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	(713^74897-1)/712	213685	Jinyuan Wang	08/2023
1752	2^709773+25907	213663	Enzo Doria	12/2023
1753	2^708468-114329	213271	Enzo Doria	02/2015
1754	2^708293+27557	213218	Enzo Doria	01/2024
1755	2^707277+28997	212912	Enzo Doria	02/2024
1756	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
1757	2^706838-69041	212780	Enzo Doria	11/2015
1758	2^705653+25907	212423	Enzo Doria	12/2023
1759	22*10^212339+7	212341	Robert Price	10/2022
1760	2^704577-113871	212099	Enzo Doria	10/2014
1761	(2^704548-19)/3	212090	Stefano Morozzi	08/2022
1762	2^704110-2792441	211959	Enzo Doria	02/2016
1763	2^704084+28531	211951	Enzo Doria	02/2024
1764	2^703943-1862947	211908	Enzo Doria	12/2015
1765	(60^119083+1)/61	211746	Paul Bourdelais	10/2018
1766	(184*10^211682-1)/3	211684	Robert Price	12/2022
1767	(10^211610-91)/9	211610	Serge Batalov	12/2014
1768	227^89797+2	211565	Lelio R Paula	08/2012
1769	2^702194-3	211382	Paul Bourdelais	03/2012
1770	2^702064+1874911	211343	Enzo Doria	07/2016
1771	2^701968-113873	211314	Enzo Doria	10/2014
1772	(14*10^211262-41)/9	211263	Serge Batalov	01/2023
1773	2^701713-113779	211237	Enzo Doria	09/2014
1774	2^701616-216803	211208	Enzo Doria	01/2024
1775	2^701449-25201	211158	Enzo Doria	09/2013
1776	2^701403-2786977	211144	Enzo Doria	11/2015
1777	2^701189-25423	211079	Enzo Doria	09/2013
1778	2^701162-459161	211071	Enzo Doria	05/2015
1779	2^700793+219407	210960	Enzo Doria	03/2024
1780	(24^152783-1)/23	210872	Paul Bourdelais	04/2018
1781	2^700400+9385	210842	Lelio R Paula	01/2014
1782	2^700304-17	210813	Stefano Morozzi	07/2022
1783	2^700131+1874693	210761	Enzo Doria	06/2016
1784	(2^700095+225414)/2	210750	Stefano Morozzi	04/2020
1785	(2^700090+278254)/2	210748	Stefano Morozzi	04/2020
1786	(2^700075+303666)/2	210744	Stefano Morozzi	04/2020
1787	(2^700073+75882)/2	210743	Stefano Morozzi	04/2020
1788	(2^700074+328890)/2	210743	Stefano Morozzi	04/2020
1789	(2^700052+79162)/2	210737	Stefano Morozzi	04/2020
1790	(2^700052+304458)/2	210737	Stefano Morozzi	04/2020
1791	(2^700048+376578)/2	210736	Stefano Morozzi	04/2020
1792	11^202357-1140	210734	Enzo Doria	12/2012
1793	(2^700021+25874)/2	210728	Stefano Morozzi	04/2020
1794	(2^700018+377518)/2	210727	Stefano Morozzi	04/2020
1795	2^699999+300729	210721	Norman Luhn	09/2023
1796	(238*10^210712-1)/3	210714	Robert Price	09/2023
1797	2^699740+25	210643	Stefano Morozzi	05/2021
1798	(23*10^210525-143)/3	210526	Robert Price	12/2023
1799	2^698929-2788423	210399	Enzo Doria	11/2015
1800	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
1801	2^698316+1878601	210215	Enzo Doria	08/2016
1802	34*10^210097-9	210099	Robert Price	05/2023
1803	(19*10^210011-49)/3	210012	Robert Price	06/2023
1804	6*10^209846-91	209847	Robert Price	05/2023
1805	2^697036+1878751	209829	Enzo Doria	08/2016
1806	2^696813+28607	209762	Enzo Doria	02/2024
1807	(238*10^209715-1)/3	209717	Robert Price	09/2023
1808	6^269407+5	209640	Paul Bourdelais	02/2021
1809	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
1810	2^696254-115151	209594	Enzo Doria	06/2015
1811	(35^135623+1)/36	209410	Paul Bourdelais	07/2018
1812	7*10^209161+39	209162	Robert Price	01/2023
1813	2^694633+1887257	209106	Enzo Doria	05/2017
1814	fibonacci(999790)-4	208944	Jon Grantham	08/2023
