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 | (14*10^154773+37)/3 | 154774 | Robert Price | 12/2018 |
1752 | 6*10^154742-31 | 154743 | Robert Price | 07/2020 |
1753 | 2^513437+1879337 | 154560 | Enzo Doria | 09/2016 |
1754 | 2^513306-113201 | 154521 | Enzo Doria | 07/2014 |
1755 | (10^154494-13)/3 | 154494 | Robert Price | 12/2017 |
1756 | 2^513042-113787 | 154442 | Enzo Doria | 09/2014 |
1757 | (151*10^154434-7)/9 | 154436 | Robert Price | 01/2020 |
1758 | 2^512628-114053 | 154317 | Enzo Doria | 11/2014 |
1759 | 2^512529-49783 | 154287 | Enzo Doria | 10/2015 |
1760 | (355573#+6991)/(6991*2031599) | 154285 | Makoto Morimoto | 06/2019 |
1761 | 2^512315-115297 | 154223 | Enzo Doria | 06/2015 |
1762 | 2^512168+79561 | 154178 | Enzo Doria | 06/2016 |
1763 | 4*10^154078-57 | 154079 | Robert Price | 10/2018 |
1764 | (355049#+1859)/(11*13*10148891*62587751) | 154051 | Makoto Morimoto | 06/2019 |
1765 | 7*10^154038-57 | 154039 | Robert Price | 06/2020 |
1766 | 2^511658-114371 | 154025 | Enzo Doria | 02/2015 |
1767 | (57^87719+1)/58 | 154022 | Paul Bourdelais | 11/2017 |
1768 | 2^511580-1846679 | 154001 | Enzo Doria | 07/2015 |
1769 | (259*10^153998-1)/3 | 154000 | Robert Price | 12/2020 |
1770 | 2^511541-113713 | 153990 | Enzo Doria | 09/2014 |
1771 | 49958^32768+49957^32768 | 153965 | Kellen Shenton | 11/2020 |
1772 | 10^153935-1000001 | 153935 | Robert Price | 08/2020 |
1773 | (16*10^153868-73)/3 | 153869 | Robert Price | 07/2020 |
1774 | 9*10^153851-67 | 153852 | Robert Price | 11/2020 |
1775 | 2^511077-112723 | 153850 | Enzo Doria | 06/2014 |
1776 | 69^83653-68^83653 | 153826 | Robert Price | 12/2013 |
1777 | 2^510963-113707 | 153816 | Enzo Doria | 09/2014 |
1778 | (154*10^153810-1)/9 | 153812 | Serge Batalov | 12/2014 |
1779 | (181*25^109991-75077)/8 | 153763 | Curtis Bright | 05/2015 |
1780 | 2*10^153746-3 | 153747 | Robert Price | 07/2015 |
1781 | 2^510626+1179379 | 153714 | Enzo Doria | 05/2016 |
1782 | (7*10^153664+113)/3 | 153665 | Robert Price | 02/2018 |
1783 | 2^510420+81121 | 153652 | Enzo Doria | 07/2016 |
1784 | (197*7^181761-1)/2 | 153608 | Karsten Bonath | 05/2017 |
1785 | 2^509894-459161 | 153494 | Enzo Doria | 05/2015 |
1786 | 2^509841+71657 | 153478 | Enzo Doria | 04/2016 |
1787 | 9*10^153446+41 | 153447 | Robert Price | 08/2020 |
1788 | 2^509533-1846723 | 153385 | Enzo Doria | 07/2015 |
1789 | 2^509468-39989 | 153366 | Enzo Doria | 09/2015 |
1790 | 70^83117-69^83117 | 153360 | Robert Price | 01/2014 |
1791 | (112*10^153025-1)/3 | 153027 | Serge Batalov | 12/2014 |
1792 | (19*10^153010+131)/3 | 153011 | Robert Price | 06/2020 |
