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 ? |
1751 | 2^741362-1845251 | 223173 | Enzo Doria | 07/2015 |
1752 | 3^467546-5*2^467546 | 223077 | Jon Grantham | 08/2023 |
1753 | 2^740455-1863877 | 222900 | Enzo Doria | 12/2015 |
1754 | 2^740274+217519 | 222845 | Enzo Doria | 01/2024 |
1755 | (14*10^222718-41)/9 | 222719 | Serge Batalov | 01/2023 |
1756 | 2^739636-2792219 | 222653 | Enzo Doria | 02/2016 |
1757 | 11^213654-180 | 222498 | Enzo Doria | 01/2013 |
1758 | 2^738957-1859743 | 222449 | Enzo Doria | 11/2015 |
1759 | 4*10^222253-21 | 222254 | Robert Price | 12/2022 |
1760 | 2^737825+57 | 222108 | Stefano Morozzi | 05/2021 |
1761 | (54^128189+1)/55 | 222073 | Paul Bourdelais | 11/2018 |
1762 | 2^737166+220099 | 221910 | Enzo Doria | 03/2024 |
1763 | (10^221654+179)/9 | 221654 | Serge Batalov | 12/2014 |
1764 | 2^736281+79817 | 221643 | Enzo Doria | 06/2016 |
1765 | 10^221631+247617 | 221632 | Patrick De Geest | 10/2013 |
1766 | 10^221631-9 | 221631 | Alexander Gramolin | 02/2011 |
1767 | 10^221628+7 | 221629 | Alfred Reich | 04/2021 |
1768 | 2^735970-1839821 | 221550 | Enzo Doria | 06/2015 |
1769 | 2^735367+60293 | 221368 | Enzo Doria | 03/2016 |
1770 | 77*10^221343+3 | 221345 | Robert Price | 11/2023 |
1771 | (241^92821-1)/240 | 221099 | Anonymous | 04/2024 |
1772 | (202*10^221092-1)/3 | 221094 | Robert Price | 06/2023 |
1773 | (29^151153+1)/30 | 221045 | Paul Bourdelais | 09/2017 |
1774 | 2^734228+24751 | 221025 | Enzo Doria | 10/2023 |
1775 | (28*10^220800+173)/3 | 220801 | Robert Price | 07/2024 |
1776 | 2^733264-2784089 | 220735 | Enzo Doria | 10/2015 |
1777 | 2^733114-24555 | 220690 | Enzo Doria | 09/2013 |
1778 | 2^731891-636259 | 220322 | Enzo Doria | 12/2013 |
1779 | 98*10^220185-9 | 220187 | Robert Price | 05/2023 |
1780 | 418319^39164+418318 | 220161 | Alfred Reich | 11/2023 |
1781 | 2^731124-25539 | 220091 | Enzo Doria | 09/2013 |
1782 | 2^730972-462029 | 220045 | Enzo Doria | 07/2015 |
1783 | 2^730833+1868627 | 220003 | Enzo Doria | 04/2016 |
1784 | 2^730645-2787133 | 219947 | Enzo Doria | 11/2015 |
1785 | 2^730547-25581 | 219917 | Enzo Doria | 09/2013 |
1786 | (113*13^197420-5)/12 | 219916 | Anonymous | 11/2022 |
1787 | (13^197420*113-5)/12 | 219916 | Eric Chen | 10/2023 |
1788 | 2^730460+82291 | 219891 | Enzo Doria | 09/2016 |
1789 | (5*10^219847-101)/3 | 219848 | Robert Price | 08/2023 |
1790 | (2^730339+1)/(3*27839062003*7943469324347) | 219831 | Gord Palameta | 12/2018 |
1791 | L(1051849) | 219824 | Renaud Lifchitz | 03/2009 |
1792 | 3*2^730149+5 | 219798 | Jon Grantham | 07/2023 |
1793 | 8*10^219740-3 | 219741 | Serge Batalov | 01/2023 |
1794 | 11^210961-240 | 219694 | Enzo Doria | 01/2013 |
1795 | (26*10^219639-77)/3 | 219640 | Robert Price | 03/2023 |
1796 | 2^729611-113437 | 219635 | Enzo Doria | 08/2014 |
1797 | 7^259710-2 | 219481 | Paul Bourdelais | 01/2021 |
1798 | F(1049897) | 219416 | Henri Lifchitz | 10/2008 |
1799 | (1488^69151-1)/1487 | 219386 | Alexander Zhirkov | 02/2023 |
1800 | 2^728604+1879321 | 219332 | Enzo Doria | 10/2016 |
