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 | 2^572592-114893 | 172368 | Enzo Doria | 05/2015 |
1752 | 4*10^172354-39 | 172355 | Robert Price | 09/2020 |
1753 | 37535^37674+37674^37535 | 172338 | Norbert Schneider | 05/2022 |
1754 | (11*10^172322-119)/9 | 172323 | Robert Price | 11/2021 |
1755 | 5^246497-4^246497 | 172295 | Jean-Louis Charton | 11/2008 |
1756 | (38^109037-1)/37 | 172254 | Paul Bourdelais | 10/2017 |
1757 | (4*10^172241+89)/3 | 172242 | Robert Price | 08/2021 |
1758 | 3*10^172219+73 | 172220 | Robert Price | 08/2018 |
1759 | A352736(15) | 172032 | Kellen Shenton | 05/2022 |
1760 | (36^110503+1)/37 | 171975 | Lelio R Paula | 04/2017 |
1761 | 8*10^171934+71 | 171935 | Robert Price | 05/2022 |
1762 | (11*10^171933+601)/9 | 171934 | Robert Price | 02/2022 |
1763 | (22*10^171929-73)/3 | 171930 | Robert Price | 04/2019 |
1764 | (49*10^171892-319)/9 | 171893 | Robert Price | 10/2021 |
1765 | 4*10^171891-63 | 171892 | Robert Price | 10/2018 |
1766 | 67*10^171882-9 | 171884 | Robert Price | 03/2021 |
1767 | 2^570980-2782289 | 171883 | Enzo Doria | 09/2015 |
1768 | (25*10^171849-37)/3 | 171850 | Robert Price | 10/2019 |
1769 | 10^171832+387909 | 171833 | Patrick De Geest | 08/2021 |
1770 | 10^171832-10001 | 171832 | Robert Price | 02/2021 |
1771 | (2^(12*47563+13)-9)/7 | 171818 | Kevin Acres | 11/2013 |
1772 | (74*10^171651-29)/9 | 171652 | Robert Price | 06/2022 |
1773 | (536*10^171601-23)/9 | 171603 | Robert Price | 02/2020 |
1774 | 7*10^171535-99 | 171536 | Robert Price | 06/2019 |
1775 | (28*10^171534+101)/3 | 171535 | Robert Price | 09/2020 |
1776 | 2^569563-1854607 | 171456 | Enzo Doria | 09/2015 |
1777 | 3*10^171391+59 | 171392 | Robert Price | 08/2018 |
1778 | (13*10^171306-37)/3 | 171307 | Robert Price | 01/2019 |
1779 | 8*10^171296+87 | 171297 | Robert Price | 10/2019 |
1780 | (55^98419-1)/54 | 171284 | Paul Bourdelais | 12/2017 |
1781 | (29*10^171275+67)/3 | 171276 | Robert Price | 12/2019 |
1782 | (194*10^171193+1)/3 | 171195 | Robert Price | 01/2022 |
1783 | 2^568642+1876129 | 171179 | Enzo Doria | 07/2016 |
1784 | 4*10^171146-47 | 171147 | Robert Price | 10/2021 |
1785 | (19*10^170970+131)/3 | 170971 | Robert Price | 06/2020 |
1786 | (46*10^170932+143)/9 | 170933 | Robert Price | 01/2019 |
1787 | (79*10^170901-1)/3 | 170903 | Robert Price | 02/2020 |
1788 | (58*10^170842+221)/9 | 170843 | Robert Price | 02/2017 |
1789 | (29*10^170830+583)/9 | 170831 | Robert Price | 06/2021 |
1790 | 3*10^170800+73 | 170801 | Robert Price | 08/2018 |
1791 | (29*10^170799-119)/9 | 170800 | Robert Price | 12/2021 |
1792 | 11^164009-270 | 170798 | Enzo Doria | 10/2012 |
1793 | 2*10^170767+41 | 170768 | Robert Price | 05/2018 |
1794 | 3^357706-112358 | 170670 | Enzo Doria | 07/2014 |
1795 | TheodorusPrime(170657) | 170657 | Eric W. Weisstein | 08/2013 |
1796 | 2^566871+1876163 | 170646 | Enzo Doria | 07/2016 |
1797 | (10657#+(404267#)/(10657#))/(1675379) | 170624 | Makoto Morimoto | 10/2017 |
1798 | 2^566496+7 | 170533 | Donovan Johnson | 07/2006 |
1799 | (7^201653+1)/8 | 170416 | Paul Bourdelais | 02/2010 |