1793 | 2^508174-1855151 | 152976 | Enzo Doria | 09/2015 |
1794 | 181^67757-2 | 152974 | Lelio R Paula | 12/2017 |
1795 | 2^508160-1864829 | 152972 | Enzo Doria | 01/2016 |
1796 | 10^152960-50000000001 | 152960 | Robert Price | 12/2020 |
1797 | 2^507857-1848199 | 152881 | Enzo Doria | 07/2015 |
1798 | 2^507638-115361 | 152815 | Enzo Doria | 07/2015 |
1799 | 2^507551-114025 | 152789 | Enzo Doria | 11/2014 |
1800 | (6^196337+1)/7 | 152780 | Paul Bourdelais | 02/2010 |
1801 | (22*10^152670-13)/9 | 152671 | Robert Price | 06/2018 |
1802 | 2^506451-22339 | 152457 | Enzo Doria | 07/2013 |
1803 | 2^505995-113185 | 152320 | Enzo Doria | 07/2014 |
1804 | (4*10^152253+149)/9 | 152253 | Robert Price | 04/2018 |
1805 | 578^55117-577^55117 | 152230 | Jean-Louis Charton | 08/2012 |
1806 | 2^505431-505431 | 152150 | Henri Lifchitz | 04/2005 |
1807 | (203*10^152143+1)/3 | 152145 | Robert Price | 03/2020 |
1808 | 2^505053+73097 | 152037 | Enzo Doria | 04/2016 |
1809 | 22*10^151998+3 | 152000 | Robert Price | 01/2020 |
1810 | (238*10^151979-1)/3 | 151981 | Robert Price | 04/2020 |
1811 | (2^504793-7)/46765 | 151954 | Lelio R Paula | 12/2017 |
1812 | 350377#+797581 | 151937 | Nicolas PALAU | 08/2017 |
1813 | 2^504618-343991 | 151906 | Enzo Doria | 07/2015 |
1814 | 2^504212-461939 | 151783 | Enzo Doria | 07/2015 |
1815 | 2^504054-2231 | 151736 | Yves Minet | 10/2011 |
1816 | (28*10^151682+191)/3 | 151683 | Robert Price | 02/2020 |
1817 | 2^503361-39883 | 151527 | Enzo Doria | 09/2015 |
1818 | 2^503225+382667 | 151486 | Enzo Doria | 10/2016 |
1819 | (26*10^151391-503)/9 | 151392 | Robert Price | 07/2018 |
1820 | 2^502769+1877567 | 151349 | Enzo Doria | 08/2016 |
1821 | 2^502576-4019 | 151291 | Yves Minet | 10/2011 |
1822 | 5*10^151257+41 | 151258 | Robert Price | 03/2019 |
1823 | 2^502290-2792501 | 151205 | Enzo Doria | 02/2016 |
1824 | 2^502181+1868417 | 151172 | Enzo Doria | 04/2016 |
1825 | 2^501781-1850503 | 151052 | Enzo Doria | 08/2015 |
1826 | (5*10^151007+37)/3 | 151008 | Robert Price | 03/2018 |
1827 | 2^501627-991 | 151005 | Yves Minet | 02/2014 |
1828 | 2^501577-115333 | 150990 | Enzo Doria | 07/2015 |
1829 | 8*10^150975+3 | 150976 | Robert Price | 08/2015 |
1830 | 2^501512-113669 | 150971 | Enzo Doria | 09/2014 |
1831 | (12^139739+1)/13 | 150803 | Paul Bourdelais | 09/2011 |
1832 | (31^101111-1)/30 | 150792 | Alexander Zhirkov | 11/2010 |
1833 | 2^500899-500899 | 150786 | Henri Lifchitz | 04/2005 |
1834 | 2^500832+1876801 | 150766 | Enzo Doria | 07/2016 |
1835 | (23*10^150763-59)/9 | 150764 | Robert Price | 05/2018 |
1836 | 2^500699+1884953 | 150726 | Enzo Doria | 02/2017 |
