215 | Stefano Morozzi | 08/2022 |
1843 | 19^184650-2 | 236122 | Robert Price | 10/2014 |
1844 | 10^236059+216513 | 236060 | Patrick De Geest | 04/2016 |
1845 | 10^236059-20909 | 236059 | Robert Price | 09/2015 |
1846 | 2^783988+38011 | 236004 | Enzo Doria | 10/2024 |
1847 | 2^783893-21 | 235976 | Stefano Morozzi | 07/2022 |
1848 | (47^140983-1)/2792206142311142462 | 235719 | Paul Vanderveen | 06/2025 |
1849 | 2^782821+37577 | 235653 | Enzo Doria | 10/2024 |
1850 | (87^121487-1)/86 | 235625 | Paul Bourdelais | 12/2018 |
1851 | 2^782634-113981 | 235597 | Enzo Doria | 11/2014 |
1852 | 2^782423+1879733 | 235533 | Enzo Doria | 09/2016 |
1853 | (10^(2*117707+1)+12*10^117707-1)/3 | 235415 | Robert Price | 10/2023 |
1854 | (2^781970)/(781970^2) | 235385 | Henri Lifchitz | 06/2025 |
1855 | 2^781682-2789543 | 235310 | Enzo Doria | 12/2015 |
1856 | 2^780481+21489 | 234949 | Enzo Doria | 05/2024 |
1857 | 2^780408-113453 | 234927 | Enzo Doria | 08/2014 |
1858 | 7*10^234915+9 | 234916 | Robert Price | 04/2023 |
1859 | 2^780368-1864829 | 234915 | Enzo Doria | 01/2016 |
1860 | 2^780284+7 | 234889 | Jon Grantham | 08/2023 |
1861 | 2^779593-1836559 | 234681 | Enzo Doria | 05/2015 |
1862 | (8713#+(549391#)/(8713#))/360295171 | 234487 | Makoto Morimoto | 11/2017 |
1863 | (5^335429+1)/6 | 234455 | Paul Bourdelais | 08/2010 |
1864 | 2^778788+22201 | 234439 | Enzo Doria | 09/2023 |
1865 | 2^778395-113617 | 234321 | Enzo Doria | 08/2014 |
1866 | 5*2^778090+3 | 234230 | Jon Grantham | 07/2023 |
1867 | (21430^54289-1)/(21430^233-1) | 234118 | Ryan Propper | 11/2023 |
1868 | (5*10^234054-101)/3 | 234055 | Robert Price | 08/2023 |
1869 | 23*10^234025-7 | 234027 | Robert Price | 10/2022 |
1870 | 2^777170+21489 | 233952 | Enzo Doria | 05/2024 |
1871 | Phi(78125,5517) | 233857 | Anonymous | 09/2022 |
1872 | 5^334359-3^334359-1 | 233707 | Jon Grantham | 08/2023 |
1873 | 2^776245-2792353 | 233674 | Enzo Doria | 02/2016 |
1874 | 49748^49748+49735^49735 | 233656 | Henri Lifchitz | 11/2024 |
1875 | 2^776060-114029 | 233618 | Enzo Doria | 11/2014 |
1876 | 2^775987-2789557 | 233596 | Enzo Doria | 12/2015 |
1877 | 2*10^233564-91 | 233565 | Robert Price | 02/2023 |
1878 | 2^775865+21489 | 233559 | Enzo Doria | 05/2024 |
1879 | 2^775672+1866721 | 233501 | Enzo Doria | 03/2016 |
1880 | 2^775238+57 | 233370 | Stefano Morozzi | 05/2021 |
1881 | (11^223999+1)/12 | 233270 | Paul Bourdelais | 02/2010 |
1882 | U(1302049) | 233238 | Serge Batalov | 07/2024 |
1883 | 2^774118+1885789 | 233033 | Enzo Doria | 04/2017 |
1884 | 21^176191-20^176191 | 232964 | Jean-Louis Charton | 01/2015 |
1885 | 2^773723+217523 | 232914 | Enzo Doria | 01/2024 |
1886 | 2^773679-113425 | 232901 | Enzo Doria | 08/2014 |
1887 | (7*10^232620+23)/3 | 232621 | Robert Price | 05/2023 |
1888 | 10^232599+192489 | 232600 | Patrick De Geest | 12/2013 |
1889 | 10^232599-3 | 232599 | Markus Tervooren | 10/2010 |
1890 | 2^772552-458879 | 232562 | Enzo Doria | 04/2015 |
1891 | 2^772214+1874899 | 232460 | Enzo Doria | 06/2016 |
1892 | 2^771994-1862771 | 232394 | Enzo Doria | 12/2015 |
1893 | 2^771889+1876037 | 232362 | Enzo Doria | 07/2016 |
1894 | 2^771660+1866511 | 232293 | Enzo Doria | 02/2016 |
1895 | 5^332150-18188 | 232163 | Enzo Doria | 06/2014 |
