## PRP Records

### Probable Primes Top 10000

#### (294613 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) !!!

See the Top discoverers
See the Latest PRPs
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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 (467617#+14534)/(2^2*13*43) 202603 Makoto Morimoto 06/2019 1752 2^672773+219407 202525 Enzo Doria 03/2024 1753 2^672556-1835519 202460 Enzo Doria 04/2015 1754 (7*10^202267+179)/3 202268 Robert Price 02/2023 1755 2^671446-351401 202126 Enzo Doria 07/2015 1756 2^671373+77747 202104 Enzo Doria 05/2016 1757 (2*10^202059+7)/9 202059 Rytis Slatkevicius 01/2023 1758 98*10^202021-9 202023 Robert Price 05/2023 1759 2^670726-114845 201909 Enzo Doria 05/2015 1760 2^670539-25045 201853 Enzo Doria 09/2013 1761 10^201801-93 201801 Robert Price 02/2023 1762 43284^43519-43519^43284 201769 Norbert Schneider 08/2018 1763 2^670213+282317 201755 Enzo Doria 09/2016 1764 2^670133+89 201731 Stefano Morozzi 05/2021 1765 2^669854-113501 201647 Enzo Doria 08/2014 1766 2^669718+81619 201606 Enzo Doria 08/2016 1767 (299*10^201547-17)/3 201549 Robert Price 02/2023 1768 (145*10^201504-1)/9 201506 Serge Batalov 12/2014 1769 2^668938-1839821 201371 Enzo Doria 06/2015 1770 2^668492+1879303 201237 Enzo Doria 08/2016 1771 7*10^201140-87 201141 Robert Price 03/2023 1772 6^258413-5^258413 201085 Jean-Louis Charton 03/2013 1773 10194^50161-50161^10194 201063 Norbert Schneider 09/2020 1774 2^667894+1875589 201057 Enzo Doria 06/2016 1775 2^667569-1836559 200959 Enzo Doria 05/2015 1776 (172*10^200746-1)/9 200748 Serge Batalov 12/2014 1777 2^666430+782569 200616 Enzo Doria 10/2016 1778 (13*10^200610-43)/3 200611 Robert Price 08/2023 1779 (8*10^200408-11)/3 200409 Robert Price 07/2023 1780 (19*10^200260+101)/3 200261 Robert Price 06/2023 1781 (86^103471+1)/87 200163 Paul Bourdelais 05/2018 1782 (10^(2*100072+1)+36*10^100072-1)/9 200145 Robert Price 09/2023 1783 103*(10^100000+20110)^2-4707*(10^100000+20110)+50383 200003 Robert Price 05/2017 1784 103*(10^100000+33798)^2-4707*(10^100000+33798)+50383 200003 Robert Price 01/2018 1785 numbpart(32235776596) 200002 Serge Batalov 04/2017 1786 (10^200001+149)/3 200001 Serge Batalov 12/2014 1787 10^200000+571791 200001 Patrick De Geest 08/2019 1788 (3^419180-621444)/3 200000 Stefano Morozzi 06/2019 1789 (3^419180-1941384)/3 200000 Stefano Morozzi 08/2019 1790 10^200000-45557 200000 Patrick De Geest 08/2019 1791 (10^200000-1)/9-10^58838 200000 Akihiko Yoshida 04/2020 1792 2593604092947240127723272^8192+2593604092947240127722755^8192 200000 Youcef Lemsafer 01/2023 1793 (2593604092947240127723019^8192+2593604092947240127723011^8192)/2 199999 Youcef Lemsafer 01/2023 1794 (2593604092947240127723087^8192+2593604092947240127722984^8192)/147457 199994 Youcef Lemsafer 01/2023 1795 (2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986 199989 Youcef Lemsafer 01/2023 1796 (2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169 199986 Youcef Lemsafer 01/2023 1797 92*10^199980-9 199982 Robert Price 12/2021 1798 (2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649 199977 Youcef Lemsafer 01/2023 1799 (85*10^199951-139)/9 199952 Robert Price 08/2021 1800 (10^199926+7)/29/373/2339 199919 Alfred Reich 08/2021 1801 2^663838+25819 199836 Enzo Doria 11/2023 1802 23*10^199833-9 199835 Robert Price 10/2021 1803 fibonacci(956176)-4 