1800 | 7*10^170348+33 | 170349 | Robert Price | 06/2020 |
1801 | 2^565183-352021 | 170138 | Enzo Doria | 07/2015 |
1802 | 2^565143-114457 | 170125 | Enzo Doria | 02/2015 |
1803 | 2^564976-49869 | 170075 | Enzo Doria | 10/2015 |
1804 | (7*10^169944+23)/3 | 169945 | Robert Price | 06/2020 |
1805 | (37*10^169943+251)/9 | 169944 | Robert Price | 09/2021 |
1806 | 2^564526-351401 | 169940 | Enzo Doria | 07/2015 |
1807 | 4*10^169759+19 | 169760 | Robert Price | 10/2018 |
1808 | 21^128327-20^128327 | 169677 | Jean-Louis Charton | 11/2014 |
1809 | 2^563583+89 | 169656 | Stefano Morozzi | 04/2021 |
1810 | (4*10^169559+83)/3 | 169560 | Robert Price | 02/2018 |
1811 | (194*10^169461-17)/3 | 169463 | Robert Price | 09/2020 |
1812 | 2^562749+2793047 | 169405 | Enzo Doria | 02/2016 |
1813 | (154*10^169337-1)/9 | 169339 | Serge Batalov | 12/2014 |
1814 | (109*10^169337+11)/3 | 169339 | Robert Price | 06/2022 |
1815 | (56*10^169311+691)/9 | 169312 | Robert Price | 05/2019 |
1816 | 2^562369-29503 | 169290 | Enzo Doria | 08/2015 |
1817 | (17*10^169283+19)/9 | 169284 | Robert Price | 03/2021 |
1818 | 8*10^169071+59 | 169072 | Robert Price | 11/2021 |
1819 | (10^169044+173)/3 | 169044 | Robert Price | 05/2021 |
1820 | (22*10^169019+383)/9 | 169020 | Robert Price | 05/2018 |
1821 | (64*10^168935+143)/9 | 168936 | Robert Price | 05/2021 |
1822 | (22*10^168906+47)/3 | 168907 | Robert Price | 06/2021 |
1823 | 5*10^168807+87 | 168808 | Robert Price | 02/2019 |
1824 | (77*10^168803-149)/9 | 168804 | Robert Price | 03/2022 |
1825 | 4*10^168788-47 | 168789 | Robert Price | 10/2021 |
1826 | (154*10^168781+17)/9 | 168783 | Robert Price | 06/2022 |
1827 | (418*10^168751-31)/9 | 168753 | Robert Price | 05/2022 |
1828 | (29*10^168711+691)/9 | 168712 | Robert Price | 08/2021 |
1829 | 2^560405-39943 | 168699 | Enzo Doria | 09/2015 |
1830 | (397*10^168634+17)/9 | 168636 | Robert Price | 03/2022 |
1831 | 89*10^168614-7 | 168616 | Robert Price | 04/2020 |
1832 | (23*10^168608-83)/3 | 168609 | Robert Price | 08/2019 |
1833 | (94*10^168541+11)/3 | 168543 | Robert Price | 04/2020 |
1834 | 2^559686-350471 | 168483 | Enzo Doria | 06/2015 |
1835 | 2^559672-1855889 | 168479 | Enzo Doria | 09/2015 |
1836 | (5*10^168379-473)/9 | 168379 | Robert Price | 01/2018 |
1837 | 2^559000-59939 | 168276 | Enzo Doria | 11/2015 |
1838 | (16*10^168181+41)/3 | 168182 | Robert Price | 03/2019 |
1839 | (19*10^168173+77)/3 | 168174 | Robert Price | 05/2019 |
1840 | (74*10^168170+529)/9 | 168171 | Robert Price | 02/2022 |
1841 | 2^558640-114149 | 168168 | Enzo Doria | 12/2014 |
1842 | 2^558498-1849277 | 168125 | Enzo Doria | 08/2015 |
1843 | 2^558476-1850249 | 168119 | Enzo Doria | 08/2015 |
1844 | (7*10^168067+71)/3 | 168068 | Robert Price | 05/2018 |
1845 | 2^558150-1852211 | 168020 | Enzo Doria | 08/2015 |
1846 | 2^558125-113661 | 168013 | Enzo Doria | 09/2014 |
1847 | 393^64747-392^64747 | 167980 | Jean-Louis Charton | 08/2012 |
1848 | (13*10^167911+179)/3 | 167912 | Robert Price | 11/2018 |
