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 | 6*10^203365+53 | 203366 | Robert Price | 09/2023 |
1752 | 10247^50678-50678^10247 | 203250 | Norbert Schneider | 03/2022 |
1753 | 2^674627-25161 | 203083 | Enzo Doria | 09/2013 |
1754 | 2^674603-69337 | 203076 | Enzo Doria | 12/2015 |
1755 | (182*10^203048+1)/3 | 203050 | Robert Price | 09/2023 |
1756 | 2^674459+74213 | 203033 | Enzo Doria | 04/2016 |
1757 | 2^674116-458879 | 202930 | Enzo Doria | 04/2015 |
1758 | 2^674076-114755 | 202918 | Enzo Doria | 04/2015 |
1759 | 5^289937-4^289937 | 202658 | Jean-Louis Charton | 03/2013 |
1760 | (2^673184-7)/3 | 202649 | Stefano Morozzi | 08/2022 |
1761 | (467617#+14534)/(2^2*13*43) | 202603 | Makoto Morimoto | 06/2019 |
1762 | 2^672773+219407 | 202525 | Enzo Doria | 03/2024 |
1763 | 2^672556-1835519 | 202460 | Enzo Doria | 04/2015 |
1764 | (7*10^202267+179)/3 | 202268 | Robert Price | 02/2023 |
1765 | 2^671446-351401 | 202126 | Enzo Doria | 07/2015 |
1766 | 2^671373+77747 | 202104 | Enzo Doria | 05/2016 |
1767 | (2*10^202059+7)/9 | 202059 | Rytis Slatkevicius | 01/2023 |
1768 | 98*10^202021-9 | 202023 | Robert Price | 05/2023 |
1769 | 2^670726-114845 | 201909 | Enzo Doria | 05/2015 |
1770 | 2^670539-25045 | 201853 | Enzo Doria | 09/2013 |
1771 | 10^201801-93 | 201801 | Robert Price | 02/2023 |
1772 | 43284^43519-43519^43284 | 201769 | Norbert Schneider | 08/2018 |
1773 | 2^670213+282317 | 201755 | Enzo Doria | 09/2016 |
1774 | 2^670133+89 | 201731 | Stefano Morozzi | 05/2021 |
1775 | 2^669854-113501 | 201647 | Enzo Doria | 08/2014 |
1776 | 2^669718+81619 | 201606 | Enzo Doria | 08/2016 |
1777 | (299*10^201547-17)/3 | 201549 | Robert Price | 02/2023 |
1778 | (145*10^201504-1)/9 | 201506 | Serge Batalov | 12/2014 |
1779 | 2^668938-1839821 | 201371 | Enzo Doria | 06/2015 |
1780 | 2^668492+1879303 | 201237 | Enzo Doria | 08/2016 |
1781 | 7*10^201140-87 | 201141 | Robert Price | 03/2023 |
1782 | 6^258413-5^258413 | 201085 | Jean-Louis Charton | 03/2013 |
1783 | 10194^50161-50161^10194 | 201063 | Norbert Schneider | 09/2020 |
1784 | 2^667894+1875589 | 201057 | Enzo Doria | 06/2016 |
1785 | 2^667569-1836559 | 200959 | Enzo Doria | 05/2015 |
1786 | (172*10^200746-1)/9 | 200748 | Serge Batalov | 12/2014 |
1787 | 2^666430+782569 | 200616 | Enzo Doria | 10/2016 |
1788 | (13*10^200610-43)/3 | 200611 | Robert Price | 08/2023 |
1789 | (8*10^200408-11)/3 | 200409 | Robert Price | 07/2023 |
1790 | (19*10^200260+101)/3 | 200261 | Robert Price | 06/2023 |
1791 | (86^103471+1)/87 | 200163 | Paul Bourdelais | 05/2018 |
1792 | (10^(2*100072+1)+36*10^100072-1)/9 | 200145 | Robert Price | 09/2023 |
1793 | 103*(10^100000+20110)^2-4707*(10^100000+20110)+50383 | 200003 | Robert Price | 05/2017 |
1794 | 103*(10^100000+33798)^2-4707*(10^100000+33798)+50383 | 200003 | Robert Price | 01/2018 |
1795 | numbpart(32235776596) | 200002 | Serge Batalov | 04/2017 |
1796 | (10^200001+149)/3 | 200001 | Serge Batalov | 12/2014 |
1797 | 10^200000+571791 | 200001 | Patrick De Geest | 08/2019 |
1798 | (3^419180-621444)/3 | 200000 | Stefano Morozzi | 06/2019 |
1799 | (3^419180-1941384)/3 | 200000 | Stefano Morozzi | 08/2019 |
