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 | 2^609846-1834251 | 183582 | Enzo Doria | 07/2015 |
1752 | 10^183546+1547323 | 183547 | Patrick De Geest | 02/2021 |
1754 | 10^183546-800000001 | 183546 | Robert Price | 09/2020 |
1753 | 10^183546-584297 | 183546 | Patrick De Geest | 02/2021 |
1755 | 7*10^183511+39 | 183512 | Robert Price | 01/2023 |
1756 | (23*10^183477-71)/3 | 183478 | Robert Price | 07/2020 |
1757 | 11^176176-240 | 183469 | Enzo Doria | 11/2012 |
1758 | (41^113749+1)/42 | 183451 | Paul Bourdelais | 11/2017 |
1759 | 6*10^183429+53 | 183430 | Robert Price | 05/2020 |
1760 | (28*10^183403+191)/3 | 183404 | Robert Price | 02/2020 |
1761 | (101^91463+1)/102 | 183320 | Paul Bourdelais | 11/2017 |
1762 | 2^608965-113989 | 183317 | Enzo Doria | 10/2014 |
1763 | A005165(43592) | 183312 | Serge Batalov | 07/2017 |
1764 | (61*10^183294+119)/9 | 183295 | Robert Price | 05/2019 |
1765 | 2^608814-461261 | 183272 | Enzo Doria | 06/2015 |
1766 | (163*10^183227-1)/9 | 183229 | Serge Batalov | 12/2014 |
1767 | 2^608541-608541^2 | 183190 | Henri Lifchitz | 02/2018 |
1768 | 2^608293+143807 | 183115 | Enzo Doria | 10/2016 |
1769 | 2^608164-462419 | 183076 | Enzo Doria | 08/2015 |
1770 | 2^607950-1862303 | 183012 | Enzo Doria | 12/2015 |
1771 | (46*10^182896+683)/9 | 182897 | Robert Price | 03/2019 |
1772 | (2*10^182787+73)/3 | 182787 | Robert Price | 09/2020 |
1773 | 2^607101+1871987 | 182756 | Enzo Doria | 05/2016 |
1774 | 2^606869-69175 | 182686 | Enzo Doria | 11/2015 |
1775 | 8*10^182671+71 | 182672 | Robert Price | 05/2022 |
1776 | (23*10^182666-71)/3 | 182667 | Robert Price | 07/2020 |
1777 | 3*10^182614-11 | 182615 | Robert Price | 07/2018 |
1778 | 2^606560-357 | 182593 | Enzo Doria | 05/2014 |
1779 | 66*10^182420+7 | 182422 | Robert Price | 07/2020 |
1780 | 2^605687+1866983 | 182330 | Enzo Doria | 03/2016 |
1781 | 2^605655-114445 | 182321 | Enzo Doria | 02/2015 |
1782 | 94*10^182291-3 | 182293 | Robert Price | 05/2020 |
1783 | (20^140053+1)/21 | 182212 | Paul Bourdelais | 04/2010 |
1784 | (14*10^182177-221)/9 | 182178 | Robert Price | 04/2018 |
1785 | 2^605174-112751 | 182176 | Enzo Doria | 06/2014 |
1786 | 2^604761+1874507 | 182052 | Enzo Doria | 06/2016 |
1787 | 2^604705+1871957 | 182035 | Enzo Doria | 05/2016 |
1788 | (14*10^182000+229)/9 | 182001 | Robert Price | 03/2018 |
1789 | (10^181996+41)/3 | 181996 | Robert Price | 12/2017 |
1790 | (17*10^181979+91)/9 | 181980 | Robert Price | 02/2022 |
1791 | (5*10^181950-101)/3 | 181951 | Robert Price | 04/2018 |
1792 | 2^603915+75233 | 181797 | Enzo Doria | 04/2016 |
1793 | 39470^39537+39537^39470 | 181723 | Norbert Schneider | 12/2022 |
1794 | (10^181710+7)/563747/2019847 | 181698 | Alfred Reich | 08/2021 |
1795 | 7*10^181594-57 | 181595 | Robert Price | 06/2020 |
1796 | 8*10^181580+29 | 181581 | Robert Price | 11/2021 |
1797 | (83*10^181544+61)/9 | 181545 | Serge Batalov | 01/2023 |
1798 | (2*10^181457+7)/9 | 181457 | Rytis Slatkevicius | 01/2023 |
1799 | 3*10^181445+23 | 181446 | Robert Price | 03/2022 |
1800 | (194*10^181369-11)/3 | 181371 | Robert Price | 09/2020 |