199829 Jon Grantham 08/2023 1804 (299*10^199801-17)/3 199803 Robert Price 04/2020 1805 6*10^199788+77 199789 Robert Price 06/2020 1806 (23*10^199615+37)/3 199616 Robert Price 02/2022 1807 (17*10^199607-167)/3 199608 Robert Price 05/2022 1808 2^663020-933075 199589 Paul Bourdelais 06/2021 1809 2^663007+29963 199585 Enzo Doria 03/2024 1810 3*2^662703-5 199494 Jon Grantham 07/2023 1811 (14*10^199447+73)/3 199448 Robert Price 12/2018 1812 (2^662424-15)/7 199409 Stefano Morozzi 08/2022 1813 2^662194+22189 199341 Enzo Doria 09/2023 1814 2^662103-29287 199313 Enzo Doria 08/2015 1815 (2*10^199283+457)/9 199283 Robert Price 01/2018 1816 (10^199248-19)/9 199248 Robert Price 01/2018 1817 (83*10^199213+529)/9 199214 Robert Price 12/2021 1818 (194*10^199146-17)/3 199148 Robert Price 09/2020 1819 (151*10^199003-1)/3 199005 Robert Price 03/2020 1820 9*10^198946-73 198947 Robert Price 01/2021 1821 45*10^198931-7 198933 Robert Price 07/2020 1822 2^660482-2891 198825 Yves Minet 05/2016 1823 2^659589-21 198557 Stefano Morozzi 07/2022 1824 2^659583+1879223 198555 Enzo Doria 08/2016 1825 (53*10^198529+1)/9 198530 Serge Batalov 07/2010 1826 (49*10^198403+311)/9 198404 Robert Price 06/2019 1827 96*10^198376-7 198378 Robert Price 03/2021 1828 (10^198375+7)/59/1201/87589 198366 Alfred Reich 08/2021 1829 2^658828-29819 198327 Enzo Doria 08/2015 1830 2^658776-2791229 198312 Enzo Doria 01/2016 1831 (35*10^198294-377)/9 198295 Robert Price 07/2018 1832 (4*10^198268+137)/3 198269 Robert Price 03/2018 1833 2^658544-1854029 198242 Enzo Doria 09/2015 1834 (62*10^198229-233)/9 198230 Robert Price 02/2022 1835 (26*10^198200-41)/3 198201 Robert Price 02/2022 1836 (157^90239-1)/156 198154 Alexander Zhirkov 06/2016 1837 2^657815+26213 198023 Enzo Doria 12/2023 1838 2*10^197959-37 197960 Robert Price 11/2021 1839 (232*10^197897+17)/3 197899 Robert Price 04/2021 1840 (4*10^197778+173)/3 197779 Robert Price 02/2018 1841 2^656763+211373 197706 Enzo Doria 08/2023 1842 78*10^197702-7 197704 Robert Price 10/2020 1843 (17*10^197640-23)/3 197641 Robert Price 03/2021 1844 (29*10^197629-77)/3 197630 Robert Price 02/2020 1845 2^656462+1874419 197615 Enzo Doria 06/2016 1846 (89^101363+1)/90 197595 Paul Bourdelais 11/2017 1847 2^655893-344563 197444 Enzo Doria 07/2015 1848 2^655875+71333 197439 Enzo Doria 04/2016 1849 2^655845-9 197430 Robert Price 01/2017 1850 (299*10^197426+1)/3 197428 Robert Price 04/2020 1851 2^655682-1849121 197380 Enzo Doria 08/2015 1852 4*10^197268-89 197269 Robert Price 11/2018 1853 (11*10^197198-89)/3 197199 Robert Price 05/2021 1854 2^655045-49603 197189 Enzo Doria 10/2015 1855 2^655000-2784089 197175 Enzo Doria 10/2015 1856 (18^157051-1)/17 197141 Paul Bourdelais 03/2010 1857 (4*10^197061+41)/9 197061 Serge Batalov 11/2022 1858 (154*10^197005+17)/9 197007 Robert Price 06/2022 1859 2^654400-39719 196995 Enzo Doria 09/2015 1860 (5^281807-2^281807)/3 196975 Jon Grantham 08/2023 1861 (14*10^196965-221)/9 196966 Robert Price 04/2018 1862 2^654216-459995 196939 Enzo Doria 06/2015 1863 (17*10^196921+31)/3 196922 Robert Price 01/2019 1864 (14*10^196885-89)/3 196886 Robert Price 05/2020 1865 3*10^196881-59 196882 Robert Price 09/2018 1866 2^653851+82295 196829 Enzo Doria 09/2016 1867 (38*10^196792+691)/9 196793 Robert Price 10/2018 1868 (65*10^196768+493)/9 196769 Robert Price 08/2021 1870 2^653636-29429 