Henri & Renaud Lifchitz's PRP Top records

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	2^824565-114265	248219	Enzo Doria	01/2015
1752	2^824325-25	248147	Boyan Hu	12/2024
1753	(73*10^248145-1)/9	248146	Robert Price	01/2015
1754	2^823321+219407	247845	Enzo Doria	02/2024
1755	(2^823337+1)/(3*362268281)	247841	Gord Palameta	08/2018
1756	(13*10^247793-43)/3	247794	Robert Price	08/2023
1757	(2^822971-1)/6583769/28211445881/21255852651726486149207	247700	Robert Kinser	09/2016
1758	2^822296+76501	247536	Enzo Doria	05/2016
1759	2^821590-114167	247324	Enzo Doria	12/2014
1760	2^821512-2790659	247300	Enzo Doria	12/2015
1761	(21996^57121-1)/(21996^239-1)	247002	Ryan Propper	11/2023
1762	2^820356+7	246952	Jon Grantham	08/2023
1763	2^820077+382847	246868	Enzo Doria	11/2016
1764	2^820008+81	246848	Henri Lifchitz	01/2025
1765	2^820001+81269	246845	Enzo Doria	07/2016
1766	2^819463-59197	246683	Enzo Doria	10/2015
1767	2^819296+80581	246633	Enzo Doria	07/2016
1768	2^818764+21573	246473	Enzo Doria	11/2023
1769	2^817852+215491	246198	Enzo Doria	11/2023
1770	2^817160-350369	245990	Enzo Doria	06/2015
1771	2^816039-19	245653	Stefano Morozzi	07/2022
1772	2^816029+219407	245650	Enzo Doria	02/2024
1773	(71*10^245558-17)/9	245559	Serge Batalov	01/2023
1774	5*3^514648+2^514648	245551	Jon Grantham	08/2023
1775	88093#+(653879#)/(88093#)	245374	Makoto Morimoto	11/2017
1776	2^815111-113857	245373	Enzo Doria	10/2014
1777	(34555^54289-1)/(34555^233-1)	245334	Ryan Propper	11/2023
1778	2^814914-4001	245314	Yves Minet	05/2017
1779	846^83761-845^83761	245200	Jean-Louis Charton	12/2012
1780	2^814356-2790449	245146	Enzo Doria	12/2015
1781	2^814276-459029	245122	Enzo Doria	04/2015
1782	2^814023+180923	245046	Enzo Doria	07/2016
1783	2^813496+216751	244887	Enzo Doria	12/2023
1784	(3^513059-2^513059)/(1026119*5430216457)	244776	Mike Oakes	03/2017
1785	3^513007+16	244767	Robert Price	04/2020
1786	(46^147197-31^147197)/15	244752	Aurel Gibier	06/2024
1787	2^811882+27289	244401	Enzo Doria	12/2023
1788	2^811842-113675	244389	Enzo Doria	09/2014
1789	2^811132-2787929	244176	Enzo Doria	11/2015
1790	2^809746-2790971	243758	Enzo Doria	01/2016
1791	(14*10^243724-197)/3	243725	Robert Price	03/2023
1792	2^808767-3295	243464	Yves Minet	12/2016
1793	2^808621-113809	243420	Enzo Doria	09/2014
1794	2^808199+29693	243293	Enzo Doria	03/2024
1795	2^807724+1879621	243150	Enzo Doria	09/2016
1796	2^807417+217787	243057	Enzo Doria	01/2024
1797	(23*10^242909+91)/3	242910	Robert Price	03/2023
1798	2^806708+20371	242844	Enzo Doria	08/2023
1799	2*10^242822-91	242823	Robert Price	02/2023
1800	20^186554-3	242713	Paul Bourdelais	12/2020
1801	2^805843-113611	242583	Enzo Doria	08/2014
1802	2^805745-459763	242554	Enzo Doria	05/2015
1803	2^805353+782687	242436	Enzo Doria	11/2016
1804	(19*10^242362-7)/3	242363	Robert Price	12/2023
1805	2^804895+29963	242298	Enzo Doria	03/2024
1806	2^804725+28229	242247	Enzo Doria	01/2024
1807	6^311257+5	242206	Paul Bourdelais	02/2021
1808	(21^242194)%(10^242194)	242194	Henri Lifchitz	06/2025
1809	2^804277-417933	242112	Enzo Doria	01/2014
1810	2^803468-269039	241868	Enzo Doria	10/2013
1811	2^803172+80851	241779	Enzo Doria	07/2016
1812	2^803011+220073	241731	Enzo Doria	03/2024