1815	2^693959+180923	208903	Enzo Doria	07/2016
1816	(2^693747-11)/3	208839	Stefano Morozzi	08/2022
1817	2^693462-1847561	208753	Enzo Doria	07/2015
1818	2^690890-59981	207979	Enzo Doria	11/2015
1819	(38^131591+1)/39	207884	Paul Bourdelais	07/2018
1820	3*2^690484+5	207857	Jon Grantham	07/2023
1821	2^690163+1877063	207760	Enzo Doria	07/2016
1822	7^245608-2	207563	Paul Bourdelais	01/2021
1823	(67*10^207556+23)/9	207557	Serge Batalov	01/2023
1824	2^689286-29381	207496	Enzo Doria	08/2015
1825	2^689122-114521	207447	Enzo Doria	04/2015
1826	9*10^207254-89	207255	Robert Price	02/2023
1827	2^688373+6077	207221	Enzo Doria	02/2016
1828	2^688201+1875527	207170	Enzo Doria	07/2016
1829	(42^127609+1)/43	207140	Paul Bourdelais	07/2018
1830	2^687938+213589	207090	Enzo Doria	10/2023
1831	2^687619+81563	206994	Enzo Doria	08/2016
1832	3*10^206927+37	206928	Robert Price	08/2023
1833	2^687383+21803	206923	Enzo Doria	09/2023
1834	(11*10^206688+19)/3	206689	Robert Price	07/2024
1835	2^686572-1845299	206679	Enzo Doria	07/2015
1836	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
1837	(2^685739+1)/(3*87774593)	206420	Gord Palameta	08/2018
1838	2^685578+3	206380	Paul Bourdelais	04/2012
1839	2^685078+218599	206230	Enzo Doria	01/2024
1840	2^684836-49349	206157	Enzo Doria	10/2015
1841	(73^110603-1)/72	206088	Paul Bourdelais	06/2018
1842	2^684163-2790967	205954	Enzo Doria	12/2015
1843	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
1844	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
1845	(68*10^205510+13)/9	205511	Serge Batalov	01/2023
1846	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
1847	2^682414+215029	205428	Enzo Doria	11/2023
1848	(963^68821-1)/962	205334	Jinyuan Wang	01/2024
1849	(43*10^205183-421)/9	205184	Robert Price	10/2023
1850	2^681545+467	205166	Lelio R Paula	11/2013
1851	2^681306+81049	205094	Enzo Doria	07/2016
1852	2^680697+1877057	204911	Enzo Doria	07/2016
1853	2^680415+71783	204826	Enzo Doria	04/2016
1854	10^204764-8001	204764	Robert Price	03/2023
1855	(26*10^204730-77)/3	204731	Robert Price	03/2023
1856	2^679860-459995	204659	Enzo Doria	06/2015
1857	2^679593+1879547	204578	Enzo Doria	09/2016
1858	2^678899+220073	204369	Enzo Doria	03/2024
1859	2^678753+21677	204326	Enzo Doria	08/2023
1860	2^678651+1875023	204295	Enzo Doria	07/2016
1861	2^678561+678561	204268	Henri Lifchitz	05/2006
1862	5*3^427884+2^427884	204154	Jon Grantham	08/2023
1863	2^678101-114043	204129	Enzo Doria	11/2014
1864	2^678028+1875631	204107	Enzo Doria	06/2016
1865	2^677721+28607	204015	Enzo Doria	01/2024
1866	(19*10^203798-7)/3	203799	Robert Price	12/2023
1867	2^676992-59783	203795	Enzo Doria	10/2015
1868	2^676972+1866871	203789	Enzo Doria	03/2016
1869	2^676815+22583	203742	Enzo Doria	09/2023
1870	2^676761-9	203726	Robert Price	01/2017
1871	2^676592-23	203675	Stefano Morozzi	07/2022
1872	2^676563-2792407	203666	Enzo Doria	02/2016
1873	2^676306-114713	203589	Enzo Doria	04/2015
1874	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
1875	6*10^203365+53	203366	Robert Price	09/2023
1876	10247^50678-50678^10247	203250	Norbert Schneider	03/2022
1877	2^674627-25161	203083	Enzo Doria	09/2013
1878	2^674603-69337	203076	Enzo Doria	12/2015
1879	(182*10^203048+1)/3	203050	Robert Price	09/2023
1880	2^674459+74213	203033	Enzo Doria	04/2016
1881	2^674116-458879	202930	Enzo Doria	04/2015
