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	2^687619+81563	206994	Enzo Doria	08/2016
1752	3*10^206927+37	206928	Robert Price	08/2023
1753	2^687383+21803	206923	Enzo Doria	09/2023
1754	2^686572-1845299	206679	Enzo Doria	07/2015
1755	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
1756	(2^685739+1)/(3*87774593)	206420	Gord Palameta	08/2018
1757	2^685578+3	206380	Paul Bourdelais	04/2012
1758	2^685078+218599	206230	Enzo Doria	01/2024
1759	2^684836-49349	206157	Enzo Doria	10/2015
1760	(73^110603-1)/72	206088	Paul Bourdelais	06/2018
1761	2^684163-2790967	205954	Enzo Doria	12/2015
1762	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
1763	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
1764	(68*10^205510+13)/9	205511	Serge Batalov	01/2023
1765	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
1766	2^682414+215029	205428	Enzo Doria	11/2023
1767	(963^68821-1)/962	205334	Jinyuan Wang	01/2024
1768	(43*10^205183-421)/9	205184	Robert Price	10/2023
1769	2^681545+467	205166	Lelio R Paula	11/2013
1770	2^681306+81049	205094	Enzo Doria	07/2016
1771	2^680697+1877057	204911	Enzo Doria	07/2016
1772	2^680415+71783	204826	Enzo Doria	04/2016
1773	10^204764-8001	204764	Robert Price	03/2023
1774	(26*10^204730-77)/3	204731	Robert Price	03/2023
1775	2^679860-459995	204659	Enzo Doria	06/2015
1776	2^679593+1879547	204578	Enzo Doria	09/2016
1777	2^678899+220073	204369	Enzo Doria	03/2024
1778	2^678753+21677	204326	Enzo Doria	08/2023
1779	2^678651+1875023	204295	Enzo Doria	07/2016
1780	2^678561+678561	204268	Henri Lifchitz	05/2006
1781	5*3^427884+2^427884	204154	Jon Grantham	08/2023
1782	2^678101-114043	204129	Enzo Doria	11/2014
1783	2^678028+1875631	204107	Enzo Doria	06/2016
1784	2^677721+28607	204015	Enzo Doria	01/2024
1785	(19*10^203798-7)/3	203799	Robert Price	12/2023
1786	2^676992-59783	203795	Enzo Doria	10/2015
1787	2^676972+1866871	203789	Enzo Doria	03/2016
1788	2^676815+22583	203742	Enzo Doria	09/2023
1789	2^676761-9	203726	Robert Price	01/2017
1790	2^676592-23	203675	Stefano Morozzi	07/2022
1791	2^676563-2792407	203666	Enzo Doria	02/2016
1792	2^676306-114713	203589	Enzo Doria	04/2015
1793	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
1794	6*10^203365+53	203366	Robert Price	09/2023
1795	10247^50678-50678^10247	203250	Norbert Schneider	03/2022
1796	2^674627-25161	203083	Enzo Doria	09/2013
1797	2^674603-69337	203076	Enzo Doria	12/2015
1798	(182*10^203048+1)/3	203050	Robert Price	09/2023
1799	2^674459+74213	203033	Enzo Doria	04/2016
1800	2^674116-458879	202930	Enzo Doria	04/2015
1801	2^674076-114755	202918	Enzo Doria	04/2015
1802	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
1803	(2^673184-7)/3	202649	Stefano Morozzi	08/2022
1804	(467617#+14534)/(2^21343)	202603	Makoto Morimoto	06/2019
1805	2^672773+219407	202525	Enzo Doria	03/2024
1806	2^672556-1835519	202460	Enzo Doria	04/2015
1807	(7*10^202267+179)/3	202268	Robert Price	02/2023
1808	2^671446-351401	202126	Enzo Doria	07/2015
1809	2^671373+77747	202104	Enzo Doria	05/2016
1810	(2*10^202059+7)/9	202059	Rytis Slatkevicius	01/2023
1811	98*10^202021-9	202023	Robert Price	05/2023
1812	2^670726-114845	201909	Enzo Doria	05/2015
1813	2^670539-25045	201853	Enzo Doria	09/2013
1814	10^201801-93	201801	Robert Price	02/2023
1815	43284^43519-43519^43284	201769	Norbert Schneider	08/2018