1801 | 11^174145-360 | 181354 | Enzo Doria | 10/2012 |
1802 | 2^602351-396765 | 181326 | Enzo Doria | 08/2013 |
1803 | 6*10^181306+17 | 181307 | Robert Price | 04/2019 |
1804 | (286*10^181220-1)/3 | 181222 | Robert Price | 11/2020 |
1805 | 2^601957-113833 | 181208 | Enzo Doria | 09/2014 |
1806 | 66^99581-65^99581 | 181193 | Robert Price | 09/2013 |
1807 | 10^181182+383973 | 181183 | Patrick De Geest | 04/2016 |
1808 | 10^181182-21 | 181182 | Serge Batalov | 12/2014 |
1809 | (797*10^181171-41)/9 | 181173 | Robert Price | 04/2022 |
1810 | (5*10^181127-29)/3 | 181128 | Robert Price | 03/2018 |
1811 | 2^601521-29143 | 181076 | Enzo Doria | 07/2015 |
1812 | 2^601442-2797811 | 181053 | Enzo Doria | 04/2016 |
1813 | 44*10^181029+3 | 181031 | Robert Price | 04/2020 |
1814 | 5*10^180992-9 | 180993 | Robert Price | 05/2015 |
1815 | 10^180979+79477 | 180980 | Patrick De Geest | 04/2016 |
1816 | 10^180979+107739 | 180980 | Patrick De Geest | 04/2016 |
1817 | 10^180979-11 | 180979 | Serge Batalov | 12/2014 |
1818 | 2^601023-113851 | 180926 | Enzo Doria | 10/2014 |
1819 | (23*10^180862-143)/3 | 180863 | Robert Price | 12/2019 |
1820 | 3*10^180852+29 | 180853 | Robert Price | 05/2018 |
1821 | (277*10^180782-7)/9 | 180784 | Robert Price | 02/2022 |
1822 | (8*10^180725-629)/9 | 180725 | Robert Price | 01/2022 |
1823 | (79*10^180710-1)/3 | 180712 | Robert Price | 02/2020 |
1824 | 2^600300-1852559 | 180709 | Enzo Doria | 08/2015 |
1825 | (2*10^180706-77)/3 | 180706 | Robert Price | 02/2021 |
1826 | (10^180689+71)/9 | 180689 | Serge Batalov | 07/2015 |
1827 | 2^600209+76487 | 180681 | Enzo Doria | 05/2016 |
1828 | (8*10^180536-269)/9 | 180536 | Robert Price | 09/2021 |
1829 | 2^599702-369885 | 180529 | Enzo Doria | 11/2013 |
1830 | Tau(643^11688) | 180524 | Nik Lygeros / Olivier Rozier | 05/2015 |
1831 | (2951*29^123418-3)/4 | 180490 | Curtis Bright | 05/2015 |
1832 | (29*10^180432-17)/3 | 180433 | Robert Price | 09/2019 |
1833 | 4*10^180360+93 | 180361 | Robert Price | 08/2018 |
1834 | 2^598942+80779 | 180300 | Enzo Doria | 07/2016 |
1835 | (38*10^180296+403)/9 | 180297 | Robert Price | 10/2018 |
1836 | (85*10^180241+77)/9 | 180242 | Robert Price | 07/2022 |
1837 | 2^598591-1844797 | 180194 | Enzo Doria | 06/2015 |
1838 | (100^90089+1)/101 | 180176 | Paul Bourdelais | 08/2017 |
1839 | (29*10^180072+691)/9 | 180073 | Robert Price | 08/2021 |
1840 | (59*10^180038+157)/9 | 180039 | Robert Price | 12/2021 |
1841 | 95*10^180019-9 | 180021 | Robert Price | 01/2022 |
1842 | 6*10^179970+91 | 179971 | Robert Price | 05/2019 |
1843 | (4*10^179963-79)/3 | 179964 | Robert Price | 02/2018 |
1844 | (403*10^179944-43)/9 | 179946 | Robert Price | 06/2021 |
1845 | Gamma-Prime(179849) | 179849 | Eric W. Weisstein | 06/2011 |
1846 | 2^597424-1859729 | 179843 | Enzo Doria | 11/2015 |
1847 | Phi(180683,10) | 179760 | Maksym Voznyy | 09/2015 |
1848 | (10^180683-1)*9/(10^643-1)/(10^281-1) | 179760 | Robert Price | 07/2016 |
1849 | (3^376657-2^376657)/22301107657 | 179701 | Mike Oakes | 04/2017 |