1837 | (13*10^150675-37)/3 | 150676 | Robert Price | 01/2019 |
1838 | (2^500527+lucasV(1,2,500527)+1)/4 | 150674 | Mike Oakes | 11/2016 |
1840 | 2^500337-71101 | 150617 | Enzo Doria | 04/2016 |
1839 | (74*10^150616+133)/9 | 150617 | Robert Price | 06/2019 |
1841 | 4*10^150577+91 | 150578 | Robert Price | 08/2018 |
1842 | 2^500160+80071 | 150564 | Enzo Doria | 06/2016 |
1843 | (2^500120+5)/9 | 150551 | Lelio R Paula | 12/2017 |
1844 | (43*10^150515-421)/9 | 150516 | Robert Price | 01/2019 |
1846 | (10^150551-1)/9/385207015049/57498437921/7808738631274081 | 150512 | Maksym Voznyy | 08/2014 |
1845 | (10^150551-1)/1556587827131683185788921941743157225041 | 150512 | Robert Price | 07/2016 |
1847 | 2^499861-29503 | 150474 | Enzo Doria | 08/2015 |
1848 | 2^499653-113533 | 150411 | Enzo Doria | 08/2014 |
1849 | (14*10^150391-191)/3 | 150392 | Robert Price | 10/2020 |
1850 | 2^499534-221 | 150375 | Yves Minet | 06/2012 |
1851 | 2^499225+49727 | 150282 | Enzo Doria | 09/2016 |
1852 | 2^499054-29261 | 150231 | Enzo Doria | 07/2015 |
1853 | (2^498898-7)/9 | 150183 | Lelio R Paula | 10/2015 |
1854 | 3*10^150182+17 | 150183 | Robert Price | 07/2018 |
1855 | 5*10^150175+63 | 150176 | Robert Price | 09/2020 |
1856 | 2^498623+1866983 | 150101 | Enzo Doria | 03/2016 |
1857 | (25*10^150050-403)/9 | 150051 | Robert Price | 12/2020 |
1858 | numbpart(18140942830) | 150033 | Serge Batalov | 04/2017 |
1859 | 10^150029+4381 | 150030 | Patrick De Geest | 05/2016 |
1860 | 10^150029-41 | 150029 | Serge Batalov | 12/2014 |
1861 | 10^150000+1158603 | 150001 | Patrick De Geest | 09/2018 |
1862 | 10^150000-245703 | 150000 | Patrick De Geest | 09/2018 |
1863 | (38*10^149999+691)/9 | 150000 | Robert Price | 10/2018 |
1864 | 2^498238-53 | 149985 | Lelio R Paula | 12/2017 |
1865 | 45728^1905+1905^45728 | 149984 | Hans Havermann | 10/2020 |
1866 | 5*10^149907+23 | 149908 | Robert Price | 03/2019 |
1867 | 39347^6442+6442^39347 | 149874 | Hans Havermann | 09/2020 |
1868 | 2^497850+81049 | 149868 | Enzo Doria | 07/2016 |
1869 | 37228^10575+10575^37228 | 149816 | Hans Havermann | 10/2020 |
1870 | (5*2^497673+1)/2743 | 149812 | Lelio R Paula | 10/2015 |
1871 | (5*2^497671+1)/373703 | 149810 | Lelio R Paula | 10/2015 |
1872 | (2*10^149803-143)/3 | 149803 | Robert Price | 03/2018 |
1873 | 33845^26604+26604^33845 | 149763 | Hans Havermann | 09/2020 |
1874 | 2^497434-2784191 | 149743 | Enzo Doria | 10/2015 |
1875 | (865*10^149737-1)/9 | 149739 | Robert Price | 04/2020 |
1876 | 38237^8214+8214^38237 | 149681 | Hans Havermann | 09/2020 |
1877 | (23*10^149655+19)/3 | 149656 | Robert Price | 07/2019 |
1878 | 2^497068-113579 | 149633 | Enzo Doria | 08/2014 |