1849 | (26*10^167861-167)/3 | 167862 | Robert Price | 10/2019 |
1850 | 39^105456+2 | 167788 | Robert Price | 04/2015 |
1851 | (28^115877-1)/27 | 167691 | Paul Bourdelais | 12/2017 |
1852 | 10^167639+121911 | 167640 | Patrick De Geest | 07/2018 |
1853 | 10^167639-8001 | 167639 | Robert Price | 03/2018 |
1854 | 2^556504-462059 | 167525 | Enzo Doria | 07/2015 |
1855 | (88*10^167522-637)/9 | 167523 | Robert Price | 11/2020 |
1856 | 5*10^167510+9 | 167511 | Robert Price | 08/2015 |
1857 | 7*10^167437-93 | 167438 | Robert Price | 08/2020 |
1858 | 11^160663+6 | 167314 | Paul Bourdelais | 02/2021 |
1859 | (7*10^167308-493)/9 | 167308 | Robert Price | 04/2021 |
1860 | 2^555343+1874333 | 167175 | Enzo Doria | 06/2016 |
1861 | 2^555210-461261 | 167135 | Enzo Doria | 07/2015 |
1862 | 9*10^166996+59 | 166997 | Robert Price | 01/2020 |
1863 | (68*10^166976-329)/9 | 166977 | Robert Price | 03/2021 |
1864 | (64*10^166901+683)/9 | 166902 | Robert Price | 06/2022 |
1865 | 2^554372+1880527 | 166883 | Enzo Doria | 11/2016 |
1866 | 2^554299+72173 | 166861 | Enzo Doria | 04/2016 |
1867 | (185*10^166837+7)/3 | 166839 | Robert Price | 03/2020 |
1868 | (14*10^166813+139)/9 | 166814 | Robert Price | 11/2021 |
1869 | 2^554037-2797063 | 166782 | Enzo Doria | 03/2016 |
1870 | (49*10^166721-139)/9 | 166722 | Robert Price | 03/2019 |
1871 | 2*10^166646+69 | 166647 | Robert Price | 06/2020 |
1872 | 2^553484-29819 | 166616 | Enzo Doria | 08/2015 |
1873 | (188*10^166611+7)/3 | 166613 | Robert Price | 03/2020 |
1874 | 2^553383-2784217 | 166585 | Enzo Doria | 10/2015 |
1875 | 2^553069+76427 | 166491 | Enzo Doria | 05/2016 |
1876 | 2*10^166458+51 | 166459 | Robert Price | 05/2018 |
1877 | 589^60089-588^60089 | 166454 | Jean-Louis Charton | 09/2012 |
1878 | 11^159756-2424 | 166369 | Mike Oakes | 06/2010 |
1879 | 2^552649-361275 | 166364 | Enzo Doria | 05/2014 |
1880 | 2^552628-113669 | 166358 | Enzo Doria | 09/2014 |
1881 | (19*10^166325+137)/3 | 166326 | Robert Price | 03/2022 |
1882 | 10^166324+550603 | 166325 | Patrick De Geest | 07/2018 |
1883 | 10^166324-801 | 166324 | Robert Price | 02/2018 |
1884 | (85*10^166297-1)/3 | 166299 | Robert Price | 02/2020 |
1885 | 8*10^166227+87 | 166228 | Robert Price | 10/2019 |
1886 | 2^552137+1879397 | 166210 | Enzo Doria | 09/2016 |
1887 | (103*10^166126+11)/3 | 166128 | Robert Price | 01/2021 |
1888 | (22*10^166077+179)/3 | 166078 | Robert Price | 02/2022 |
1889 | (23^121949-1)/22 | 166061 | Paul Bourdelais | 10/2017 |
1890 | 2^551542+19249 | 166031 | Payam Samidoost | 08/2002 |
1891 | 2^551535-23821 | 166029 | Enzo Doria | 08/2013 |
1892 | 2^551507-23557 | 166021 | Enzo Doria | 08/2013 |
1893 | 10^165947-7000000001 | 165947 | Robert Price | 12/2021 |
1894 | 4*10^165938-47 | 165939 | Robert Price | 10/2021 |
1895 | 7*10^165916-3 | 165917 | Robert Price | 08/2015 |
1896 | (29*10^165796+67)/3 | 165797 | Robert Price | 12/2019 |
1897 | 81^86837-80^86837 | 165728 | Robert Price | 01/2015 |
1898 | (71*10^165663-539)/9 | 165664 | Robert Price | 07/2019 |
1899 | 2^550270-69551 | 165648 | Enzo Doria | 12/2015 |