1896 | 2^771227+61121 | 232163 | Boyan Hu | 05/2024 |
1897 | 2^770623+212543 | 231981 | Enzo Doria | 09/2023 |
1898 | 3^485977-2^485977 | 231870 | Mike Oakes | 09/2009 |
1899 | 2^770082-114161 | 231818 | Enzo Doria | 01/2015 |
1900 | 2^769791+25523 | 231731 | Enzo Doria | 11/2023 |
1901 | 7^274120-2 | 231659 | Paul Bourdelais | 08/2023 |
1902 | (20^177967+1)/21 | 231540 | Paul Bourdelais | 05/2013 |
1903 | 2^769011+81 | 231496 | Henri Lifchitz | 01/2025 |
1904 | (71^125029-1)/105024430 | 231453 | Paul Vanderveen | 06/2025 |
1905 | (4*10^231254+23)/9 | 231254 | Serge Batalov | 11/2022 |
1906 | 2^768205+22217 | 231253 | Enzo Doria | 09/2023 |
1907 | 49262^49262-49247^49247 | 231163 | Henri Lifchitz | 11/2024 |
1908 | 2^767622-9221 | 231078 | Lelio R Paula | 01/2016 |
1909 | 2^767344+1880311 | 230994 | Enzo Doria | 09/2016 |
1910 | 8*10^230921-13 | 230922 | Robert Price | 08/2023 |
1911 | (3^483611-1)/2 | 230741 | Paul Bourdelais | 02/2010 |
1912 | (10^230706+179)/9 | 230706 | Serge Batalov | 12/2014 |
1913 | 2^766309+1875257 | 230682 | Enzo Doria | 06/2016 |
1914 | (26131^52441-1)/(26131^229-1) | 230629 | Ryan Propper | 11/2023 |
1915 | 2^765635+1879883 | 230480 | Enzo Doria | 09/2016 |
1916 | 43^141090+141090 | 230467 | Kellen Shenton | 06/2023 |
1917 | (26*10^230394-119)/3 | 230395 | Robert Price | 07/2023 |
1918 | 2^764348-113697 | 230092 | Enzo Doria | 09/2014 |
1919 | 2^764131+78863 | 230027 | Enzo Doria | 05/2016 |
1920 | 2^763701+60197 | 229897 | Enzo Doria | 03/2016 |
1921 | 4*10^229836+21 | 229837 | Robert Price | 12/2022 |
1922 | 2^763362+27799 | 229795 | Enzo Doria | 01/2024 |
1923 | 2^762841-25905 | 229639 | Enzo Doria | 10/2013 |
1924 | 2^762659+212633 | 229584 | Enzo Doria | 09/2023 |
1925 | 77*10^229211+3 | 229213 | Robert Price | 11/2023 |
1926 | 2^761117-113569 | 229120 | Enzo Doria | 08/2014 |
1927 | (29022^51529-1)/(29022^227-1) | 228947 | Ryan Propper | 11/2023 |
1928 | (98^114859+1)/99 | 228709 | Paul Bourdelais | 12/2018 |
1929 | 5*3^479067-2^479067 | 228574 | Jon Grantham | 08/2023 |
1930 | 2^758645+216011 | 228375 | Enzo Doria | 12/2023 |
1931 | (2^758231+1)/(3*27146942976539*73236839266867) | 228223 | Gord Palameta | 12/2018 |
1932 | 10^228208+111 | 228209 | Boyan Hu | 10/2024 |
1933 | (298*10^228177-7)/3 | 228179 | Robert Price | 02/2023 |
1934 | 2^757985-2790013 | 228177 | Enzo Doria | 12/2015 |
1935 | 34*10^228129-9 | 228131 | Robert Price | 05/2023 |
1936 | 2^757038-1862081 | 227892 | Enzo Doria | 12/2015 |
1937 | 2^756839+95849 | 227832 | Makoto Morimoto | 10/2013 |
1939 | (2^756839+6989)/756091 | 227826 | Makoto Morimoto | 09/2016 |
1938 | (2^756839-50211)/(137*3203) | 227826 | Makoto Morimoto | 08/2019 |
1940 | 2^756773-112723 | 227812 | Enzo Doria | 07/2014 |
1941 | (7*10^(2*113887+1)+9*10^113887-7)/9 | 227775 | Robert Price | 08/2024 |
1942 | (10^227542)/(227542^10) | 227489 | Henri Lifchitz | 05/2025 |
1943 | 524309#+616367 | 227431 | Makoto Morimoto | 02/2016 |
1944 | 2^755404+226575 | 227400 | Enzo Doria | 09/2024 |
1945 | 2^755116+81 | 227313 | Henri Lifchitz | 11/2024 |
1946 | 2^755097-114193 | 227307 | Enzo Doria | 12/2014 |
1947 | 7*10^227178+39 | 227179 | Robert Price | 01/2023 |
1948 | 9*10^227153-89 | 227154 | Robert Price | 02/2023 |