1813	3^506233-2	241535	Robert Price	11/2013
1814	2^802025-25999	241434	Enzo Doria	10/2013
1815	(3^505823+3^252912+1)/7	241339	Serge Batalov	03/2014
1816	2^801575+25073	241299	Enzo Doria	11/2023
1817	2^801303+1872923	241217	Enzo Doria	05/2016
1818	2^801105+216977	241157	Enzo Doria	12/2023
1819	(23*10^241048-143)/3	241049	Robert Price	12/2023
1820	2^800579-1862947	240999	Enzo Doria	12/2015
1821	2^799999+16205	240824	Norman Luhn	09/2023
1822	3^504206+2	240568	Luke W. Richards	03/2018
1823	2^798973-26283	240515	Enzo Doria	10/2013
1824	2^798671-69487	240424	Enzo Doria	12/2015
1825	2^797220+79831	239988	Enzo Doria	06/2016
1826	2^796910-26001	239894	Enzo Doria	10/2013
1827	(97^120721-1)/811245216	239837	Paul Vanderveen	06/2025
1828	2^796598+653119	239800	Enzo Doria	12/2016
1829	2^796432-1859729	239750	Enzo Doria	11/2015
1830	2^796002-1852211	239621	Enzo Doria	08/2015
1831	2^795884+214081	239585	Enzo Doria	10/2023
1832	2^795709+75767	239533	Enzo Doria	04/2016
1833	2^795708+81721	239532	Enzo Doria	08/2016
1834	2^795468-2786249	239460	Enzo Doria	10/2015
1835	2^795442+80779	239452	Enzo Doria	07/2016
1836	2^795075-1852057	239342	Enzo Doria	08/2015
1837	(86^123677+1)/87	239252	Paul Bourdelais	01/2019
1838	2^794043+1875023	239031	Enzo Doria	06/2016
1839	2^793347-69577	238822	Enzo Doria	01/2016
1840	5*2^793288+3	238805	Jon Grantham	07/2023
1841	2^792988-344429	238714	Enzo Doria	08/2015
1842	2^792700-2786369	238627	Enzo Doria	11/2015
1843	2^792663-1844797	238616	Enzo Doria	06/2015
1844	2^792605-291943	238598	Enzo Doria	07/2015
1845	2^792366+218599	238526	Enzo Doria	01/2024
1846	(2^792061-2^396031+1)/5	238434	Thomas Ritschel	03/2014
1847	2^791321+30077	238212	Enzo Doria	03/2024
1848	4*10^238163+21	238164	Robert Price	12/2022
1849	(26*10^238157-77)/3	238158	Robert Price	03/2023
1850	10^237670+9	237671	Robert Price	08/2023
1851	2^789373+1869377	237625	Enzo Doria	05/2016
1852	((10^59387+1)^3(10^59387+1+10^29694)-(10^118774+10^59387)(10^29694-1)+10^178161)/27961	237544	Serge Batalov	04/2015
1853	Phi(1187740M,10)	237544	Anonymous	03/2025
1854	2^789033+218537	237523	Enzo Doria	01/2024
1855	2^788942+1866409	237496	Enzo Doria	02/2016
1856	2^788844-114329	237466	Enzo Doria	01/2015
1857	2^788705-1859713	237424	Enzo Doria	11/2015
1858	2^788325+224789	237310	Enzo Doria	07/2024
1859	15^201475+14	236953	Alfred Reich	10/2023
1860	2^786663+219173	236810	Enzo Doria	02/2024
1861	2^786180+1871971	236664	Enzo Doria	05/2016
1862	11^227092-90	236492	Enzo Doria	11/2012
1863	2^785260+1866361	236387	Enzo Doria	02/2016
1864	2^785220+1880611	236375	Enzo Doria	10/2016
1865	(2^784689-15)/7	236215	Stefano Morozzi	08/2022
1866	19^184650-2	236122	Robert Price	10/2014
1867	10^236059+216513	236060	Patrick De Geest	04/2016
1868	10^236059-20909	236059	Robert Price	09/2015
1869	2^783988+38011	236004	Enzo Doria	10/2024
1870	2^783893-21	235976	Stefano Morozzi	07/2022
1871	(47^140983-1)/2792206142311142462	235719	Paul Vanderveen	06/2025
1872	2^782821+37577	235653	Enzo Doria	10/2024
1873	(87^121487-1)/86	235625	Paul Bourdelais	12/2018
1874	2^782634-113981	235597	Enzo Doria	11/2014
1875	2^782423+1879733	235533	Enzo Doria	09/2016
1876	(10^(2117707+1)+1210^117707-1)/3	235415	Robert Price	10/2023