1800 | 10^200000-45557 | 200000 | Patrick De Geest | 08/2019 |
1802 | (10^200000-1)/9-10^58838 | 200000 | Akihiko Yoshida | 04/2020 |
1801 | 2593604092947240127723272^8192+2593604092947240127722755^8192 | 200000 | Youcef Lemsafer | 01/2023 |
1803 | (2593604092947240127723019^8192+2593604092947240127723011^8192)/2 | 199999 | Youcef Lemsafer | 01/2023 |
1804 | (2593604092947240127723087^8192+2593604092947240127722984^8192)/147457 | 199994 | Youcef Lemsafer | 01/2023 |
1805 | (2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986 | 199989 | Youcef Lemsafer | 01/2023 |
1806 | (2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169 | 199986 | Youcef Lemsafer | 01/2023 |
1807 | 92*10^199980-9 | 199982 | Robert Price | 12/2021 |
1808 | (2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649 | 199977 | Youcef Lemsafer | 01/2023 |
1809 | (85*10^199951-139)/9 | 199952 | Robert Price | 08/2021 |
1810 | (10^199926+7)/29/373/2339 | 199919 | Alfred Reich | 08/2021 |
1811 | 2^663838+25819 | 199836 | Enzo Doria | 11/2023 |
1812 | 23*10^199833-9 | 199835 | Robert Price | 10/2021 |
1813 | fibonacci(956176)-4 | 199829 | Jon Grantham | 08/2023 |
1814 | (299*10^199801-17)/3 | 199803 | Robert Price | 04/2020 |
1815 | 6*10^199788+77 | 199789 | Robert Price | 06/2020 |
1816 | (23*10^199615+37)/3 | 199616 | Robert Price | 02/2022 |
1817 | (17*10^199607-167)/3 | 199608 | Robert Price | 05/2022 |
1818 | 2^663020-933075 | 199589 | Paul Bourdelais | 06/2021 |
1819 | 2^663007+29963 | 199585 | Enzo Doria | 03/2024 |
1820 | 3*2^662703-5 | 199494 | Jon Grantham | 07/2023 |
1821 | (14*10^199447+73)/3 | 199448 | Robert Price | 12/2018 |
1822 | (2^662424-15)/7 | 199409 | Stefano Morozzi | 08/2022 |
1823 | 2^662194+22189 | 199341 | Enzo Doria | 09/2023 |
1824 | 2^662103-29287 | 199313 | Enzo Doria | 08/2015 |
1825 | (2*10^199283+457)/9 | 199283 | Robert Price | 01/2018 |
1826 | (10^199248-19)/9 | 199248 | Robert Price | 01/2018 |
1827 | (83*10^199213+529)/9 | 199214 | Robert Price | 12/2021 |
1828 | (194*10^199146-17)/3 | 199148 | Robert Price | 09/2020 |
1829 | (151*10^199003-1)/3 | 199005 | Robert Price | 03/2020 |
1830 | 9*10^198946-73 | 198947 | Robert Price | 01/2021 |
1831 | 45*10^198931-7 | 198933 | Robert Price | 07/2020 |
1832 | 2^660482-2891 | 198825 | Yves Minet | 05/2016 |
1833 | 2^659589-21 | 198557 | Stefano Morozzi | 07/2022 |
1834 | 2^659583+1879223 | 198555 | Enzo Doria | 08/2016 |
1835 | (53*10^198529+1)/9 | 198530 | Serge Batalov | 07/2010 |
1836 | (49*10^198403+311)/9 | 198404 | Robert Price | 06/2019 |
1837 | 96*10^198376-7 | 198378 | Robert Price | 03/2021 |
1838 | (10^198375+7)/59/1201/87589 | 198366 | Alfred Reich | 08/2021 |
1839 | 2^658828-29819 | 198327 | Enzo Doria | 08/2015 |
1840 | 2^658776-2791229 | 198312 | Enzo Doria | 01/2016 |
1841 | (35*10^198294-377)/9 | 198295 | Robert Price | 07/2018 |
1842 | (4*10^198268+137)/3 | 198269 | Robert Price | 03/2018 |
1843 | 2^658544-1854029 | 198242 | Enzo Doria | 09/2015 |
1844 | (62*10^198229-233)/9 | 198230 | Robert Price | 02/2022 |
1845 | (26*10^198200-41)/3 | 198201 | Robert Price | 02/2022 |