196765 Enzo Doria 08/2015 1869 2^653638-11 196765 Stefano Morozzi 07/2022 1871 2^653601-69673 196754 Enzo Doria 02/2016 1872 (44*10^196684+1)/9 196685 Serge Batalov 07/2010 1873 2^652786-1852571 196509 Enzo Doria 08/2015 1874 2^652752-1325 196498 Yves Minet 07/2015 1875 2^652470-1859141 196414 Enzo Doria 10/2015 1876 2^652346+29329 196376 Enzo Doria 02/2024 1877 2^652307+1877483 196364 Enzo Doria 08/2016 1878 2^652293-115273 196360 Enzo Doria 06/2015 1879 (47*10^196281+403)/9 196282 Robert Price 03/2019 1880 2^652025+218027 196280 Enzo Doria 01/2024 1881 2^652004+23961 196273 Enzo Doria 10/2023 1882 (7*10^196125-31)/3 196126 Robert Price 12/2021 1883 33^129128+129128^33 196083 Norbert Schneider 06/2022 1884 6*10^196070+73 196071 Robert Price 04/2019 1885 2^651218-1868201 196037 Enzo Doria 04/2016 1886 2^651047-49687 195985 Enzo Doria 10/2015 1887 10^195968-700001 195968 Robert Price 08/2021 1888 fibonacci(937485)+3 195923 Jon Grantham 08/2023 1889 (29*10^195875-197)/3 195876 Robert Price 08/2021 1890 (25*10^195808-97)/9 195809 Robert Price 01/2022 1891 2^650285-2785333 195756 Enzo Doria 10/2015 1892 (10^195732+7)/18089/49605893 195721 Alfred Reich 08/2021 1893 (69^106397-1)/68 195647 Paul Bourdelais 10/2017 1894 2^649811+1877573 195613 Enzo Doria 08/2016 1895 2^649662-170531 195568 Hans Havermann 10/2018 1896 2^649586+182839 195545 Enzo Doria 11/2016 1897 2^649537-1867363 195531 Enzo Doria 04/2016 1898 2^649536-1861499 195530 Enzo Doria 12/2015 1899 2^649493+25907 195517 Enzo Doria 11/2023 1900 (103*10^195478-1)/3 195480 Serge Batalov 12/2014 1901 2^649102-59351 195400 Enzo Doria 10/2015 1902 (2*10^195399+529)/9 195399 Robert Price 01/2018 1903 (202*10^195383-13)/9 195385 Robert Price 01/2020 1904 2^648988+1178971 195365 Enzo Doria 06/2016 1905 2^648975-114319 195361 Enzo Doria 02/2015 1906 (11*10^195350-137)/9 195351 Robert Price 01/2018 1907 2^648619-24835 195254 Enzo Doria 09/2013 1908 5*10^195250-21 195251 Robert Price 12/2021 1909 (14*10^195234-83)/3 195235 Robert Price 12/2018 1910 5*10^195221+81 195222 Robert Price 03/2019 1911 10^195143-5001 195143 Robert Price 12/2021 1912 2^648190-24737 195125 Enzo Doria 09/2013 1913 (57^111119+1)/58 195110 Paul Bourdelais 10/2017 1914 (29*10^195098-197)/3 195099 Robert Price 08/2021 1915 10^195060+89701 195061 Patrick De Geest 02/2021 1917 10^195060-40000000001 195060 Robert Price 09/2020 1916 10^195060-110337 195060 Patrick De Geest 02/2021 1918 56*10^195032-3 195034 Robert Price 03/2020 1919 11^187185-90 194934 Enzo Doria 09/2012 1920 (86*10^194818-437)/9 194819 Robert Price 03/2021 1921 2^647068+77281 194787 Enzo Doria 05/2016 1922 2*10^194716-93 194717 Robert Price 12/2021 1923 15^165559-14^165559 194713 Jean-Louis Charton 03/2011 1924 F(931517) 194676 Henri Lifchitz 09/2008 1925 4*10^194668+49 194669 Robert Price 01/2019 1926 2^646589+1179407 194643 Enzo Doria 06/2016 1927 2^646289-114621 194553 Enzo Doria 05/2015 1928 2^646236-39659 194537 Enzo Doria 09/2015 1929 (16*10^194536+53)/3 194537 Robert Price 03/2019 1930 2^646161-59833 194514 Enzo Doria 11/2015 1931 (17*10^194502+31)/3 194503 Robert Price 01/2019 1932 (19*10^194428+287)/9 194429 Robert Price 10/2021 1933 2*10^194413+3 194414 Robert Price 07/2015 1934 2^645360-1848599 194273 Enzo Doria 08/2015 1935 22470^44641+44641^22470 194260 Norbert Schneider 08/2023 1936 (112*10^194150-1)/3 