1900 | (202*10^165569-13)/9 | 165571 | Robert Price | 01/2020 |
1901 | 2^550000-23625 | 165567 | Enzo Doria | 08/2013 |
1902 | 2^549675-1852057 | 165469 | Enzo Doria | 08/2015 |
1903 | (529*10^165394-7)/9 | 165396 | Robert Price | 08/2021 |
1904 | -tau(103^14938) | 165374 | Nik Lygeros / Olivier Rozier | 10/2013 |
1905 | (28*10^165358-1)/9 | 165359 | Serge Batalov | 10/2014 |
1906 | 2^549278+1879669 | 165350 | Enzo Doria | 09/2016 |
1907 | (7*10^165350-439)/9 | 165350 | Robert Price | 02/2018 |
1908 | 2^549252-351269 | 165342 | Enzo Doria | 06/2015 |
1909 | 67*10^165327-9 | 165329 | Robert Price | 03/2021 |
1911 | (14*10^165282+73)/3 | 165283 | Robert Price | 12/2018 |
1910 | (8*10^165283-629)/9 | 165283 | Robert Price | 01/2022 |
1912 | 2^549049+2797607 | 165281 | Enzo Doria | 04/2016 |
1913 | (218*10^165258+7)/9 | 165260 | Robert Price | 06/2022 |
1914 | (7*10^165239+107)/3 | 165240 | Robert Price | 02/2018 |
1915 | (44^100511-1)/43 | 165184 | Paul Bourdelais | 11/2017 |
1916 | (7*10^165134+107)/3 | 165135 | Robert Price | 02/2018 |
1917 | (301*10^165082+23)/9 | 165084 | Robert Price | 06/2021 |
1918 | (23*10^165060-83)/3 | 165061 | Robert Price | 08/2019 |
1919 | (76*10^164984+77)/9 | 164985 | Robert Price | 10/2019 |
1920 | (4*10^164929-211)/9 | 164929 | Robert Price | 03/2022 |
1921 | 10^164878-500001 | 164878 | Robert Price | 03/2022 |
1922 | 9*10^164791-89 | 164792 | Robert Price | 04/2020 |
1923 | 2^547178-1856501 | 164717 | Enzo Doria | 10/2015 |
1924 | 11^158160-60 | 164707 | Enzo Doria | 07/2012 |
1925 | (26*10^164643-167)/3 | 164644 | Robert Price | 10/2019 |
1926 | (10^164643+83)/3 | 164643 | Robert Price | 08/2021 |
1927 | 2^546398-59201 | 164483 | Enzo Doria | 10/2015 |
1928 | 2^546332-114893 | 164463 | Enzo Doria | 05/2015 |
1929 | (65*10^164427+277)/9 | 164428 | Robert Price | 08/2021 |
1930 | 2^545958+1876189 | 164350 | Enzo Doria | 07/2016 |
1931 | 2^545878-49841 | 164326 | Enzo Doria | 10/2015 |
1932 | (10^164284+77)/3 | 164284 | Robert Price | 01/2018 |
1933 | 2^545668-4019 | 164263 | Yves Minet | 04/2017 |
1934 | 10^164216+780639 | 164217 | Patrick De Geest | 08/2021 |
1936 | 10^164216-50000000001 | 164216 | Robert Price | 12/2020 |
1935 | 10^164216-891051 | 164216 | Patrick De Geest | 08/2021 |
1937 | (13*53^238539*617^9)/10^247183 | 164151 | Hans Havermann | 07/2017 |
1938 | (16*10^164122+197)/3 | 164123 | Robert Price | 04/2019 |
1939 | 2^545185+76757 | 164118 | Enzo Doria | 05/2016 |
1940 | 2^545076-114329 | 164085 | Enzo Doria | 01/2015 |
1941 | (2*10^164043-143)/3 | 164043 | Robert Price | 03/2018 |
1942 | (29^112153+1)/30 | 164011 | Lelio R Paula | 03/2017 |
1943 | 2^544757+1874777 | 163989 | Enzo Doria | 06/2016 |
1944 | 2^544444-457199 | 163894 | Enzo Doria | 01/2015 |
1945 | 2^544264-343529 | 163840 | Enzo Doria | 07/2015 |
1946 | 7*10^163780+9 | 163781 | Robert Price | 09/2015 |
1947 | 2^543989+2793047 | 163758 | Enzo Doria | 02/2016 |
1948 | (28*10^163709+113)/3 | 163710 | Robert Price | 03/2020 |
1949 | (23*10^163523+301)/9 | 163524 | Robert Price | 06/2021 |