1877	(2^781970)/(781970^2)	235385	Henri Lifchitz	06/2025
1878	2^781682-2789543	235310	Enzo Doria	12/2015
1879	2^780481+21489	234949	Enzo Doria	05/2024
1880	2^780408-113453	234927	Enzo Doria	08/2014
1881	7*10^234915+9	234916	Robert Price	04/2023
1882	2^780368-1864829	234915	Enzo Doria	01/2016
1883	2^780284+7	234889	Jon Grantham	08/2023
1884	2^779593-1836559	234681	Enzo Doria	05/2015
1885	(8713#+(549391#)/(8713#))/360295171	234487	Makoto Morimoto	11/2017
1886	(5^335429+1)/6	234455	Paul Bourdelais	08/2010
1887	2^778788+22201	234439	Enzo Doria	09/2023
1888	2^778395-113617	234321	Enzo Doria	08/2014
1889	5*2^778090+3	234230	Jon Grantham	07/2023
1890	(21430^54289-1)/(21430^233-1)	234118	Ryan Propper	11/2023
1891	(5*10^234054-101)/3	234055	Robert Price	08/2023
1892	23*10^234025-7	234027	Robert Price	10/2022
1893	2^777170+21489	233952	Enzo Doria	05/2024
1894	Phi(78125,5517)	233857	Anonymous	09/2022
1895	5^334359-3^334359-1	233707	Jon Grantham	08/2023
1896	2^776245-2792353	233674	Enzo Doria	02/2016
1897	49748^49748+49735^49735	233656	Henri Lifchitz	11/2024
1898	2^776060-114029	233618	Enzo Doria	11/2014
1899	2^775987-2789557	233596	Enzo Doria	12/2015
1900	2*10^233564-91	233565	Robert Price	02/2023
1901	2^775865+21489	233559	Enzo Doria	05/2024
1902	2^775672+1866721	233501	Enzo Doria	03/2016
1903	2^775238+57	233370	Stefano Morozzi	05/2021
1904	(11^223999+1)/12	233270	Paul Bourdelais	02/2010
1905	U(1302049)	233238	Serge Batalov	07/2024
1906	2^774118+1885789	233033	Enzo Doria	04/2017
1907	21^176191-20^176191	232964	Jean-Louis Charton	01/2015
1908	2^773723+217523	232914	Enzo Doria	01/2024
1909	2^773679-113425	232901	Enzo Doria	08/2014
1910	(7*10^232620+23)/3	232621	Robert Price	05/2023
1911	10^232599+192489	232600	Patrick De Geest	12/2013
1912	10^232599-3	232599	Markus Tervooren	10/2010
1913	2^772552-458879	232562	Enzo Doria	04/2015
1914	2^772214+1874899	232460	Enzo Doria	06/2016
1915	2^771994-1862771	232394	Enzo Doria	12/2015
1916	2^771889+1876037	232362	Enzo Doria	07/2016
1917	2^771660+1866511	232293	Enzo Doria	02/2016
1918	5^332150-18188	232163	Enzo Doria	06/2014
1919	2^771227+61121	232163	Boyan Hu	05/2024
1920	2^770623+212543	231981	Enzo Doria	09/2023
1921	3^485977-2^485977	231870	Mike Oakes	09/2009
1922	2^770082-114161	231818	Enzo Doria	01/2015
1923	2^769791+25523	231731	Enzo Doria	11/2023
1924	7^274120-2	231659	Paul Bourdelais	08/2023
1925	(20^177967+1)/21	231540	Paul Bourdelais	05/2013
1926	2^769011+81	231496	Henri Lifchitz	01/2025
1927	(71^125029-1)/105024430	231453	Paul Vanderveen	06/2025
1928	(4*10^231254+23)/9	231254	Serge Batalov	11/2022
1929	2^768205+22217	231253	Enzo Doria	09/2023
1930	49262^49262-49247^49247	231163	Henri Lifchitz	11/2024
1931	2^767622-9221	231078	Lelio R Paula	01/2016
1932	2^767344+1880311	230994	Enzo Doria	09/2016
1933	8*10^230921-13	230922	Robert Price	08/2023
1934	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
1935	(10^230706+179)/9	230706	Serge Batalov	12/2014
1936	2^766309+1875257	230682	Enzo Doria	06/2016
1937	(26131^52441-1)/(26131^229-1)	230629	Ryan Propper	11/2023
1938	2^765635+1879883	230480	Enzo Doria	09/2016
1939	43^141090+141090	230467	Kellen Shenton	06/2023
1940	(26*10^230394-119)/3	230395	Robert Price	07/2023
