PRP Records

Probable Primes Top 10000

(295461 PRPs in the top)

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) !!!

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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 1751 (2^704548-19)/3 212090 Stefano Morozzi 08/2022 1752 2^704110-2792441 211959 Enzo Doria 02/2016 1753 2^704084+28531 211951 Enzo Doria 02/2024 1754 2^703943-1862947 211908 Enzo Doria 12/2015 1755 (60^119083+1)/61 211746 Paul Bourdelais 10/2018 1756 (184*10^211682-1)/3 211684 Robert Price 12/2022 1757 (10^211610-91)/9 211610 Serge Batalov 12/2014 1758 227^89797+2 211565 Lelio R Paula 08/2012 1759 2^702194-3 211382 Paul Bourdelais 03/2012 1760 2^702064+1874911 211343 Enzo Doria 07/2016 1761 2^701968-113873 211314 Enzo Doria 10/2014 1762 (14*10^211262-41)/9 211263 Serge Batalov 01/2023 1763 2^701713-113779 211237 Enzo Doria 09/2014 1764 2^701616-216803 211208 Enzo Doria 01/2024 1765 2^701449-25201 211158 Enzo Doria 09/2013 1766 2^701403-2786977 211144 Enzo Doria 11/2015 1767 2^701189-25423 211079 Enzo Doria 09/2013 1768 2^701162-459161 211071 Enzo Doria 05/2015 1769 2^700793+219407 210960 Enzo Doria 03/2024 1770 (24^152783-1)/23 210872 Paul Bourdelais 04/2018 1771 2^700400+9385 210842 Lelio R Paula 01/2014 1772 2^700304-17 210813 Stefano Morozzi 07/2022 1773 2^700131+1874693 210761 Enzo Doria 06/2016 1774 (2^700095+225414)/2 210750 Stefano Morozzi 04/2020 1775 (2^700090+278254)/2 210748 Stefano Morozzi 04/2020 1776 (2^700075+303666)/2 210744 Stefano Morozzi 04/2020 1777 (2^700073+75882)/2 210743 Stefano Morozzi 04/2020 1778 (2^700074+328890)/2 210743 Stefano Morozzi 04/2020 1779 (2^700052+79162)/2 210737 Stefano Morozzi 04/2020 1780 (2^700052+304458)/2 210737 Stefano Morozzi 04/2020 1781 (2^700048+376578)/2 210736 Stefano Morozzi 04/2020 1782 11^202357-1140 210734 Enzo Doria 12/2012 1783 (2^700021+25874)/2 210728 Stefano Morozzi 04/2020 1784 (2^700018+377518)/2 210727 Stefano Morozzi 04/2020 1785 2^699999+300729 210721 Norman Luhn 09/2023 1786 (238*10^210712-1)/3 210714 Robert Price 09/2023 1787 2^699740+25 210643 Stefano Morozzi 05/2021 1788 (23*10^210525-143)/3 210526 Robert Price 12/2023 1789 2^698929-2788423 210399 Enzo Doria 11/2015 1790 (5^300893+4^300893)/9 210315 Jean-Louis Charton 11/2011 1791 2^698316+1878601 210215 Enzo Doria 08/2016 1792 34*10^210097-9 210099 Robert Price 05/2023 1793 (19*10^210011-49)/3 210012 Robert Price 06/2023 1794 6*10^209846-91 209847 Robert Price 05/2023 1795 2^697036+1878751 209829 Enzo Doria 08/2016 1796 2^696813+28607 209762 Enzo Doria 02/2024 1797 (238*10^209715-1)/3 209717 Robert Price 09/2023 1798 6^269407+5 209640 Paul Bourdelais 02/2021 1799 (2^696343-1)/11141489/36009913139329 209600 Tony Prest / Never Odd Or Even 02/2014 1800 2^696254-115151 209594 Enzo Doria 06/2015 1801 (35^135623+1)/36 209410 Paul Bourdelais 07/2018 1802 7*10^209161+39 209162 Robert Price 01/2023 1803 2^694633+1887257 209106 Enzo Doria 05/2017 1804 fibonacci(999790)-4 208944 Jon Grantham 08/2023 1805 2^693959+180923 208903 Enzo Doria 07/2016 1806 (2^693747-11)/3 208839 Stefano Morozzi 08/2022 1807 2^693462-1847561 208753 Enzo Doria 07/2015 1808 2^690890-59981 207979 Enzo Doria 11/2015 1809 (38^131591+1)/39 207884 Paul Bourdelais 07/2018 1810 3*2^690484+5 207857 Jon Grantham 07/2023 1811 2^690163+1877063 207760 Enzo Doria 07/2016 1812 7^245608-2 