194152 Serge Batalov 12/2014 1937 Phi(293127,10) 194041 Makoto Kamada 12/2023 1938 2*10^193981-43 193982 Robert Price 04/2018 1939 2^644382+75169 193979 Enzo Doria 04/2016 1940 2^644304-1861409 193955 Enzo Doria 11/2015 1941 (29*10^193950-23)/3 193951 Robert Price 03/2022 1942 5*10^193907-9 193908 Robert Price 05/2015 1943 2^644043+1876703 193877 Enzo Doria 07/2016 1944 2*10^193841-63 193842 Robert Price 01/2022 1945 2^643735+1879733 193784 Enzo Doria 09/2016 1946 (5^277183+1)/6 193742 Paul Bourdelais 07/2010 1947 9*10^193712+71 193713 Robert Price 08/2020 1948 2^643216-286565 193628 Enzo Doria 07/2015 1949 2^643204+215011 193624 Enzo Doria 11/2023 1950 10^193566+1126339 193567 Patrick De Geest 09/2022 1952 10^193566-10000000001 193566 Robert Price 04/2021 1951 10^193566-454041 193566 Patrick De Geest 08/2021 1954 2^642888-24965 193529 Enzo Doria 09/2013 1953 2^642889+25367 193529 Enzo Doria 11/2023 1955 2^642448-114825 193397 Enzo Doria 05/2015 1956 2^642437-1856623 193393 Enzo Doria 10/2015 1957 2^642039-59797 193273 Enzo Doria 11/2015 1958 2^641987+39 193258 Jon Grantham 08/2023 1959 10^193230+513861 193231 Patrick De Geest 07/2018 1960 10^193230-8001 193230 Robert Price 03/2018 1961 (62*10^193225-233)/9 193226 Robert Price 02/2022 1962 2^641692-286349 193169 Enzo Doria 07/2015 1963 2^641690-24737 193168 Enzo Doria 09/2013 1964 22268^44421+44421^22268 193129 Norbert Schneider 06/2023 1965 2^641514+1876549 193115 Enzo Doria 07/2016 1966 2^640888-2785619 192927 Enzo Doria 10/2015 1967 2^640874-2783741 192923 Enzo Doria 09/2015 1968 10^192922+192207 192923 Patrick De Geest 08/2021 1969 10^192922-7001 192922 Robert Price 04/2021 1970 2^640854+25 192917 Stefano Morozzi 05/2021 1971 34*10^192868-9 192870 Robert Price 06/2020 1972 (46*10^192841+683)/9 192842 Robert Price 03/2019 1973 2^640181+467 192714 Lelio R Paula 08/2013 1974 2^640072+27541 192681 Enzo Doria 01/2024 1975 2^639536-1850249 192520 Enzo Doria 08/2015 1976 40714<>40712<>...<>1086421357911<>...<>40711<>40713 192464 Hans Havermann 12/2019 1977 5*10^192422-43 192423 Robert Price 01/2019 1978 2^639110-2792441 192392 Enzo Doria 02/2016 1979 2^638955-29827 192345 Enzo Doria 08/2015 1980 15^163539+14 192337 Alfred Reich 10/2023 1981 2^638713-2784223 192272 Enzo Doria 10/2015 1982 (10^192216+7)/149 192214 Alfred Reich 07/2021 1983 2^638490-113507 192205 Enzo Doria 08/2014 1984 2^638189-39943 192115 Enzo Doria 09/2015 1985 2^638110+1877119 192091 Enzo Doria 07/2016 1986 2^638066-2785211 192078 Enzo Doria 10/2015 1987 (35*10^191973-341)/9 191974 Robert Price 08/2021 1988 (112*10^191900+17)/3 191902 Robert Price 03/2020 1989 2^637475-115309 191900 Enzo Doria 07/2015 1990 (68*10^191754-113)/9 191755 Robert Price 03/2021 1991 2^636930-11 191736 Stefano Morozzi 07/2022 1992 (47*10^191732+259)/9 191733 Robert Price 03/2022 1993 2^636661+1876577 191655 Enzo Doria 07/2016 1994 (9^200807-2^200807)/7 191618 Jon Grantham 07/2023 1995 (34^125101-1)/33 191589 Paul Bourdelais 11/2017 1996 fibonacci(916540)-2 191546 Jon Grantham 08/2023 1997 2^636177-1855123 191509 Enzo Doria 09/2015 1998 2^636158-113627 191503 Enzo Doria 08/2014 1999 (37*25^136966+63)/4 191472 Curtis Bright 05/2015 2000 2^636035+79823 191466 Enzo Doria 06/2016

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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