1879 | 2^497037+73727 | 149624 | Enzo Doria | 04/2016 |
1880 | 34942^19067+19067^34942 | 149562 | Hans Havermann | 09/2020 |
1881 | 33696^27449+27449^33696 | 149561 | Hans Havermann | 09/2020 |
1882 | 2^496773+77747 | 149544 | Enzo Doria | 05/2016 |
1883 | (206*10^149459+7)/3 | 149461 | Robert Price | 07/2020 |
1884 | 34589^20940+20940^34589 | 149459 | Hans Havermann | 09/2020 |
1885 | 2^496477-113485 | 149455 | Enzo Doria | 08/2014 |
1886 | ((10^74703-1)*10000/9+7481)*10^74703+(10^74703-1)/9 | 149410 | Hans Havermann | 09/2019 |
1887 | 2^496270-49451 | 149393 | Enzo Doria | 10/2015 |
1888 | 2^496238-1865081 | 149383 | Enzo Doria | 01/2016 |
1889 | 33831^26030+26030^33831 | 149380 | Hans Havermann | 09/2020 |
1890 | 34131^23780+23780^34131 | 149365 | Hans Havermann | 09/2020 |
1891 | (5*10^149335-53)/3 | 149336 | Robert Price | 09/2020 |
1892 | 2^495968-1853699 | 149302 | Enzo Doria | 09/2015 |
1893 | 2^495935-4117 | 149292 | Yves Minet | 02/2018 |
1894 | 35816^14709+14709^35816 | 149267 | Hans Havermann | 09/2020 |
1895 | 2^495712-396765 | 149225 | Enzo Doria | 07/2013 |
1896 | (21*2^495676-1)/4835 | 149211 | Lelio R Paula | 10/2015 |
1897 | 2^495420+1880701 | 149137 | Enzo Doria | 10/2016 |
1898 | 2^495337-1847293 | 149112 | Enzo Doria | 07/2015 |
1899 | (2^495193-7)/5 | 149068 | Lelio R Paula | 10/2015 |
1900 | 33282^30097+30097^33282 | 149055 | Hans Havermann | 09/2020 |
1901 | 37384^9705+9705^37384 | 149050 | Hans Havermann | 09/2020 |
1902 | 34808^19143+19143^34808 | 149049 | Hans Havermann | 09/2020 |
1903 | 413^56963-412^56963 | 149013 | Jean-Louis Charton | 08/2012 |
1904 | 47^89113-46^89113 | 149006 | Robert Price | 10/2012 |
1905 | 2^494916+87855 | 148985 | Lelio R Paula | 01/2016 |
1906 | 6*10^148982+73 | 148983 | Robert Price | 04/2019 |
1907 | 10^148934-1000000001 | 148934 | Robert Price | 11/2020 |
1908 | 39000^6571+6571^39000 | 148888 | Hans Havermann | 10/2020 |
1909 | 2^494586-2791991 | 148886 | Enzo Doria | 02/2016 |
1910 | 8*10^148860-3 | 148861 | Ray Chandler | 04/2011 |
1911 | 38262^7769+7769^38262 | 148854 | Hans Havermann | 10/2020 |
1912 | 2^494333-286183 | 148810 | Enzo Doria | 06/2015 |
1913 | 2^494144-264119 | 148753 | Enzo Doria | 05/2014 |
1914 | 36502^11823+11823^36502 | 148663 | Hans Havermann | 11/2020 |
1915 | (5*2^493838-1)/3721 | 148658 | Lelio R Paula | 10/2015 |
1916 | 64239^206+206^64239 | 148641 | Hans Havermann | 10/2020 |
1917 | (23*2^493761-1)/555 | 148636 | Lelio R Paula | 10/2015 |
1918 | (151*10^148601-1)/3 | 148603 | Robert Price | 03/2020 |
1919 | 2^493636+82081 | 148600 | Enzo Doria | 09/2016 |