1801 | 33^144412+2 | 219292 | Robert Price | 04/2015 |
1802 | 2^728277-183313 | 219234 | Hans Havermann | 10/2018 |
1803 | 2^727998-1862711 | 219150 | Enzo Doria | 12/2015 |
1804 | (29*10^219124+91)/3 | 219125 | Robert Price | 12/2022 |
1805 | 2^727729-114073 | 219069 | Enzo Doria | 12/2014 |
1806 | 2^727496-1851809 | 218999 | Enzo Doria | 08/2015 |
1807 | 2^727025+25907 | 218857 | Enzo Doria | 12/2023 |
1808 | 2^726591+2793143 | 218726 | Enzo Doria | 02/2016 |
1809 | (7*10^218644+17)/3 | 218645 | Robert Price | 06/2023 |
1810 | 2^725534-2791931 | 218408 | Enzo Doria | 02/2016 |
1811 | Phi(220531,10)/2686456812680882641 | 217774 | Makoto Kamada | 10/2020 |
1812 | 2^722184+1877821 | 217400 | Enzo Doria | 08/2016 |
1813 | (109*10^217360-1)/9 | 217362 | Serge Batalov | 12/2014 |
1814 | 2^721721-4453 | 217260 | Yves Minet | 03/2021 |
1815 | 10^216950+49 | 216951 | Robert Price | 02/2023 |
1816 | 281*499979#/46410-2702372 | 216849 | Robert Smith | 08/2016 |
1817 | 281*499979#/46410+2400766 | 216849 | Robert Smith | 08/2016 |
1818 | tau(311^15786) | 216429 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
1819 | 2^718756-114107 | 216368 | Enzo Doria | 12/2014 |
1820 | 2^717672+121 | 216041 | Stefano Morozzi | 05/2021 |
1821 | 2^717305+80327 | 215931 | Enzo Doria | 07/2016 |
1822 | 2^717069-59773 | 215860 | Enzo Doria | 10/2015 |
1823 | 10^215802+33 | 215803 | Robert Price | 08/2023 |
1824 | 30^146021-29^146021 | 215691 | Jean-Louis Charton | 09/2018 |
1825 | 277^88301-276^88301 | 215674 | Jean-Louis Charton | 06/2012 |
1826 | 2^716428+215011 | 215667 | Enzo Doria | 11/2023 |
1827 | (13*10^215592-43)/3 | 215593 | Robert Price | 08/2023 |
1828 | 227^91413-40 | 215372 | Enzo Doria | 04/2015 |
1829 | (2^715008-21)/5 | 215239 | Stefano Morozzi | 08/2022 |
1830 | 2^714717+782897 | 215152 | Enzo Doria | 11/2016 |
1831 | tau(373^15186) | 214796 | Nik Lygeros / Olivier Rozier / LR team | 10/2013 |
1832 | 2^713241+1879157 | 214707 | Enzo Doria | 08/2016 |
1833 | (23*10^214633+91)/3 | 214634 | Robert Price | 03/2023 |
1834 | 11^206081-10^206081 | 214612 | Jean-Louis Charton | 10/2011 |
1835 | 2^712801-69553 | 214575 | Enzo Doria | 01/2016 |
1836 | 2^712603-25357 | 214515 | Enzo Doria | 09/2013 |
1837 | 2^711721-1846723 | 214250 | Enzo Doria | 07/2015 |
1838 | 2^710730-396765 | 213952 | Enzo Doria | 09/2013 |
1839 | (19*10^213934-37)/9 | 213935 | Alfred Reich | 12/2023 |
1840 | (19*10^213730-37)/9 | 213731 | Alfred Reich | 12/2023 |
1841 | (713^74897-1)/712 | 213685 | Jinyuan Wang | 08/2023 |
1842 | 2^709773+25907 | 213663 | Enzo Doria | 12/2023 |
1843 | 2^708468-114329 | 213271 | Enzo Doria | 02/2015 |
1844 | 2^708293+27557 | 213218 | Enzo Doria | 01/2024 |
1845 | 2^707277+28997 | 212912 | Enzo Doria | 02/2024 |
1846 | (163*10^212779-1)/9 | 212781 | Serge Batalov | 12/2014 |
1847 | 2^706838-69041 | 212780 | Enzo Doria | 11/2015 |
1848 | 2^705653+25907 | 212423 | Enzo Doria | 12/2023 |
1849 | 22*10^212339+7 | 212341 | Robert Price | 10/2022 |
1850 | 2^704577-113871 | 212099 | Enzo Doria | 10/2014 |