1816	2^670213+282317	201755	Enzo Doria	09/2016
1817	2^670133+89	201731	Stefano Morozzi	05/2021
1818	2^669854-113501	201647	Enzo Doria	08/2014
1819	2^669718+81619	201606	Enzo Doria	08/2016
1820	(299*10^201547-17)/3	201549	Robert Price	02/2023
1821	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
1822	2^668938-1839821	201371	Enzo Doria	06/2015
1823	2^668492+1879303	201237	Enzo Doria	08/2016
1824	7*10^201140-87	201141	Robert Price	03/2023
1825	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
1826	10194^50161-50161^10194	201063	Norbert Schneider	09/2020
1827	2^667894+1875589	201057	Enzo Doria	06/2016
1828	2^667569-1836559	200959	Enzo Doria	05/2015
1829	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
1830	2^666430+782569	200616	Enzo Doria	10/2016
1831	(13*10^200610-43)/3	200611	Robert Price	08/2023
1832	(8*10^200408-11)/3	200409	Robert Price	07/2023
1833	(19*10^200260+101)/3	200261	Robert Price	06/2023
1834	43183^43183+4^4	200167	Serge Batalov	04/2024
1835	(86^103471+1)/87	200163	Paul Bourdelais	05/2018
1836	(10^(2100072+1)+3610^100072-1)/9	200145	Robert Price	09/2023
1837	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
1838	103(10^100000+33798)^2-4707(10^100000+33798)+50383	200003	Robert Price	01/2018
1839	numbpart(32235776596)	200002	Serge Batalov	04/2017
1840	(10^200001+149)/3	200001	Serge Batalov	12/2014
1841	10^200000+571791	200001	Patrick De Geest	08/2019
1842	(3^419180-621444)/3	200000	Stefano Morozzi	06/2019
1843	(3^419180-1941384)/3	200000	Stefano Morozzi	08/2019
1844	10^200000-45557	200000	Patrick De Geest	08/2019
1846	(10^200000-1)/9-10^58838	200000	Akihiko Yoshida	04/2020
1845	2593604092947240127723272^8192+2593604092947240127722755^8192	200000	Youcef Lemsafer	01/2023
1847	(2593604092947240127723019^8192+2593604092947240127723011^8192)/2	199999	Youcef Lemsafer	01/2023
1848	(2593604092947240127723087^8192+2593604092947240127722984^8192)/147457	199994	Youcef Lemsafer	01/2023
1849	(2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986	199989	Youcef Lemsafer	01/2023
1850	(2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169	199986	Youcef Lemsafer	01/2023
1851	92*10^199980-9	199982	Robert Price	12/2021
1852	(2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649	199977	Youcef Lemsafer	01/2023
1853	(85*10^199951-139)/9	199952	Robert Price	08/2021
1854	(10^199926+7)/29/373/2339	199919	Alfred Reich	08/2021
1855	2^663838+25819	199836	Enzo Doria	11/2023
1856	23*10^199833-9	199835	Robert Price	10/2021
1857	fibonacci(956176)-4	199829	Jon Grantham	08/2023
1858	(299*10^199801-17)/3	199803	Robert Price	04/2020
1859	6*10^199788+77	199789	Robert Price	06/2020
1860	(23*10^199615+37)/3	199616	Robert Price	02/2022
1861	(17*10^199607-167)/3	199608	Robert Price	05/2022
1862	2^663020-933075	199589	Paul Bourdelais	06/2021
1863	2^663007+29963	199585	Enzo Doria	03/2024
1864	3*2^662703-5	199494	Jon Grantham	07/2023
1865	(14*10^199447+73)/3	199448	Robert Price	12/2018
1866	(2^662424-15)/7	199409	Stefano Morozzi	08/2022
1867	2^662194+22189	199341	Enzo Doria	09/2023
1868	2^662103-29287	199313	Enzo Doria	08/2015
1869	(2*10^199283+457)/9	199283	Robert Price	01/2018
1870	(10^199248-19)/9	199248	Robert Price	01/2018
1871	(83*10^199213+529)/9	199214	Robert Price	12/2021
1872	(194*10^199146-17)/3	199148	Robert Price	09/2020