1950 | (68*10^163521-329)/9 | 163522 | Robert Price | 03/2021 |
1951 | 35820^35899+35899^35820 | 163489 | Norbert Schneider | 11/2021 |
1952 | 2^542870-69551 | 163421 | Enzo Doria | 12/2015 |
1953 | 2^542395+72533 | 163278 | Enzo Doria | 04/2016 |
1954 | 2^542072-3683 | 163180 | Yves Minet | 03/2017 |
1955 | (682*10^163106-7)/9 | 163108 | Robert Price | 08/2021 |
1956 | 2^541779-1867357 | 163092 | Enzo Doria | 04/2016 |
1957 | (29*10^163056+313)/9 | 163057 | Robert Price | 04/2021 |
1958 | 8*10^162924+9 | 162925 | Robert Price | 12/2015 |
1959 | 2^540905+81557 | 162829 | Enzo Doria | 08/2016 |
1960 | 2^540628-2939 | 162746 | Yves Minet | 09/2014 |
1961 | 919^54919-918^54919 | 162743 | Jean-Louis Charton | 01/2013 |
1962 | (203*10^162689+1)/3 | 162691 | Robert Price | 03/2020 |
1963 | 3*10^162620-59 | 162621 | Robert Price | 09/2018 |
1964 | 3^340694-112960 | 162553 | Enzo Doria | 07/2014 |
1965 | 2^539807-114081 | 162499 | Enzo Doria | 12/2014 |
1966 | 414^62093+62093^414 | 162498 | Norbert Schneider | 03/2022 |
1967 | 2^539654-114893 | 162453 | Enzo Doria | 05/2015 |
1968 | 9*10^162449-71 | 162450 | Robert Price | 11/2020 |
1969 | 2^539617-1851583 | 162441 | Enzo Doria | 08/2015 |
1970 | (91*10^162410+11)/3 | 162412 | Robert Price | 02/2020 |
1971 | 2^539346+81049 | 162360 | Enzo Doria | 07/2016 |
1972 | 2^539220-115499 | 162322 | Enzo Doria | 07/2015 |
1973 | 2^539217-113713 | 162321 | Enzo Doria | 09/2014 |
1974 | 9^170099-8^170099 | 162316 | Jean-Louis Charton | 05/2005 |
1975 | 4*10^162263-39 | 162264 | Robert Price | 09/2020 |
1976 | (115*10^162153-1)/3 | 162155 | Serge Batalov | 12/2014 |
1977 | (10^162138+11)/3 | 162138 | Serge Batalov | 07/2015 |
1978 | (61*10^162100-403)/9 | 162101 | Robert Price | 10/2021 |
1979 | 2^538473-112723 | 162097 | Enzo Doria | 06/2014 |
1980 | 2^538157+79337 | 162002 | Enzo Doria | 06/2016 |
1981 | 2^538136-114749 | 161996 | Enzo Doria | 05/2015 |
1982 | 2^538104+1531 | 161986 | Lelio R Paula | 01/2013 |
1983 | (9*29^110727-1199)/14 | 161927 | Curtis Bright | 05/2015 |
1984 | 2^537815-22737 | 161899 | Enzo Doria | 07/2013 |
1985 | 2^537804-39839 | 161896 | Enzo Doria | 09/2015 |
1986 | (754*10^161816-7)/9 | 161818 | Robert Price | 05/2020 |
1987 | 2^537458-59201 | 161791 | Enzo Doria | 10/2015 |
1988 | 2*10^161766+51 | 161767 | Robert Price | 05/2018 |
1989 | (7*10^161760+131)/3 | 161761 | Robert Price | 06/2020 |
1990 | 2^537209-49849 | 161717 | Enzo Doria | 10/2015 |
1991 | (58*10^161691+329)/9 | 161692 | Robert Price | 05/2019 |
1992 | 23*10^161668-3 | 161670 | Robert Price | 10/2021 |
1993 | 2^536937+1879397 | 161635 | Enzo Doria | 09/2016 |
1994 | 34*10^161593-9 | 161595 | Robert Price | 06/2020 |
1995 | (31*10^161582-1)/3 | 161584 | Robert Price | 02/2020 |
1996 | 2^536569-22881 | 161524 | Enzo Doria | 07/2013 |
1997 | (46*10^161505+593)/9 | 161506 | Robert Price | 04/2022 |
1998 | 10^161253+573493 | 161254 | Patrick De Geest | 07/2018 |
1999 | 10^161253-8001 | 161253 | Robert Price | 03/2018 |
2000 | 97*10^161247-3 | 161249 | Robert Price | 05/2020 |