1850 | (29*10^179697+223)/9 | 179698 | Robert Price | 09/2018 |
1851 | 2^596884+73 | 179680 | Stefano Morozzi | 04/2021 |
1852 | (11*10^179679+13)/3 | 179680 | Robert Price | 03/2022 |
1853 | (68*10^179656+7)/3 | 179658 | Robert Price | 01/2020 |
1854 | (10^179643+173)/3 | 179643 | Robert Price | 05/2021 |
1855 | 2^596690-461261 | 179622 | Enzo Doria | 07/2015 |
1856 | 2^596684-113939 | 179620 | Enzo Doria | 10/2014 |
1857 | 2*10^179602+63 | 179603 | Robert Price | 05/2018 |
1858 | (25*10^179488-403)/9 | 179489 | Robert Price | 01/2021 |
1859 | 7*10^179460+99 | 179461 | Robert Price | 05/2021 |
1860 | 3^375887-112696 | 179344 | Enzo Doria | 07/2014 |
1861 | 4*10^179265-71 | 179266 | Robert Price | 12/2018 |
1862 | 2*10^179193+83 | 179194 | Robert Price | 12/2021 |
1863 | 2^595144-1850429 | 179157 | Enzo Doria | 08/2015 |
1864 | 2^595122-5 | 179150 | Stefano Morozzi | 07/2022 |
1865 | 3*10^179138+89 | 179139 | Robert Price | 10/2018 |
1866 | (52*10^179062-133)/9 | 179063 | Robert Price | 09/2021 |
1867 | 2^594531+82253 | 178972 | Enzo Doria | 09/2016 |
1868 | (664*10^178939-61)/9 | 178941 | Robert Price | 09/2021 |
1869 | 2^594260-2787899 | 178891 | Enzo Doria | 11/2015 |
1870 | (14*10^178822+67)/9 | 178823 | Robert Price | 05/2022 |
1871 | (29*10^178732-119)/9 | 178733 | Robert Price | 12/2021 |
1872 | 2^593631+101381 | 178701 | Jorge Menendez | 04/2018 |
1873 | 10^178695+136719 | 178696 | Patrick De Geest | 05/2016 |
1874 | 10^178695-71 | 178695 | Serge Batalov | 12/2014 |
1875 | (2*10^178649-161)/3 | 178649 | Robert Price | 12/2020 |
1876 | (691^62903-1)/690 | 178609 | Michael Stocker | 05/2020 |
1877 | (2^148330+1)^4-2 | 178608 | Cletus Emmanuel | 12/2003 |
1878 | 2^593222-14145 | 178578 | Jorge Menendez | 10/2017 |
1879 | 7*10^178566+33 | 178567 | Robert Price | 06/2020 |
1880 | 2^593178+1867219 | 178565 | Enzo Doria | 03/2016 |
1881 | (38*10^178456+151)/9 | 178457 | Robert Price | 03/2022 |
1882 | (302*10^178369+13)/9 | 178371 | Robert Price | 02/2020 |
1883 | (26*10^178296-113)/3 | 178297 | Robert Price | 06/2020 |
1884 | (18^142031-1)/17 | 178287 | Paul Bourdelais | 03/2010 |
1885 | (13*10^178233+137)/3 | 178234 | Robert Price | 06/2021 |
1886 | (5*10^178206+91)/3 | 178207 | Robert Price | 04/2018 |
1887 | 2^591872-291929 | 178172 | Enzo Doria | 07/2015 |
1888 | 2^591682-286871 | 178115 | Enzo Doria | 07/2015 |
1889 | 4*10^178091+9 | 178092 | Robert Price | 05/2015 |
1890 | 410747#+478483 | 178007 | Makoto Morimoto | 02/2016 |
1891 | 3*10^177872+73 | 177873 | Robert Price | 08/2018 |
1892 | 2^590762-396765 | 177838 | Enzo Doria | 08/2013 |
1893 | (136*10^177754-1)/9 | 177756 | Serge Batalov | 12/2014 |
1895 | ReverseConsecutiveIntegerPrime(37765) | 177719 | Eric W. Weisstein | 04/2010 |
1894 | Smr(37765) | 177719 | Eric W. Weisstein | 12/2021 |
1896 | (266*10^177577-11)/3 | 177579 | Robert Price | 04/2020 |
1897 | (11*10^177466-113)/3 | 177467 | Robert Price | 10/2018 |
1898 | 3*10^177373-97 | 177374 | Robert Price | 07/2018 |
1899 | 2^589204+1881151 | 177369 | Enzo Doria | 11/2016 |
1900 | 2^589132-69479 | 177347 | Enzo Doria | 01/2016 |