1882	2^674076-114755	202918	Enzo Doria	04/2015
1883	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
1884	5^289926-289926^5	202650	Henri Lifchitz	07/2024
1885	(2^673184-7)/3	202649	Stefano Morozzi	08/2022
1886	(467617#+14534)/(2^21343)	202603	Makoto Morimoto	06/2019
1887	(155^92479-1)/154	202558	Anonymous	06/2024
1888	2^672773+219407	202525	Enzo Doria	03/2024
1889	2^672556-1835519	202460	Enzo Doria	04/2015
1890	(7*10^202267+179)/3	202268	Robert Price	02/2023
1891	2^671446-351401	202126	Enzo Doria	07/2015
1892	2^671373+77747	202104	Enzo Doria	05/2016
1893	(2*10^202059+7)/9	202059	Rytis Slatkevicius	01/2023
1894	98*10^202021-9	202023	Robert Price	05/2023
1895	2^670726-114845	201909	Enzo Doria	05/2015
1896	2^670539-25045	201853	Enzo Doria	09/2013
1897	10^201801-93	201801	Robert Price	02/2023
1898	43284^43519-43519^43284	201769	Norbert Schneider	08/2018
1899	2^670213+282317	201755	Enzo Doria	09/2016
1900	2^670133+89	201731	Stefano Morozzi	05/2021
1901	2^669854-113501	201647	Enzo Doria	08/2014
1902	2^669718+81619	201606	Enzo Doria	08/2016
1903	(299*10^201547-17)/3	201549	Robert Price	02/2023
1904	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
1905	2^668938-1839821	201371	Enzo Doria	06/2015
1906	(198^87623-1)/197	201239	Anonymous	06/2024
1907	2^668492+1879303	201237	Enzo Doria	08/2016
1908	7*10^201140-87	201141	Robert Price	03/2023
1909	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
1910	10194^50161-50161^10194	201063	Norbert Schneider	09/2020
1911	2^667894+1875589	201057	Enzo Doria	06/2016
1912	2^667569-1836559	200959	Enzo Doria	05/2015
1913	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
1914	(166^90407-1)/165	200712	Anonymous	06/2024
1915	2^666430+782569	200616	Enzo Doria	10/2016
1916	(13*10^200610-43)/3	200611	Robert Price	08/2023
1917	(8*10^200408-11)/3	200409	Robert Price	07/2023
1918	(19*10^200260+101)/3	200261	Robert Price	06/2023
1919	43183^43183+4^4	200167	Serge Batalov	04/2024
1920	(86^103471+1)/87	200163	Paul Bourdelais	05/2018
1921	(10^(2100072+1)+3610^100072-1)/9	200145	Robert Price	09/2023
1922	2^664778+34789	200119	Enzo Doria	07/2024
1923	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
1924	103(10^100000+33798)^2-4707(10^100000+33798)+50383	200003	Robert Price	01/2018
1925	numbpart(32235776596)	200002	Serge Batalov	04/2017
1926	(10^200001+149)/3	200001	Serge Batalov	12/2014
1927	10^200000+571791	200001	Patrick De Geest	08/2019
1928	(3^419180-621444)/3	200000	Stefano Morozzi	06/2019
1929	(3^419180-1941384)/3	200000	Stefano Morozzi	08/2019
1930	10^200000-45557	200000	Patrick De Geest	08/2019
1931	(10^200000-1)/9-10^58838	200000	Akihiko Yoshida	04/2020
1932	2593604092947240127723272^8192+2593604092947240127722755^8192	200000	Youcef Lemsafer	01/2023
1933	(2593604092947240127723019^8192+2593604092947240127723011^8192)/2	199999	Youcef Lemsafer	01/2023
1934	(2593604092947240127723087^8192+2593604092947240127722984^8192)/147457	199994	Youcef Lemsafer	01/2023
1935	(2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986	199989	Youcef Lemsafer	01/2023
1936	(2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169	199986	Youcef Lemsafer	01/2023
1937	92*10^199980-9	199982	Robert Price	12/2021
1938	(2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649	199977	Youcef Lemsafer	01/2023