1846 | (157^90239-1)/156 | 198154 | Alexander Zhirkov | 06/2016 |
1847 | 2^657815+26213 | 198023 | Enzo Doria | 12/2023 |
1848 | 2*10^197959-37 | 197960 | Robert Price | 11/2021 |
1849 | (232*10^197897+17)/3 | 197899 | Robert Price | 04/2021 |
1850 | (4*10^197778+173)/3 | 197779 | Robert Price | 02/2018 |
1851 | 2^656763+211373 | 197706 | Enzo Doria | 08/2023 |
1852 | 78*10^197702-7 | 197704 | Robert Price | 10/2020 |
1853 | (17*10^197640-23)/3 | 197641 | Robert Price | 03/2021 |
1854 | (29*10^197629-77)/3 | 197630 | Robert Price | 02/2020 |
1855 | 2^656462+1874419 | 197615 | Enzo Doria | 06/2016 |
1856 | (89^101363+1)/90 | 197595 | Paul Bourdelais | 11/2017 |
1857 | 2^655893-344563 | 197444 | Enzo Doria | 07/2015 |
1858 | 2^655875+71333 | 197439 | Enzo Doria | 04/2016 |
1859 | 2^655845-9 | 197430 | Robert Price | 01/2017 |
1860 | (299*10^197426+1)/3 | 197428 | Robert Price | 04/2020 |
1861 | 2^655682-1849121 | 197380 | Enzo Doria | 08/2015 |
1862 | 4*10^197268-89 | 197269 | Robert Price | 11/2018 |
1863 | (11*10^197198-89)/3 | 197199 | Robert Price | 05/2021 |
1864 | 2^655045-49603 | 197189 | Enzo Doria | 10/2015 |
1865 | 2^655000-2784089 | 197175 | Enzo Doria | 10/2015 |
1866 | (18^157051-1)/17 | 197141 | Paul Bourdelais | 03/2010 |
1867 | (4*10^197061+41)/9 | 197061 | Serge Batalov | 11/2022 |
1868 | (154*10^197005+17)/9 | 197007 | Robert Price | 06/2022 |
1869 | 2^654400-39719 | 196995 | Enzo Doria | 09/2015 |
1870 | (5^281807-2^281807)/3 | 196975 | Jon Grantham | 08/2023 |
1871 | (14*10^196965-221)/9 | 196966 | Robert Price | 04/2018 |
1872 | 2^654216-459995 | 196939 | Enzo Doria | 06/2015 |
1873 | (17*10^196921+31)/3 | 196922 | Robert Price | 01/2019 |
1874 | (14*10^196885-89)/3 | 196886 | Robert Price | 05/2020 |
1875 | 3*10^196881-59 | 196882 | Robert Price | 09/2018 |
1876 | 2^653851+82295 | 196829 | Enzo Doria | 09/2016 |
1877 | (38*10^196792+691)/9 | 196793 | Robert Price | 10/2018 |
1878 | (65*10^196768+493)/9 | 196769 | Robert Price | 08/2021 |
1880 | 2^653636-29429 | 196765 | Enzo Doria | 08/2015 |
1879 | 2^653638-11 | 196765 | Stefano Morozzi | 07/2022 |
1881 | 2^653601-69673 | 196754 | Enzo Doria | 02/2016 |
1882 | (44*10^196684+1)/9 | 196685 | Serge Batalov | 07/2010 |
1883 | 2^652786-1852571 | 196509 | Enzo Doria | 08/2015 |
1884 | 2^652752-1325 | 196498 | Yves Minet | 07/2015 |
1885 | 2^652470-1859141 | 196414 | Enzo Doria | 10/2015 |
1886 | 2^652346+29329 | 196376 | Enzo Doria | 02/2024 |
1887 | 2^652307+1877483 | 196364 | Enzo Doria | 08/2016 |
1888 | 2^652293-115273 | 196360 | Enzo Doria | 06/2015 |
1889 | (47*10^196281+403)/9 | 196282 | Robert Price | 03/2019 |
1890 | 2^652025+218027 | 196280 | Enzo Doria | 01/2024 |
1891 | 2^652004+23961 | 196273 | Enzo Doria | 10/2023 |
1892 | (7*10^196125-31)/3 | 196126 | Robert Price | 12/2021 |
1893 | 33^129128+129128^33 | 196083 | Norbert Schneider | 06/2022 |
1894 | 6*10^196070+73 | 196071 | Robert Price | 04/2019 |
1895 | 2^651218-1868201 | 196037 | Enzo Doria | 04/2016 |
1896 | 2^651047-49687 | 195985 | Enzo Doria | 10/2015 |
1897 | 10^195968-700001 | 195968 | Robert Price | 08/2021 |