207563 Paul Bourdelais 01/2021 1813 (67*10^207556+23)/9 207557 Serge Batalov 01/2023 1814 2^689286-29381 207496 Enzo Doria 08/2015 1815 2^689122-114521 207447 Enzo Doria 04/2015 1816 9*10^207254-89 207255 Robert Price 02/2023 1817 2^688373+6077 207221 Enzo Doria 02/2016 1818 2^688201+1875527 207170 Enzo Doria 07/2016 1819 (42^127609+1)/43 207140 Paul Bourdelais 07/2018 1820 2^687938+213589 207090 Enzo Doria 10/2023 1821 2^687619+81563 206994 Enzo Doria 08/2016 1822 3*10^206927+37 206928 Robert Price 08/2023 1823 2^687383+21803 206923 Enzo Doria 09/2023 1824 2^686572-1845299 206679 Enzo Doria 07/2015 1825 (21^156217-1)/20 206552 Paul Bourdelais 04/2010 1826 (2^685739+1)/(3*87774593) 206420 Gord Palameta 08/2018 1827 2^685578+3 206380 Paul Bourdelais 04/2012 1828 2^685078+218599 206230 Enzo Doria 01/2024 1829 2^684836-49349 206157 Enzo Doria 10/2015 1830 (73^110603-1)/72 206088 Paul Bourdelais 06/2018 1831 2^684163-2790967 205954 Enzo Doria 12/2015 1832 326^81943-325^81943 205941 Jean-Louis Charton 07/2012 1833 (2^684127-1)/23765203727 205933 Jens K. Andersen 04/2009 1834 (68*10^205510+13)/9 205511 Serge Batalov 01/2023 1835 4^341233-3^341233 205443 Jean-Louis Charton 01/2006 1836 2^682414+215029 205428 Enzo Doria 11/2023 1837 (963^68821-1)/962 205334 Jinyuan Wang 01/2024 1838 (43*10^205183-421)/9 205184 Robert Price 10/2023 1839 2^681545+467 205166 Lelio R Paula 11/2013 1840 2^681306+81049 205094 Enzo Doria 07/2016 1841 2^680697+1877057 204911 Enzo Doria 07/2016 1842 2^680415+71783 204826 Enzo Doria 04/2016 1843 10^204764-8001 204764 Robert Price 03/2023 1844 (26*10^204730-77)/3 204731 Robert Price 03/2023 1845 2^679860-459995 204659 Enzo Doria 06/2015 1846 2^679593+1879547 204578 Enzo Doria 09/2016 1847 2^678899+220073 204369 Enzo Doria 03/2024 1848 2^678753+21677 204326 Enzo Doria 08/2023 1849 2^678651+1875023 204295 Enzo Doria 07/2016 1850 2^678561+678561 204268 Henri Lifchitz 05/2006 1851 5*3^427884+2^427884 204154 Jon Grantham 08/2023 1852 2^678101-114043 204129 Enzo Doria 11/2014 1853 2^678028+1875631 204107 Enzo Doria 06/2016 1854 2^677721+28607 204015 Enzo Doria 01/2024 1855 (19*10^203798-7)/3 203799 Robert Price 12/2023 1856 2^676992-59783 203795 Enzo Doria 10/2015 1857 2^676972+1866871 203789 Enzo Doria 03/2016 1858 2^676815+22583 203742 Enzo Doria 09/2023 1859 2^676761-9 203726 Robert Price 01/2017 1860 2^676592-23 203675 Stefano Morozzi 07/2022 1861 2^676563-2792407 203666 Enzo Doria 02/2016 1862 2^676306-114713 203589 Enzo Doria 04/2015 1863 (2^675977-1)/(1686378749257*7171117283326998925471) 203456 Dario Alpern 07/2015 1864 6*10^203365+53 203366 Robert Price 09/2023 1865 10247^50678-50678^10247 203250 Norbert Schneider 03/2022 1866 2^674627-25161 203083 Enzo Doria 09/2013 1867 2^674603-69337 203076 Enzo Doria 12/2015 1868 (182*10^203048+1)/3 203050 Robert Price 09/2023 1869 2^674459+74213 203033 Enzo Doria 04/2016 1870 2^674116-458879 202930 Enzo Doria 04/2015 1871 2^674076-114755 202918 Enzo Doria 04/2015 1872 5^289937-4^289937 202658 Jean-Louis Charton 03/2013 1873 5^289926-289926^5 202650 Henri Lifchitz 07/2024 1874 (2^673184-7)/3 202649 Stefano Morozzi 08/2022 1875 (467617#+14534)/(2^2*13*43) 202603 Makoto Morimoto 06/2019 1876 (155^92479-1)/154 202558 Anonymous 06/2024 1877 2^672773+219407 202525 Enzo Doria 03/2024 1878 2^672556-1835519 202460 Enzo Doria 04/2015 1879 (7*10^202267+179)/3 202268 Robert Price 02/2023 1880 2^671446-351401 202126 Enzo Doria 07/2015 1881 2^671373+77747 202104 Enzo Doria 05/2016 1882 (2*10^202059+7)/9 202059 Rytis Slatkevicius 01/2023 1883 98*10^202021-9 202023 Robert Price 05/2023 1884 2^670726-114845 201909 Enzo Doria 05/2015 1885 2^670539-25045 201853 Enzo Doria 09/2013 1886 10^201801-93 201801 Robert Price 02/2023 1887 43284^43519-43519^43284 201769 Norbert Schneider 08/2018 1888 2^670213+282317 201755 Enzo Doria 09/2016 1889 2^670133+89 201731 Stefano Morozzi 05/2021 1890 2^669854-113501 201647 Enzo Doria 08/2014 1891 2^669718+81619 201606 Enzo Doria 08/2016 1892 (299*10^201547-17)/3 201549 Robert Price 02/2023 1893 (145*10^201504-1)/9 201506 Serge Batalov 12/2014 1894 2^668938-1839821 201371 Enzo Doria 06/2015 1895 (198^87623-1)/197 201239 Anonymous 06/2024 1896 2^668492+1879303 201237 Enzo Doria 08/2016 1897 7*10^201140-87 201141 Robert Price 03/2023 1898 6^258413-5^258413 201085 Jean-Louis Charton 03/2013 1899 10194^50161-50161^10194 201063 Norbert Schneider 09/2020 1900 2^667894+1875589 201057 Enzo Doria 06/2016 1901 2^667569-1836559 200959 Enzo Doria 05/2015 1902 (172*10^200746-1)/9 200748 Serge Batalov 12/2014 1903 (166^90407-1)/165 200712 Anonymous 06/2024 1904 2^666430+782569 200616 Enzo Doria 10/2016 1905 (13*10^200610-43)/3 200611 Robert Price 08/2023 1906 (8*10^200408-11)/3 200409 Robert Price 07/2023 1907 (19*10^200260+101)/3 200261 Robert Price 06/2023 1908 43183^43183+4^4 200167 Serge Batalov 04/2024 1909 (86^103471+1)/87 200163 Paul Bourdelais 05/2018 1910 (10^(2*100072+1)+36*10^100072-1)/9 200145 Robert Price 09/2023 1911 2^664778+34789 200119 Enzo Doria 07/2024 1912 103*(10^100000+20110)^2-4707*(10^100000+20110)+50383 200003 Robert Price 05/2017 1913 103*(10^100000+33798)^2-4707*(10^100000+33798)+50383 200003 Robert Price 01/2018 1914 numbpart(32235776596) 200002 Serge Batalov 04/2017 1915 (10^200001+149)/3 200001 Serge Batalov 12/2014 1916 10^200000+571791 200001 Patrick De Geest 08/2019 1917 (3^419180-621444)/3 200000 Stefano Morozzi 06/2019 1918 (3^419180-1941384)/3 200000 Stefano Morozzi 08/2019 1919 10^200000-45557 200000 Patrick De Geest 08/2019 1920 (10^200000-1)/9-10^58838 200000 Akihiko Yoshida 04/2020 1921 2593604092947240127723272^8192+2593604092947240127722755^8192 200000 Youcef Lemsafer 01/2023 1922 (2593604092947240127723019^8192+2593604092947240127723011^8192)/2 199999 Youcef Lemsafer 01/2023 1923 (2593604092947240127723087^8192+2593604092947240127722984^8192)/147457 199994 Youcef Lemsafer 01/2023 1924 (2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986 199989 Youcef Lemsafer 01/2023 1925 (2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169 199986 Youcef Lemsafer 01/2023 1926 92*10^199980-9 199982 Robert Price 12/2021 1927 (2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649 199977 Youcef Lemsafer 01/2023 1928 (85*10^199951-139)/9 199952 Robert Price 08/2021 1929 (10^199926+7)/29/373/2339 199919 Alfred Reich 08/2021 1930 2^663838+25819 199836 Enzo Doria 11/2023 1931 23*10^199833-9 199835 Robert Price 10/2021 1932 fibonacci(956176)-4 199829 Jon Grantham 08/2023 1933 (299*10^199801-17)/3 199803 Robert Price 04/2020 1934 6*10^199788+77 199789 Robert Price 06/2020 1935 (23*10^199615+37)/3 199616 Robert Price 02/2022 1936 (17*10^199607-167)/3 199608 Robert Price 05/2022 1937 