1851 | (2^704548-19)/3 | 212090 | Stefano Morozzi | 08/2022 |
1852 | 2^704110-2792441 | 211959 | Enzo Doria | 02/2016 |
1853 | 2^704084+28531 | 211951 | Enzo Doria | 02/2024 |
1854 | 2^703943-1862947 | 211908 | Enzo Doria | 12/2015 |
1855 | (60^119083+1)/61 | 211746 | Paul Bourdelais | 10/2018 |
1856 | (184*10^211682-1)/3 | 211684 | Robert Price | 12/2022 |
1857 | (10^211610-91)/9 | 211610 | Serge Batalov | 12/2014 |
1858 | 227^89797+2 | 211565 | Lelio R Paula | 08/2012 |
1859 | 2^702194-3 | 211382 | Paul Bourdelais | 03/2012 |
1860 | 2^702064+1874911 | 211343 | Enzo Doria | 07/2016 |
1861 | 2^701968-113873 | 211314 | Enzo Doria | 10/2014 |
1862 | (14*10^211262-41)/9 | 211263 | Serge Batalov | 01/2023 |
1863 | 2^701713-113779 | 211237 | Enzo Doria | 09/2014 |
1864 | 2^701616-216803 | 211208 | Enzo Doria | 01/2024 |
1865 | 2^701449-25201 | 211158 | Enzo Doria | 09/2013 |
1866 | 2^701403-2786977 | 211144 | Enzo Doria | 11/2015 |
1867 | 2^701189-25423 | 211079 | Enzo Doria | 09/2013 |
1868 | 2^701162-459161 | 211071 | Enzo Doria | 05/2015 |
1869 | 2^700793+219407 | 210960 | Enzo Doria | 03/2024 |
1870 | (24^152783-1)/23 | 210872 | Paul Bourdelais | 04/2018 |
1871 | 2^700400+9385 | 210842 | Lelio R Paula | 01/2014 |
1872 | 2^700304-17 | 210813 | Stefano Morozzi | 07/2022 |
1873 | 2^700131+1874693 | 210761 | Enzo Doria | 06/2016 |
1874 | (2^700095+225414)/2 | 210750 | Stefano Morozzi | 04/2020 |
1875 | (2^700090+278254)/2 | 210748 | Stefano Morozzi | 04/2020 |
1876 | (2^700075+303666)/2 | 210744 | Stefano Morozzi | 04/2020 |
1877 | (2^700073+75882)/2 | 210743 | Stefano Morozzi | 04/2020 |
1878 | (2^700074+328890)/2 | 210743 | Stefano Morozzi | 04/2020 |
1879 | (2^700052+79162)/2 | 210737 | Stefano Morozzi | 04/2020 |
1880 | (2^700052+304458)/2 | 210737 | Stefano Morozzi | 04/2020 |
1881 | (2^700048+376578)/2 | 210736 | Stefano Morozzi | 04/2020 |
1882 | 11^202357-1140 | 210734 | Enzo Doria | 12/2012 |
1883 | (2^700021+25874)/2 | 210728 | Stefano Morozzi | 04/2020 |
1884 | (2^700018+377518)/2 | 210727 | Stefano Morozzi | 04/2020 |
1885 | 2^699999+300729 | 210721 | Norman Luhn | 09/2023 |
1886 | (238*10^210712-1)/3 | 210714 | Robert Price | 09/2023 |
1887 | 2^699740+25 | 210643 | Stefano Morozzi | 05/2021 |
1888 | (23*10^210525-143)/3 | 210526 | Robert Price | 12/2023 |
1889 | 2^698929-2788423 | 210399 | Enzo Doria | 11/2015 |
1890 | (5^300893+4^300893)/9 | 210315 | Jean-Louis Charton | 11/2011 |
1891 | 2^698316+1878601 | 210215 | Enzo Doria | 08/2016 |
1892 | 34*10^210097-9 | 210099 | Robert Price | 05/2023 |
1893 | (19*10^210011-49)/3 | 210012 | Robert Price | 06/2023 |
1894 | 6*10^209846-91 | 209847 | Robert Price | 05/2023 |
1895 | 2^697036+1878751 | 209829 | Enzo Doria | 08/2016 |
1896 | 2^696813+28607 | 209762 | Enzo Doria | 02/2024 |
1897 | (238*10^209715-1)/3 | 209717 | Robert Price | 09/2023 |
1898 | 6^269407+5 | 209640 | Paul Bourdelais | 02/2021 |
1899 | (2^696343-1)/11141489/36009913139329 | 209600 | Tony Prest / Never Odd Or Even | 02/2014 |