1949 | 2^754473-2791513 | 227120 | Enzo Doria | 01/2016 |
1950 | 2^754376+25 | 227090 | Stefano Morozzi | 05/2021 |
1951 | 2^754138+213289 | 227019 | Enzo Doria | 09/2023 |
1952 | 2^754038+25 | 226989 | Stefano Morozzi | 05/2021 |
1953 | 2^753263+217133 | 226755 | Enzo Doria | 12/2023 |
1954 | 7*10^226479-9 | 226480 | Robert Price | 02/2023 |
1955 | (10^226381+1)/14973418875371 | 226368 | Alfred Reich | 06/2025 |
1956 | 2^751655+33893 | 226271 | Enzo Doria | 06/2024 |
1957 | 2^751426-764321 | 226202 | Enzo Doria | 12/2013 |
1958 | (18^180181-1)/17 | 226176 | Andy Steward | 04/2007 |
1959 | 2^750740-3 | 225996 | Paul Bourdelais | 03/2012 |
1960 | 2^750725+60227 | 225991 | Enzo Doria | 02/2016 |
1961 | 2^750525-113743 | 225931 | Enzo Doria | 09/2014 |
1962 | (2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263) | 225744 | Dario Alpern | 10/2014 |
1963 | 2^749444-1861889 | 225606 | Enzo Doria | 12/2015 |
1964 | tau(311^16452) | 225560 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
1965 | (3^472721+1)/9422189991086734893916 | 225524 | Paul Vanderveen | 06/2025 |
1966 | 2^749096+1876861 | 225501 | Enzo Doria | 07/2016 |
1967 | 2^748895+26213 | 225440 | Enzo Doria | 12/2023 |
1968 | (519643#+43033)/(23*1871*2706283) | 225379 | Makoto Morimoto | 08/2019 |
1969 | 2^748657+79607 | 225369 | Enzo Doria | 06/2016 |
1970 | (2^746920-11)/5 | 224845 | Stefano Morozzi | 08/2022 |
1971 | 2^746653-291583 | 224765 | Enzo Doria | 07/2015 |
1972 | 2^746461-114043 | 224708 | Enzo Doria | 11/2014 |
1973 | 2^746302+25 | 224660 | Stefano Morozzi | 05/2021 |
1974 | (202*10^224545-1)/3 | 224547 | Robert Price | 06/2023 |
1975 | (19*10^224533-37)/9 | 224534 | Alfred Reich | 12/2023 |
1976 | 2^745674+213949 | 224471 | Enzo Doria | 10/2023 |
1977 | 2^745098-350471 | 224297 | Enzo Doria | 06/2015 |
1978 | 2^745039-4897 | 224280 | Yves Minet | 03/2021 |
1979 | 23*10^224232-7 | 224234 | Robert Price | 10/2022 |
1980 | (154*10^224061-1)/9 | 224063 | Serge Batalov | 12/2014 |
1981 | 2^744211-1845787 | 224030 | Enzo Doria | 07/2015 |
1982 | 2^743773+37757 | 223898 | Enzo Doria | 10/2024 |
1983 | 2^743592-134579 | 223844 | Hans Havermann | 10/2018 |
1984 | 2^742452+3 | 223501 | Paul Bourdelais | 06/2019 |
1985 | 234178^9+9^234178 | 223463 | Anatoly F. Selevich | 07/2011 |
1986 | 47747^47747-2512^2512 | 223406 | Henri Lifchitz | 10/2024 |
1987 | 2^741651-461197 | 223260 | Enzo Doria | 07/2015 |
1988 | 10^223236-1001 | 223236 | Robert Price | 10/2022 |
1989 | 2^741362-1845251 | 223173 | Enzo Doria | 07/2015 |
1990 | 3^467546-5*2^467546 | 223077 | Jon Grantham | 08/2023 |
1991 | 2^740455-1863877 | 222900 | Enzo Doria | 12/2015 |
1992 | 2^740274+217519 | 222845 | Enzo Doria | 01/2024 |
1993 | (14*10^222718-41)/9 | 222719 | Serge Batalov | 01/2023 |
1994 | 2^739636-2792219 | 222653 | Enzo Doria | 02/2016 |
1995 | 11^213654-180 | 222498 | Enzo Doria | 01/2013 |
1996 | 2^738957-1859743 | 222449 | Enzo Doria | 11/2015 |
1997 | 4*10^222253-21 | 222254 | Robert Price | 12/2022 |
1998 | 2^737825+57 | 222108 | Stefano Morozzi | 05/2021 |
1999 | (54^128189+1)/55 | 222073 | Paul Bourdelais | 11/2018 |
2000 | 3^232689+1^232689+4^232689+1^232689+5^232689+9^232689 | 222042 | Henri Lifchitz | 03/2025 |