1939	(85*10^199951-139)/9	199952	Robert Price	08/2021
1940	(10^199926+7)/29/373/2339	199919	Alfred Reich	08/2021
1941	2^663838+25819	199836	Enzo Doria	11/2023
1942	23*10^199833-9	199835	Robert Price	10/2021
1943	fibonacci(956176)-4	199829	Jon Grantham	08/2023
1944	(299*10^199801-17)/3	199803	Robert Price	04/2020
1945	6*10^199788+77	199789	Robert Price	06/2020
1946	(23*10^199615+37)/3	199616	Robert Price	02/2022
1947	(17*10^199607-167)/3	199608	Robert Price	05/2022
1948	2^663020-933075	199589	Paul Bourdelais	06/2021
1949	2^663007+29963	199585	Enzo Doria	03/2024
1950	3*2^662703-5	199494	Jon Grantham	07/2023
1951	(14*10^199447+73)/3	199448	Robert Price	12/2018
1952	(2^662424-15)/7	199409	Stefano Morozzi	08/2022
1953	2^662194+22189	199341	Enzo Doria	09/2023
1954	2^662103-29287	199313	Enzo Doria	08/2015
1955	(2*10^199283+457)/9	199283	Robert Price	01/2018
1956	(10^199248-19)/9	199248	Robert Price	01/2018
1957	(83*10^199213+529)/9	199214	Robert Price	12/2021
1958	(194*10^199146-17)/3	199148	Robert Price	09/2020
1959	(151*10^199003-1)/3	199005	Robert Price	03/2020
1960	9*10^198946-73	198947	Robert Price	01/2021
1961	45*10^198931-7	198933	Robert Price	07/2020
1962	2^660482-2891	198825	Yves Minet	05/2016
1963	2^659589-21	198557	Stefano Morozzi	07/2022
1964	2^659583+1879223	198555	Enzo Doria	08/2016
1965	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
1966	(49*10^198403+311)/9	198404	Robert Price	06/2019
1967	96*10^198376-7	198378	Robert Price	03/2021
1968	(10^198375+7)/59/1201/87589	198366	Alfred Reich	08/2021
1969	2^658828-29819	198327	Enzo Doria	08/2015
1970	2^658776-2791229	198312	Enzo Doria	01/2016
1971	(35*10^198294-377)/9	198295	Robert Price	07/2018
1972	(4*10^198268+137)/3	198269	Robert Price	03/2018
1973	2^658544-1854029	198242	Enzo Doria	09/2015
1974	(62*10^198229-233)/9	198230	Robert Price	02/2022
1975	(26*10^198200-41)/3	198201	Robert Price	02/2022
1976	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
1977	2^657815+26213	198023	Enzo Doria	12/2023
1978	2*10^197959-37	197960	Robert Price	11/2021
1979	(29*10^197941-41)/3	197942	Tyler Busby	03/2024
1980	(232*10^197897+17)/3	197899	Robert Price	04/2021
1981	(4*10^197778+173)/3	197779	Robert Price	02/2018
1982	2^656763+211373	197706	Enzo Doria	08/2023
1983	78*10^197702-7	197704	Robert Price	10/2020
1984	(17*10^197640-23)/3	197641	Robert Price	03/2021
1985	(29*10^197629-77)/3	197630	Robert Price	02/2020
1986	2^656462+1874419	197615	Enzo Doria	06/2016
1987	(89^101363+1)/90	197595	Paul Bourdelais	11/2017
1988	2^655893-344563	197444	Enzo Doria	07/2015
1989	2^655875+71333	197439	Enzo Doria	04/2016
1990	2^655845-9	197430	Robert Price	01/2017
1991	(299*10^197426+1)/3	197428	Robert Price	04/2020
1992	2^655682-1849121	197380	Enzo Doria	08/2015
1993	4*10^197268-89	197269	Robert Price	11/2018
1994	(11*10^197198-89)/3	197199	Robert Price	05/2021
1995	2^655045-49603	197189	Enzo Doria	10/2015
1996	2^655000-2784089	197175	Enzo Doria	10/2015
1997	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
1998	(4*10^197061+41)/9	197061	Serge Batalov	11/2022
1999	(154*10^197005+17)/9	197007	Robert Price	06/2022
2000	2^654400-39719	196995	Enzo Doria	09/2015

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Probable Primes Top 10000

(295532 PRPs in the top)