1941	2^764348-113697	230092	Enzo Doria	09/2014
1942	2^764131+78863	230027	Enzo Doria	05/2016
1943	2^763701+60197	229897	Enzo Doria	03/2016
1944	4*10^229836+21	229837	Robert Price	12/2022
1945	2^763362+27799	229795	Enzo Doria	01/2024
1946	2^762841-25905	229639	Enzo Doria	10/2013
1947	2^762659+212633	229584	Enzo Doria	09/2023
1948	77*10^229211+3	229213	Robert Price	11/2023
1949	2^761117-113569	229120	Enzo Doria	08/2014
1950	(29022^51529-1)/(29022^227-1)	228947	Ryan Propper	11/2023
1951	(98^114859+1)/99	228709	Paul Bourdelais	12/2018
1952	5*3^479067-2^479067	228574	Jon Grantham	08/2023
1953	2^758645+216011	228375	Enzo Doria	12/2023
1954	(2^758231+1)/(32714694297653973236839266867)	228223	Gord Palameta	12/2018
1955	10^228208+111	228209	Boyan Hu	10/2024
1956	(298*10^228177-7)/3	228179	Robert Price	02/2023
1957	2^757985-2790013	228177	Enzo Doria	12/2015
1958	34*10^228129-9	228131	Robert Price	05/2023
1959	2^757038-1862081	227892	Enzo Doria	12/2015
1960	2^756839+95849	227832	Makoto Morimoto	10/2013
1961	(2^756839+6989)/756091	227826	Makoto Morimoto	09/2016
1962	(2^756839-50211)/(137*3203)	227826	Makoto Morimoto	08/2019
1963	2^756773-112723	227812	Enzo Doria	07/2014
1964	(710^(2113887+1)+9*10^113887-7)/9	227775	Robert Price	08/2024
1965	(10^227542)/(227542^10)	227489	Henri Lifchitz	05/2025
1966	524309#+616367	227431	Makoto Morimoto	02/2016
1967	2^755404+226575	227400	Enzo Doria	09/2024
1968	2^755116+81	227313	Henri Lifchitz	11/2024
1969	2^755097-114193	227307	Enzo Doria	12/2014
1970	7*10^227178+39	227179	Robert Price	01/2023
1971	9*10^227153-89	227154	Robert Price	02/2023
1972	2^754473-2791513	227120	Enzo Doria	01/2016
1973	2^754376+25	227090	Stefano Morozzi	05/2021
1974	2^754138+213289	227019	Enzo Doria	09/2023
1975	2^754038+25	226989	Stefano Morozzi	05/2021
1976	2^753263+217133	226755	Enzo Doria	12/2023
1977	7*10^226479-9	226480	Robert Price	02/2023
1978	(10^226381+1)/14973418875371	226368	Alfred Reich	06/2025
1979	2^751655+33893	226271	Enzo Doria	06/2024
1980	2^751426-764321	226202	Enzo Doria	12/2013
1981	(18^180181-1)/17	226176	Andy Steward	04/2007
1982	2^750740-3	225996	Paul Bourdelais	03/2012
1983	2^750725+60227	225991	Enzo Doria	02/2016
1984	2^750525-113743	225931	Enzo Doria	09/2014
1985	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
1986	2^749444-1861889	225606	Enzo Doria	12/2015
1987	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
1988	(3^472721+1)/9422189991086734893916	225524	Paul Vanderveen	06/2025
1989	2^749096+1876861	225501	Enzo Doria	07/2016
1990	2^748895+26213	225440	Enzo Doria	12/2023
1991	(519643#+43033)/(2318712706283)	225379	Makoto Morimoto	08/2019
1992	2^748657+79607	225369	Enzo Doria	06/2016
1993	(2^746920-11)/5	224845	Stefano Morozzi	08/2022
1994	2^746653-291583	224765	Enzo Doria	07/2015
1995	2^746461-114043	224708	Enzo Doria	11/2014
1996	2^746302+25	224660	Stefano Morozzi	05/2021
1997	(202*10^224545-1)/3	224547	Robert Price	06/2023
1998	(19*10^224533-37)/9	224534	Alfred Reich	12/2023
1999	2^745674+213949	224471	Enzo Doria	10/2023
2000	2^745098-350471	224297	Enzo Doria	06/2015

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Probable Primes Top 10000

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