1898 | fibonacci(937485)+3 | 195923 | Jon Grantham | 08/2023 |
1899 | (29*10^195875-197)/3 | 195876 | Robert Price | 08/2021 |
1900 | (25*10^195808-97)/9 | 195809 | Robert Price | 01/2022 |
1901 | 2^650285-2785333 | 195756 | Enzo Doria | 10/2015 |
1902 | (10^195732+7)/18089/49605893 | 195721 | Alfred Reich | 08/2021 |
1903 | (69^106397-1)/68 | 195647 | Paul Bourdelais | 10/2017 |
1904 | 2^649811+1877573 | 195613 | Enzo Doria | 08/2016 |
1905 | 2^649662-170531 | 195568 | Hans Havermann | 10/2018 |
1906 | 2^649586+182839 | 195545 | Enzo Doria | 11/2016 |
1907 | 2^649537-1867363 | 195531 | Enzo Doria | 04/2016 |
1908 | 2^649536-1861499 | 195530 | Enzo Doria | 12/2015 |
1909 | 2^649493+25907 | 195517 | Enzo Doria | 11/2023 |
1910 | (103*10^195478-1)/3 | 195480 | Serge Batalov | 12/2014 |
1911 | 2^649102-59351 | 195400 | Enzo Doria | 10/2015 |
1912 | (2*10^195399+529)/9 | 195399 | Robert Price | 01/2018 |
1913 | (202*10^195383-13)/9 | 195385 | Robert Price | 01/2020 |
1914 | 2^648988+1178971 | 195365 | Enzo Doria | 06/2016 |
1915 | 2^648975-114319 | 195361 | Enzo Doria | 02/2015 |
1916 | (11*10^195350-137)/9 | 195351 | Robert Price | 01/2018 |
1917 | 2^648619-24835 | 195254 | Enzo Doria | 09/2013 |
1918 | 5*10^195250-21 | 195251 | Robert Price | 12/2021 |
1919 | (14*10^195234-83)/3 | 195235 | Robert Price | 12/2018 |
1920 | 5*10^195221+81 | 195222 | Robert Price | 03/2019 |
1921 | 10^195143-5001 | 195143 | Robert Price | 12/2021 |
1922 | 2^648190-24737 | 195125 | Enzo Doria | 09/2013 |
1923 | (57^111119+1)/58 | 195110 | Paul Bourdelais | 10/2017 |
1924 | (29*10^195098-197)/3 | 195099 | Robert Price | 08/2021 |
1925 | 10^195060+89701 | 195061 | Patrick De Geest | 02/2021 |
1927 | 10^195060-40000000001 | 195060 | Robert Price | 09/2020 |
1926 | 10^195060-110337 | 195060 | Patrick De Geest | 02/2021 |
1928 | 56*10^195032-3 | 195034 | Robert Price | 03/2020 |
1929 | 11^187185-90 | 194934 | Enzo Doria | 09/2012 |
1930 | 2^647468+220141 | 194908 | Enzo Doria | 03/2024 |
1931 | (86*10^194818-437)/9 | 194819 | Robert Price | 03/2021 |
1932 | 2^647068+77281 | 194787 | Enzo Doria | 05/2016 |
1933 | 2*10^194716-93 | 194717 | Robert Price | 12/2021 |
1934 | 15^165559-14^165559 | 194713 | Jean-Louis Charton | 03/2011 |
1935 | F(931517) | 194676 | Henri Lifchitz | 09/2008 |
1936 | 4*10^194668+49 | 194669 | Robert Price | 01/2019 |
1937 | 2^646589+1179407 | 194643 | Enzo Doria | 06/2016 |
1938 | 2^646289-114621 | 194553 | Enzo Doria | 05/2015 |
1939 | 2^646236-39659 | 194537 | Enzo Doria | 09/2015 |
1940 | (16*10^194536+53)/3 | 194537 | Robert Price | 03/2019 |
1941 | 2^646161-59833 | 194514 | Enzo Doria | 11/2015 |
1942 | (17*10^194502+31)/3 | 194503 | Robert Price | 01/2019 |
1943 | (19*10^194428+287)/9 | 194429 | Robert Price | 10/2021 |
1944 | 2*10^194413+3 | 194414 | Robert Price | 07/2015 |
1945 | 2^645360-1848599 | 194273 | Enzo Doria | 08/2015 |
1946 | 22470^44641+44641^22470 | 194260 | Norbert Schneider | 08/2023 |
1947 | (112*10^194150-1)/3 | 194152 | Serge Batalov | 12/2014 |
1948 | Phi(293127,10) | 194041 | Makoto Kamada | 12/2023 |