1900 | 2^696254-115151 | 209594 | Enzo Doria | 06/2015 |
1901 | (35^135623+1)/36 | 209410 | Paul Bourdelais | 07/2018 |
1902 | 7*10^209161+39 | 209162 | Robert Price | 01/2023 |
1903 | 2^694633+1887257 | 209106 | Enzo Doria | 05/2017 |
1904 | fibonacci(999790)-4 | 208944 | Jon Grantham | 08/2023 |
1905 | 2^693959+180923 | 208903 | Enzo Doria | 07/2016 |
1906 | (2^693747-11)/3 | 208839 | Stefano Morozzi | 08/2022 |
1907 | 2^693462-1847561 | 208753 | Enzo Doria | 07/2015 |
1908 | 2^690890-59981 | 207979 | Enzo Doria | 11/2015 |
1909 | (38^131591+1)/39 | 207884 | Paul Bourdelais | 07/2018 |
1910 | 3*2^690484+5 | 207857 | Jon Grantham | 07/2023 |
1911 | 2^690163+1877063 | 207760 | Enzo Doria | 07/2016 |
1912 | 7^245608-2 | 207563 | Paul Bourdelais | 01/2021 |
1913 | (67*10^207556+23)/9 | 207557 | Serge Batalov | 01/2023 |
1914 | 2^689286-29381 | 207496 | Enzo Doria | 08/2015 |
1915 | 2^689122-114521 | 207447 | Enzo Doria | 04/2015 |
1916 | 9*10^207254-89 | 207255 | Robert Price | 02/2023 |
1917 | 2^688373+6077 | 207221 | Enzo Doria | 02/2016 |
1918 | 2^688201+1875527 | 207170 | Enzo Doria | 07/2016 |
1919 | (42^127609+1)/43 | 207140 | Paul Bourdelais | 07/2018 |
1920 | 2^687938+213589 | 207090 | Enzo Doria | 10/2023 |
1921 | 2^687619+81563 | 206994 | Enzo Doria | 08/2016 |
1922 | 3*10^206927+37 | 206928 | Robert Price | 08/2023 |
1923 | 2^687383+21803 | 206923 | Enzo Doria | 09/2023 |
1924 | (11*10^206688+19)/3 | 206689 | Robert Price | 07/2024 |
1925 | 2^686572-1845299 | 206679 | Enzo Doria | 07/2015 |
1926 | (21^156217-1)/20 | 206552 | Paul Bourdelais | 04/2010 |
1927 | (2^685739+1)/(3*87774593) | 206420 | Gord Palameta | 08/2018 |
1928 | 2^685578+3 | 206380 | Paul Bourdelais | 04/2012 |
1929 | 2^685078+218599 | 206230 | Enzo Doria | 01/2024 |
1930 | 2^684836-49349 | 206157 | Enzo Doria | 10/2015 |
1931 | (73^110603-1)/72 | 206088 | Paul Bourdelais | 06/2018 |
1932 | 2^684163-2790967 | 205954 | Enzo Doria | 12/2015 |
1933 | 326^81943-325^81943 | 205941 | Jean-Louis Charton | 07/2012 |
1934 | (2^684127-1)/23765203727 | 205933 | Jens K. Andersen | 04/2009 |
1935 | (68*10^205510+13)/9 | 205511 | Serge Batalov | 01/2023 |
1936 | 4^341233-3^341233 | 205443 | Jean-Louis Charton | 01/2006 |
1937 | 2^682414+215029 | 205428 | Enzo Doria | 11/2023 |
1938 | (963^68821-1)/962 | 205334 | Jinyuan Wang | 01/2024 |
1939 | (43*10^205183-421)/9 | 205184 | Robert Price | 10/2023 |
1940 | 2^681545+467 | 205166 | Lelio R Paula | 11/2013 |
1941 | 2^681306+81049 | 205094 | Enzo Doria | 07/2016 |
1942 | 2^680697+1877057 | 204911 | Enzo Doria | 07/2016 |
1943 | 2^680415+71783 | 204826 | Enzo Doria | 04/2016 |
1944 | 10^204764-8001 | 204764 | Robert Price | 03/2023 |
1945 | (26*10^204730-77)/3 | 204731 | Robert Price | 03/2023 |
1946 | 2^679860-459995 | 204659 | Enzo Doria | 06/2015 |
1947 | 2^679593+1879547 | 204578 | Enzo Doria | 09/2016 |
1948 | 2^678899+220073 | 204369 | Enzo Doria | 03/2024 |
1949 | 2^678753+21677 | 204326 | Enzo Doria | 08/2023 |
1950 | 2^678651+1875023 | 204295 | Enzo Doria | 07/2016 |