1873	(151*10^199003-1)/3	199005	Robert Price	03/2020
1874	9*10^198946-73	198947	Robert Price	01/2021
1875	45*10^198931-7	198933	Robert Price	07/2020
1876	2^660482-2891	198825	Yves Minet	05/2016
1877	2^659589-21	198557	Stefano Morozzi	07/2022
1878	2^659583+1879223	198555	Enzo Doria	08/2016
1879	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
1880	(49*10^198403+311)/9	198404	Robert Price	06/2019
1881	96*10^198376-7	198378	Robert Price	03/2021
1882	(10^198375+7)/59/1201/87589	198366	Alfred Reich	08/2021
1883	2^658828-29819	198327	Enzo Doria	08/2015
1884	2^658776-2791229	198312	Enzo Doria	01/2016
1885	(35*10^198294-377)/9	198295	Robert Price	07/2018
1886	(4*10^198268+137)/3	198269	Robert Price	03/2018
1887	2^658544-1854029	198242	Enzo Doria	09/2015
1888	(62*10^198229-233)/9	198230	Robert Price	02/2022
1889	(26*10^198200-41)/3	198201	Robert Price	02/2022
1890	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
1891	2^657815+26213	198023	Enzo Doria	12/2023
1892	2*10^197959-37	197960	Robert Price	11/2021
1893	(29*10^197941-41)/3	197942	Tyler Busby	03/2024
1894	(232*10^197897+17)/3	197899	Robert Price	04/2021
1895	(4*10^197778+173)/3	197779	Robert Price	02/2018
1896	2^656763+211373	197706	Enzo Doria	08/2023
1897	78*10^197702-7	197704	Robert Price	10/2020
1898	(17*10^197640-23)/3	197641	Robert Price	03/2021
1899	(29*10^197629-77)/3	197630	Robert Price	02/2020
1900	2^656462+1874419	197615	Enzo Doria	06/2016
1901	(89^101363+1)/90	197595	Paul Bourdelais	11/2017
1902	2^655893-344563	197444	Enzo Doria	07/2015
1903	2^655875+71333	197439	Enzo Doria	04/2016
1904	2^655845-9	197430	Robert Price	01/2017
1905	(299*10^197426+1)/3	197428	Robert Price	04/2020
1906	2^655682-1849121	197380	Enzo Doria	08/2015
1907	4*10^197268-89	197269	Robert Price	11/2018
1908	(11*10^197198-89)/3	197199	Robert Price	05/2021
1909	2^655045-49603	197189	Enzo Doria	10/2015
1910	2^655000-2784089	197175	Enzo Doria	10/2015
1911	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
1912	(4*10^197061+41)/9	197061	Serge Batalov	11/2022
1913	(154*10^197005+17)/9	197007	Robert Price	06/2022
1914	2^654400-39719	196995	Enzo Doria	09/2015
1915	(5^281807-2^281807)/3	196975	Jon Grantham	08/2023
1916	(14*10^196965-221)/9	196966	Robert Price	04/2018
1917	2^654216-459995	196939	Enzo Doria	06/2015
1918	(17*10^196921+31)/3	196922	Robert Price	01/2019
1919	(14*10^196885-89)/3	196886	Robert Price	05/2020
1920	3*10^196881-59	196882	Robert Price	09/2018
1921	2^653851+82295	196829	Enzo Doria	09/2016
1922	(38*10^196792+691)/9	196793	Robert Price	10/2018
1923	(65*10^196768+493)/9	196769	Robert Price	08/2021
1925	2^653636-29429	196765	Enzo Doria	08/2015
1924	2^653638-11	196765	Stefano Morozzi	07/2022
1926	2^653601-69673	196754	Enzo Doria	02/2016
1927	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
1928	2^652786-1852571	196509	Enzo Doria	08/2015
1929	2^652752-1325	196498	Yves Minet	07/2015
1930	2^652470-1859141	196414	Enzo Doria	10/2015
1931	2^652346+29329	196376	Enzo Doria	02/2024
1932	2^652307+1877483	196364	Enzo Doria	08/2016
1933	2^652293-115273	196360	Enzo Doria	06/2015
1934	(47*10^196281+403)/9	196282	Robert Price	03/2019
1935	2^652025+218027	196280	Enzo Doria	01/2024
1936	2^652004+23961	196273	Enzo Doria	10/2023
1937	(7*10^196125-31)/3	196126	Robert Price	12/2021