1949 | 2*10^193981-43 | 193982 | Robert Price | 04/2018 |
1950 | 2^644382+75169 | 193979 | Enzo Doria | 04/2016 |
1951 | 2^644304-1861409 | 193955 | Enzo Doria | 11/2015 |
1952 | (29*10^193950-23)/3 | 193951 | Robert Price | 03/2022 |
1953 | 5*10^193907-9 | 193908 | Robert Price | 05/2015 |
1954 | 2^644043+1876703 | 193877 | Enzo Doria | 07/2016 |
1955 | 2*10^193841-63 | 193842 | Robert Price | 01/2022 |
1956 | 2^643735+1879733 | 193784 | Enzo Doria | 09/2016 |
1957 | (5^277183+1)/6 | 193742 | Paul Bourdelais | 07/2010 |
1958 | 9*10^193712+71 | 193713 | Robert Price | 08/2020 |
1959 | 2^643216-286565 | 193628 | Enzo Doria | 07/2015 |
1960 | 2^643204+215011 | 193624 | Enzo Doria | 11/2023 |
1961 | 10^193566+1126339 | 193567 | Patrick De Geest | 09/2022 |
1963 | 10^193566-10000000001 | 193566 | Robert Price | 04/2021 |
1962 | 10^193566-454041 | 193566 | Patrick De Geest | 08/2021 |
1965 | 2^642888-24965 | 193529 | Enzo Doria | 09/2013 |
1964 | 2^642889+25367 | 193529 | Enzo Doria | 11/2023 |
1966 | 2^642448-114825 | 193397 | Enzo Doria | 05/2015 |
1967 | 2^642437-1856623 | 193393 | Enzo Doria | 10/2015 |
1968 | 2^642039-59797 | 193273 | Enzo Doria | 11/2015 |
1969 | 2^641987+39 | 193258 | Jon Grantham | 08/2023 |
1970 | 10^193230+513861 | 193231 | Patrick De Geest | 07/2018 |
1971 | 10^193230-8001 | 193230 | Robert Price | 03/2018 |
1972 | (62*10^193225-233)/9 | 193226 | Robert Price | 02/2022 |
1973 | 2^641692-286349 | 193169 | Enzo Doria | 07/2015 |
1974 | 2^641690-24737 | 193168 | Enzo Doria | 09/2013 |
1975 | 22268^44421+44421^22268 | 193129 | Norbert Schneider | 06/2023 |
1976 | 2^641514+1876549 | 193115 | Enzo Doria | 07/2016 |
1977 | 2^640888-2785619 | 192927 | Enzo Doria | 10/2015 |
1978 | 2^640874-2783741 | 192923 | Enzo Doria | 09/2015 |
1979 | 10^192922+192207 | 192923 | Patrick De Geest | 08/2021 |
1980 | 10^192922-7001 | 192922 | Robert Price | 04/2021 |
1981 | 2^640854+25 | 192917 | Stefano Morozzi | 05/2021 |
1982 | 34*10^192868-9 | 192870 | Robert Price | 06/2020 |
1983 | (46*10^192841+683)/9 | 192842 | Robert Price | 03/2019 |
1984 | 2^640181+467 | 192714 | Lelio R Paula | 08/2013 |
1985 | 2^640072+27541 | 192681 | Enzo Doria | 01/2024 |
1986 | 2^639536-1850249 | 192520 | Enzo Doria | 08/2015 |
1987 | 40714<>40712<>...<>1086421357911<>...<>40711<>40713 | 192464 | Hans Havermann | 12/2019 |
1988 | 5*10^192422-43 | 192423 | Robert Price | 01/2019 |
1989 | 2^639110-2792441 | 192392 | Enzo Doria | 02/2016 |
1990 | 2^638955-29827 | 192345 | Enzo Doria | 08/2015 |
1991 | 15^163539+14 | 192337 | Alfred Reich | 10/2023 |
1992 | 2^638713-2784223 | 192272 | Enzo Doria | 10/2015 |
1993 | (10^192216+7)/149 | 192214 | Alfred Reich | 07/2021 |
1994 | 2^638490-113507 | 192205 | Enzo Doria | 08/2014 |
1995 | 2^638189-39943 | 192115 | Enzo Doria | 09/2015 |
1996 | 2^638110+1877119 | 192091 | Enzo Doria | 07/2016 |
1997 | 2^638066-2785211 | 192078 | Enzo Doria | 10/2015 |
1998 | (35*10^191973-341)/9 | 191974 | Robert Price | 08/2021 |
1999 | (112*10^191900+17)/3 | 191902 | Robert Price | 03/2020 |
2000 | 2^637475-115309 | 191900 | Enzo Doria | 07/2015 |