1920 | ((((((((((((((34251^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2 | 148593 | Serge Batalov | 07/2016 |
1921 | 177487#+(519643#)/(177487#) | 148558 | Makoto Morimoto | 11/2017 |
1922 | (2*10^148460-23)/3 | 148460 | Robert Price | 04/2018 |
1923 | (28*10^148445+101)/3 | 148446 | Robert Price | 09/2020 |
1924 | 36203^12556+12556^36203 | 148391 | Hans Havermann | 10/2020 |
1925 | 33912^23749+23749^33912 | 148387 | Hans Havermann | 10/2020 |
1926 | (8*10^148328+1)/9 | 148328 | Serge Batalov | 05/2010 |
1927 | 34294^21117+21117^34294 | 148309 | Hans Havermann | 10/2020 |
1928 | (71*10^148306-539)/9 | 148307 | Robert Price | 07/2019 |
1929 | 38042^7875+7875^38042 | 148222 | Hans Havermann | 10/2020 |
1930 | 5^211959-12874 | 148153 | Enzo Doria | 05/2014 |
1931 | 34142^21831+21831^34142 | 148145 | Hans Havermann | 10/2020 |
1932 | 36303^12016+12016^36303 | 148108 | Hans Havermann | 10/2020 |
1933 | (16*10^148071+41)/3 | 148072 | Robert Price | 03/2019 |
1934 | 187^65175-2 | 148068 | Lelio R Paula | 11/2017 |
1935 | 2^491851+1871453 | 148062 | Enzo Doria | 05/2016 |
1936 | (68*10^148060-257)/9 | 148061 | Robert Price | 07/2019 |
1937 | (151*10^148020-1)/3 | 148022 | Robert Price | 03/2020 |
1938 | 39153^6032+6032^39153 | 148017 | Hans Havermann | 10/2020 |
1939 | 36798^10507+10507^36798 | 147983 | Hans Havermann | 12/2020 |
1940 | (26*10^147973-23)/3 | 147974 | Robert Price | 12/2019 |
1941 | 2^491521-1865323 | 147963 | Enzo Doria | 02/2016 |
1942 | (2^491476+7)/71 | 147948 | Lelio R Paula | 10/2015 |
1943 | 2^491391-7807 | 147924 | Lelio R Paula | 01/2013 |
1944 | 39736^5279+5279^39736 | 147920 | Hans Havermann | 11/2020 |
1945 | 2^491370-113297 | 147918 | Enzo Doria | 07/2014 |
1946 | (32760^32760+32759^32759)/95546586737133567708319 | 147900 | Robert Price | 07/2016 |
1947 | 44368^2155+2155^44368 | 147899 | Hans Havermann | 12/2020 |
1948 | (17*10^147890+79)/3 | 147891 | Robert Price | 04/2019 |
1949 | 94*10^147871-3 | 147873 | Robert Price | 05/2020 |
1950 | 10^147843-50000000001 | 147843 | Robert Price | 12/2020 |
1951 | 35805^13346+13346^35805 | 147709 | Hans Havermann | 11/2020 |
1952 | 2^490660-17 | 147704 | Lelio R Paula | 12/2017 |
1953 | (229*10^147699-1)/3 | 147701 | Robert Price | 07/2020 |
1954 | 40656^4289+4289^40656 | 147678 | Hans Havermann | 11/2020 |
1955 | 2^490550+1179439 | 147671 | Enzo Doria | 06/2016 |
1956 | (23*10^147649-59)/9 | 147650 | Robert Price | 05/2018 |
1957 | 2^490303+2793653 | 147596 | Enzo Doria | 03/2016 |
1958 | 199^64181-2 | 147543 | Lelio R Paula | 11/2017 |
1959 | 32849^30958+30958^32849 | 147518 | Hans Havermann | 11/2020 |