1901 | (101*10^177302-17)/3 | 177304 | Robert Price | 02/2020 |
1902 | 2^588912-113519 | 177281 | Enzo Doria | 08/2014 |
1903 | (682*10^177266-7)/9 | 177268 | Robert Price | 08/2021 |
1904 | 15^150706+2 | 177245 | Robert Price | 06/2015 |
1905 | 2^588194-1861001 | 177065 | Enzo Doria | 11/2015 |
1906 | 5*10^177016-37 | 177017 | Robert Price | 11/2021 |
1907 | (23*10^176964-47)/3 | 176965 | Robert Price | 09/2019 |
1908 | 20530^41031+41031^20530 | 176942 | Norbert Schneider | 07/2022 |
1909 | (19*10^176932+521)/9 | 176933 | Robert Price | 05/2018 |
1910 | (8*10^176908+43)/3 | 176909 | Robert Price | 06/2018 |
1911 | (85*10^176900+203)/9 | 176901 | Robert Price | 09/2020 |
1912 | 2^587560-113699 | 176874 | Enzo Doria | 09/2014 |
1913 | 20596^40995+40995^20596 | 176844 | Norbert Schneider | 07/2022 |
1914 | (101*10^176815-17)/3 | 176817 | Robert Price | 02/2020 |
1915 | (25*10^176715-37)/3 | 176716 | Robert Price | 10/2019 |
1916 | 5^252763-12862 | 176674 | Enzo Doria | 05/2014 |
1917 | 38442^38531+38531^38442 | 176658 | Norbert Schneider | 09/2022 |
1918 | 2^586804+81721 | 176646 | Enzo Doria | 08/2016 |
1919 | (10^176584+77)/3 | 176584 | Robert Price | 01/2018 |
1920 | 2^586570+1874419 | 176576 | Enzo Doria | 06/2016 |
1921 | (157*10^176482-1)/3 | 176484 | Robert Price | 01/2022 |
1922 | 2^585994-3311 | 176402 | Yves Minet | 12/2014 |
1923 | 8*10^176383-81 | 176384 | Robert Price | 02/2021 |
1924 | (23*10^176357+61)/3 | 176358 | Robert Price | 01/2022 |
1925 | 2^585832-112799 | 176354 | Enzo Doria | 07/2014 |
1926 | (29*10^176240+49)/3 | 176241 | Robert Price | 09/2021 |
1927 | (2^585387-11)/3 | 176219 | Stefano Morozzi | 08/2022 |
1928 | 2^585336-461039 | 176204 | Enzo Doria | 06/2015 |
1929 | (25*10^176164+143)/3 | 176165 | Robert Price | 08/2020 |
1930 | 2^585095-1848127 | 176132 | Enzo Doria | 08/2015 |
1931 | (5*10^176101-311)/9 | 176101 | Robert Price | 12/2021 |
1932 | 6*10^176092+77 | 176093 | Robert Price | 06/2020 |
1933 | 2^584950-115451 | 176088 | Enzo Doria | 07/2015 |
1934 | (646*10^176044+11)/9 | 176046 | Robert Price | 10/2021 |
1935 | 2^584671-3697 | 176004 | Yves Minet | 03/2017 |
1936 | (13*10^175965-37)/3 | 175966 | Robert Price | 01/2019 |
1937 | 2*10^175860-87 | 175861 | Robert Price | 04/2018 |
1938 | (86*10^175774-221)/9 | 175775 | Robert Price | 09/2019 |
1939 | 9*10^175654+47 | 175655 | Robert Price | 01/2022 |
1940 | 10^175608+2971 | 175609 | Mike Oakes | 05/2010 |
1941 | 10^175608-55829 | 175608 | Patrick De Geest | 09/2013 |
1942 | 2^583051+1879793 | 175516 | Enzo Doria | 09/2016 |
1943 | (76*10^175514+491)/9 | 175515 | Robert Price | 10/2021 |
1944 | 2^582860-23829 | 175459 | Enzo Doria | 08/2013 |
1945 | (8*10^175428-53)/9 | 175428 | Serge Batalov | 11/2022 |
1946 | (28*10^175417-67)/3 | 175418 | Robert Price | 10/2020 |
1947 | 2^582670-23913 | 175402 | Enzo Doria | 08/2013 |
1948 | 2^582573-29563 | 175372 | Enzo Doria | 08/2015 |
1949 | 2^582435-1862767 | 175331 | Enzo Doria | 12/2015 |
1950 | 10^175295-40000001 | 175295 | Robert Price | 07/2022 |