1951 | 2^678561+678561 | 204268 | Henri Lifchitz | 05/2006 |
1952 | 5*3^427884+2^427884 | 204154 | Jon Grantham | 08/2023 |
1953 | 2^678101-114043 | 204129 | Enzo Doria | 11/2014 |
1954 | 2^678028+1875631 | 204107 | Enzo Doria | 06/2016 |
1955 | 2^677721+28607 | 204015 | Enzo Doria | 01/2024 |
1956 | (19*10^203798-7)/3 | 203799 | Robert Price | 12/2023 |
1957 | 2^676992-59783 | 203795 | Enzo Doria | 10/2015 |
1958 | 2^676972+1866871 | 203789 | Enzo Doria | 03/2016 |
1959 | 2^676815+22583 | 203742 | Enzo Doria | 09/2023 |
1960 | 2^676761-9 | 203726 | Robert Price | 01/2017 |
1961 | 2^676592-23 | 203675 | Stefano Morozzi | 07/2022 |
1962 | 2^676563-2792407 | 203666 | Enzo Doria | 02/2016 |
1963 | 2^676306-114713 | 203589 | Enzo Doria | 04/2015 |
1964 | (2^675977-1)/(1686378749257*7171117283326998925471) | 203456 | Dario Alpern | 07/2015 |
1965 | 6*10^203365+53 | 203366 | Robert Price | 09/2023 |
1966 | 10247^50678-50678^10247 | 203250 | Norbert Schneider | 03/2022 |
1967 | 2^674627-25161 | 203083 | Enzo Doria | 09/2013 |
1968 | 2^674603-69337 | 203076 | Enzo Doria | 12/2015 |
1969 | (182*10^203048+1)/3 | 203050 | Robert Price | 09/2023 |
1970 | 2^674459+74213 | 203033 | Enzo Doria | 04/2016 |
1971 | 2^674116-458879 | 202930 | Enzo Doria | 04/2015 |
1972 | 2^674076-114755 | 202918 | Enzo Doria | 04/2015 |
1973 | 5^289937-4^289937 | 202658 | Jean-Louis Charton | 03/2013 |
1974 | 5^289926-289926^5 | 202650 | Henri Lifchitz | 07/2024 |
1975 | (2^673184-7)/3 | 202649 | Stefano Morozzi | 08/2022 |
1976 | (467617#+14534)/(2^2*13*43) | 202603 | Makoto Morimoto | 06/2019 |
1977 | (155^92479-1)/154 | 202558 | Anonymous | 06/2024 |
1978 | 2^672773+219407 | 202525 | Enzo Doria | 03/2024 |
1979 | 1374^64531-64531^1374 | 202498 | Henri Lifchitz | 10/2024 |
1980 | 2^672556-1835519 | 202460 | Enzo Doria | 04/2015 |
1981 | (7*10^202267+179)/3 | 202268 | Robert Price | 02/2023 |
1982 | 2^671446-351401 | 202126 | Enzo Doria | 07/2015 |
1983 | 2^671373+77747 | 202104 | Enzo Doria | 05/2016 |
1984 | (2*10^202059+7)/9 | 202059 | Rytis Slatkevicius | 01/2023 |
1985 | 98*10^202021-9 | 202023 | Robert Price | 05/2023 |
1986 | 2^670726-114845 | 201909 | Enzo Doria | 05/2015 |
1987 | 2^670539-25045 | 201853 | Enzo Doria | 09/2013 |
1988 | 10^201801-93 | 201801 | Robert Price | 02/2023 |
1989 | 43284^43519-43519^43284 | 201769 | Norbert Schneider | 08/2018 |
1990 | 2^670213+282317 | 201755 | Enzo Doria | 09/2016 |
1991 | 2^670133+89 | 201731 | Stefano Morozzi | 05/2021 |
1992 | 2^669854-113501 | 201647 | Enzo Doria | 08/2014 |
1993 | 2^669718+81619 | 201606 | Enzo Doria | 08/2016 |
1994 | (299*10^201547-17)/3 | 201549 | Robert Price | 02/2023 |
1995 | (145*10^201504-1)/9 | 201506 | Serge Batalov | 12/2014 |
1996 | 2^668938-1839821 | 201371 | Enzo Doria | 06/2015 |
1997 | (198^87623-1)/197 | 201239 | Anonymous | 06/2024 |
1998 | 2^668492+1879303 | 201237 | Enzo Doria | 08/2016 |
1999 | 7*10^201140-87 | 201141 | Robert Price | 03/2023 |
2000 | 6^258413-5^258413 | 201085 | Jean-Louis Charton | 03/2013 |