1938	33^129128+129128^33	196083	Norbert Schneider	06/2022
1939	6*10^196070+73	196071	Robert Price	04/2019
1940	2^651218-1868201	196037	Enzo Doria	04/2016
1941	2^651047-49687	195985	Enzo Doria	10/2015
1942	10^195968-700001	195968	Robert Price	08/2021
1943	fibonacci(937485)+3	195923	Jon Grantham	08/2023
1944	(29*10^195875-197)/3	195876	Robert Price	08/2021
1945	(25*10^195808-97)/9	195809	Robert Price	01/2022
1946	2^650285-2785333	195756	Enzo Doria	10/2015
1947	(10^195732+7)/18089/49605893	195721	Alfred Reich	08/2021
1948	(29*10^195648-41)/3	195649	Tyler Busby	03/2024
1949	(69^106397-1)/68	195647	Paul Bourdelais	10/2017
1950	2^649811+1877573	195613	Enzo Doria	08/2016
1951	2^649662-170531	195568	Hans Havermann	10/2018
1952	2^649586+182839	195545	Enzo Doria	11/2016
1953	2^649537-1867363	195531	Enzo Doria	04/2016
1954	2^649536-1861499	195530	Enzo Doria	12/2015
1955	2^649493+25907	195517	Enzo Doria	11/2023
1956	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
1957	2^649102-59351	195400	Enzo Doria	10/2015
1958	(2*10^195399+529)/9	195399	Robert Price	01/2018
1959	(202*10^195383-13)/9	195385	Robert Price	01/2020
1960	2^648988+1178971	195365	Enzo Doria	06/2016
1961	2^648975-114319	195361	Enzo Doria	02/2015
1962	(11*10^195350-137)/9	195351	Robert Price	01/2018
1963	2^648619-24835	195254	Enzo Doria	09/2013
1964	5*10^195250-21	195251	Robert Price	12/2021
1965	(14*10^195234-83)/3	195235	Robert Price	12/2018
1966	5*10^195221+81	195222	Robert Price	03/2019
1967	10^195143-5001	195143	Robert Price	12/2021
1968	2^648190-24737	195125	Enzo Doria	09/2013
1969	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
1970	(29*10^195098-197)/3	195099	Robert Price	08/2021
1971	10^195060+89701	195061	Patrick De Geest	02/2021
1973	10^195060-40000000001	195060	Robert Price	09/2020
1972	10^195060-110337	195060	Patrick De Geest	02/2021
1974	56*10^195032-3	195034	Robert Price	03/2020
1975	11^187185-90	194934	Enzo Doria	09/2012
1976	2^647468+220141	194908	Enzo Doria	03/2024
1977	(86*10^194818-437)/9	194819	Robert Price	03/2021
1978	2^647068+77281	194787	Enzo Doria	05/2016
1979	2*10^194716-93	194717	Robert Price	12/2021
1980	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
1981	F(931517)	194676	Henri Lifchitz	09/2008
1982	4*10^194668+49	194669	Robert Price	01/2019
1983	2^646589+1179407	194643	Enzo Doria	06/2016
1984	2^646289-114621	194553	Enzo Doria	05/2015
1985	2^646236-39659	194537	Enzo Doria	09/2015
1986	(16*10^194536+53)/3	194537	Robert Price	03/2019
1987	2^646161-59833	194514	Enzo Doria	11/2015
1988	(17*10^194502+31)/3	194503	Robert Price	01/2019
1989	(19*10^194428+287)/9	194429	Robert Price	10/2021
1990	2*10^194413+3	194414	Robert Price	07/2015
1991	2^645360-1848599	194273	Enzo Doria	08/2015
1992	22470^44641+44641^22470	194260	Norbert Schneider	08/2023
1993	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
1994	Phi(293127,10)	194041	Makoto Kamada	12/2023
1995	2*10^193981-43	193982	Robert Price	04/2018
1996	2^644382+75169	193979	Enzo Doria	04/2016
1997	2^644304-1861409	193955	Enzo Doria	11/2015
1998	(29*10^193950-23)/3	193951	Robert Price	03/2022
1999	5*10^193907-9	193908	Robert Price	05/2015
2000	2^644043+1876703	193877	Enzo Doria	07/2016

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PRP Records

Probable Primes Top 10000

(295036 PRPs in the top)