1951 | (11*10^175250-149)/3 | 175251 | Robert Price | 09/2018 |
1952 | (29*10^175236+31)/3 | 175237 | Robert Price | 04/2021 |
1953 | 2^582072-1848599 | 175222 | Enzo Doria | 08/2015 |
1954 | (404267#+465)/(3^4*5^2*31) | 175208 | Makoto Morimoto | 06/2019 |
1955 | Phi(262767,10)/259613797 | 175168 | Makoto Kamada | 12/2022 |
1956 | (2^581871-15)/7 | 175160 | Stefano Morozzi | 08/2022 |
1957 | (5*10^175117-311)/9 | 175117 | Robert Price | 12/2021 |
1958 | (220221^32768+1)/2 | 175075 | Serge Batalov | 03/2018 |
1959 | 2^581560+1874911 | 175068 | Enzo Doria | 06/2016 |
1960 | (25*10^174987-97)/9 | 174988 | Robert Price | 01/2022 |
1961 | (75^93307-1)/74 | 174955 | Paul Bourdelais | 09/2017 |
1962 | (47*10^174790+493)/9 | 174791 | Robert Price | 03/2019 |
1963 | 2^580528-114035 | 174757 | Enzo Doria | 11/2014 |
1964 | (19*10^174754+737)/9 | 174755 | Robert Price | 07/2018 |
1965 | (35*10^174704-377)/9 | 174705 | Robert Price | 07/2018 |
1967 | (49*10^174681+293)/9 | 174682 | Robert Price | 03/2021 |
1966 | 6*10^174681+11 | 174682 | Robert Price | 07/2022 |
1968 | 3*10^174665-97 | 174666 | Robert Price | 07/2018 |
1969 | 2^580046-459161 | 174612 | Enzo Doria | 05/2015 |
1970 | 2^579992-39779 | 174595 | Enzo Doria | 09/2015 |
1971 | (29*10^174481-149)/3 | 174482 | Robert Price | 08/2022 |
1972 | (4*10^174423+101)/3 | 174424 | Robert Price | 11/2021 |
1973 | (2^579371-17)/3 | 174408 | Stefano Morozzi | 08/2022 |
1974 | (2*10^174301-71)/3 | 174301 | Robert Price | 12/2017 |
1975 | 14^152048+3 | 174267 | Paul Bourdelais | 12/2020 |
1976 | (2^578696+1)/257 | 174203 | Lelio R Paula | 09/2015 |
1977 | 2^578656-1851809 | 174193 | Enzo Doria | 08/2015 |
1978 | 2^578583-113917 | 174171 | Enzo Doria | 10/2014 |
1979 | 2^578434-83 | 174126 | Yves Minet | 07/2017 |
1980 | 15^148048-2 | 174118 | Robert Price | 06/2015 |
1981 | 5*10^174101+81 | 174102 | Robert Price | 03/2019 |
1982 | 2^578346+2794249 | 174100 | Enzo Doria | 03/2016 |
1983 | 10^173947+1372429 | 173948 | Patrick De Geest | 08/2021 |
1985 | 10^173947-500000001 | 173947 | Robert Price | 12/2020 |
1984 | 10^173947-286391 | 173947 | Patrick De Geest | 08/2021 |
1986 | 5*10^173904-13 | 173905 | Robert Price | 01/2019 |
1987 | (8*10^173862-59)/3 | 173863 | Robert Price | 08/2021 |
1988 | (71*10^173854-287)/9 | 173855 | Robert Price | 09/2019 |
1989 | (43*10^173826+101)/9 | 173827 | Robert Price | 11/2018 |
1990 | 2*10^173809-87 | 173810 | Robert Price | 04/2018 |
1991 | (2^577372-23)/7 | 173806 | Stefano Morozzi | 08/2022 |
1992 | (L!41532)/2 | 173772 | Serge Batalov | 07/2017 |
1993 | 2^577146-49877 | 173739 | Enzo Doria | 10/2015 |
1994 | 2^576889+49727 | 173661 | Enzo Doria | 09/2016 |
1995 | (167*10^173571-17)/3 | 173573 | Robert Price | 03/2020 |
1996 | 37803^37916+37916^37803 | 173562 | Norbert Schneider | 06/2022 |
1997 | 5*10^173534+29 | 173535 | Robert Price | 12/2020 |
1998 | (2^576551-1)/4612409/64758208321/242584327930759 | 173528 | Dario Alpern | 06/2014 |
1999 | 4*10^173509+99 | 173510 | Robert Price | 12/2020 |
2000 | (13*10^173467-37)/3 | 173468 | Robert Price | 01/2019 |