2^663020-933075 199589 Paul Bourdelais 06/2021 1938 2^663007+29963 199585 Enzo Doria 03/2024 1939 3*2^662703-5 199494 Jon Grantham 07/2023 1940 (14*10^199447+73)/3 199448 Robert Price 12/2018 1941 (2^662424-15)/7 199409 Stefano Morozzi 08/2022 1942 2^662194+22189 199341 Enzo Doria 09/2023 1943 2^662103-29287 199313 Enzo Doria 08/2015 1944 (2*10^199283+457)/9 199283 Robert Price 01/2018 1945 (10^199248-19)/9 199248 Robert Price 01/2018 1946 (83*10^199213+529)/9 199214 Robert Price 12/2021 1947 (194*10^199146-17)/3 199148 Robert Price 09/2020 1948 (151*10^199003-1)/3 199005 Robert Price 03/2020 1949 9*10^198946-73 198947 Robert Price 01/2021 1950 45*10^198931-7 198933 Robert Price 07/2020 1951 2^660482-2891 198825 Yves Minet 05/2016 1952 2^659589-21 198557 Stefano Morozzi 07/2022 1953 2^659583+1879223 198555 Enzo Doria 08/2016 1954 (53*10^198529+1)/9 198530 Serge Batalov 07/2010 1955 (49*10^198403+311)/9 198404 Robert Price 06/2019 1956 96*10^198376-7 198378 Robert Price 03/2021 1957 (10^198375+7)/59/1201/87589 198366 Alfred Reich 08/2021 1958 2^658828-29819 198327 Enzo Doria 08/2015 1959 2^658776-2791229 198312 Enzo Doria 01/2016 1960 (35*10^198294-377)/9 198295 Robert Price 07/2018 1961 (4*10^198268+137)/3 198269 Robert Price 03/2018 1962 2^658544-1854029 198242 Enzo Doria 09/2015 1963 (62*10^198229-233)/9 198230 Robert Price 02/2022 1964 (26*10^198200-41)/3 198201 Robert Price 02/2022 1965 (157^90239-1)/156 198154 Alexander Zhirkov 06/2016 1966 2^657815+26213 198023 Enzo Doria 12/2023 1967 2*10^197959-37 197960 Robert Price 11/2021 1968 (29*10^197941-41)/3 197942 Tyler Busby 03/2024 1969 (232*10^197897+17)/3 197899 Robert Price 04/2021 1970 (4*10^197778+173)/3 197779 Robert Price 02/2018 1971 2^656763+211373 197706 Enzo Doria 08/2023 1972 78*10^197702-7 197704 Robert Price 10/2020 1973 (17*10^197640-23)/3 197641 Robert Price 03/2021 1974 (29*10^197629-77)/3 197630 Robert Price 02/2020 1975 2^656462+1874419 197615 Enzo Doria 06/2016 1976 (89^101363+1)/90 197595 Paul Bourdelais 11/2017 1977 2^655893-344563 197444 Enzo Doria 07/2015 1978 2^655875+71333 197439 Enzo Doria 04/2016 1979 2^655845-9 197430 Robert Price 01/2017 1980 (299*10^197426+1)/3 197428 Robert Price 04/2020 1981 2^655682-1849121 197380 Enzo Doria 08/2015 1982 4*10^197268-89 197269 Robert Price 11/2018 1983 (11*10^197198-89)/3 197199 Robert Price 05/2021 1984 2^655045-49603 197189 Enzo Doria 10/2015 1985 2^655000-2784089 197175 Enzo Doria 10/2015 1986 (18^157051-1)/17 197141 Paul Bourdelais 03/2010 1987 (4*10^197061+41)/9 197061 Serge Batalov 11/2022 1988 (154*10^197005+17)/9 197007 Robert Price 06/2022 1989 2^654400-39719 196995 Enzo Doria 09/2015 1990 (5^281807-2^281807)/3 196975 Jon Grantham 08/2023 1991 (14*10^196965-221)/9 196966 Robert Price 04/2018 1992 2^654216-459995 196939 Enzo Doria 06/2015 1993 (17*10^196921+31)/3 196922 Robert Price 01/2019 1994 (14*10^196885-89)/3 196886 Robert Price 05/2020 1995 3*10^196881-59 196882 Robert Price 09/2018 1996 2^653851+82295 196829 Enzo Doria 09/2016 1997 (38*10^196792+691)/9 196793 Robert Price 10/2018 1998 (65*10^196768+493)/9 196769 Robert Price 08/2021 2000 2^653636-29429 196765 Enzo Doria 08/2015 1999 2^653638-11 196765 Stefano Morozzi 07/2022

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 19 2024 15:29 (Time in France)

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