1960 | 2^489871-286987 | 147466 | Enzo Doria | 07/2015 |
1961 | 2^489864-351899 | 147464 | Enzo Doria | 07/2015 |
1962 | 175^65724-2 | 147422 | Lelio R Paula | 11/2017 |
1963 | 2^489712+1874851 | 147419 | Enzo Doria | 06/2016 |
1964 | 34473^18830+18830^34473 | 147367 | Hans Havermann | 11/2020 |
1965 | 63^81896-2 | 147359 | Lelio R Paula | 10/2017 |
1966 | 34580^18237+18237^34580 | 147344 | Hans Havermann | 11/2020 |
1967 | (11*10^147313-107)/3 | 147314 | Robert Price | 09/2018 |
1968 | 2^489305-59815 | 147296 | Enzo Doria | 10/2015 |
1969 | (2^489280-7)/6381 | 147285 | Lelio R Paula | 09/2015 |
1970 | 33556^24457+24457^33556 | 147258 | Hans Havermann | 11/2020 |
1971 | 2^489125+80357 | 147242 | Enzo Doria | 06/2016 |
1972 | 32835^30452+30452^32835 | 147220 | Hans Havermann | 12/2020 |
1973 | (148*10^147139-1)/3 | 147141 | Robert Price | 03/2020 |
1974 | 34338^19255+19255^34338 | 147123 | Hans Havermann | 11/2020 |
1975 | 2^488648-112799 | 147098 | Enzo Doria | 07/2014 |
1976 | 2^488627-350317 | 147092 | Enzo Doria | 06/2015 |
1977 | 33432^25075+25075^33432 | 147076 | Hans Havermann | 12/2020 |
1978 | (2^488441-1)/(61543567*30051203516986199) | 147012 | Dario Alpern | 12/2014 |
1979 | 2^488280-2165 | 146987 | Yves Minet | 07/2014 |
1980 | 2^488278+45 | 146987 | Lelio R Paula | 12/2017 |
1981 | 2^487927-39 | 146881 | Lelio R Paula | 12/2017 |
1982 | (7*10^146860-13)/3 | 146861 | Robert Price | 07/2018 |
1983 | (26*10^146856-77)/3 | 146857 | Robert Price | 11/2019 |
1984 | 32948^28611+28611^32948 | 146834 | Hans Havermann | 11/2020 |
1985 | 42596^2799+2799^42596 | 146829 | Hans Havermann | 12/2020 |
1986 | 2^487726-1863341 | 146821 | Enzo Doria | 12/2015 |
1987 | 43838^2229+2229^43838 | 146775 | Hans Havermann | 11/2020 |
1988 | 35005^15594+15594^35005 | 146775 | Hans Havermann | 11/2020 |
1989 | ((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9 | 146728 | Hans Havermann | 09/2019 |
1990 | 32963^28234+28234^32963 | 146711 | Hans Havermann | 12/2020 |
1991 | (22*10^146661-19)/3 | 146662 | Robert Price | 04/2019 |
1992 | 33958^20825+20825^33958 | 146651 | Hans Havermann | 12/2020 |
1993 | 2^487121-39523 | 146639 | Enzo Doria | 09/2015 |
1994 | 61063^252+252^61063 | 146637 | Hans Havermann | 12/2020 |
1995 | (7*2^486967+1)/39 | 146591 | Lelio R Paula | 09/2015 |
1996 | 34099^19900+19900^34099 | 146587 | Hans Havermann | 11/2020 |
1997 | 2^486893-79 | 146570 | Yves Minet | 09/2017 |
1998 | 36818^9567+9567^36818 | 146565 | Hans Havermann | 12/2020 |
1999 | 2^486840+1879141 | 146554 | Enzo Doria | 08/2016 |
2000 | 2^486774-87 | 146534 | Lelio R Paula | 12/2017 |