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	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
1752	2^890122-351401	267954	Enzo Doria	07/2015
1753	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
1754	2^888852+229051	267572	Enzo Doria	11/2024
1755	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
1756	(1005^89087-1)/1004	267451	Jinyuan Wang	01/2024
1757	(485^99523-1)/484	267291	Michael Stocker	05/2020
1758	2^886324+77791	266811	Enzo Doria	06/2016
1759	7*10^266731+87	266732	Robert Price	11/2022
1760	2^886040+213901	266725	Enzo Doria	10/2023
1761	2^885242+217909	266485	Enzo Doria	01/2024
1762	2^884738+26809	266333	Enzo Doria	12/2023
1763	2^884714+1880527	266326	Enzo Doria	10/2016
1764	7*10^266024-47	266025	Robert Price	08/2023
1765	11^255426+255426^11	265999	Serge Batalov	05/2014
1766	2^883462-343421	265949	Enzo Doria	07/2015
1767	2^883442+1875019	265943	Enzo Doria	06/2016
1768	2^883333-291583	265910	Enzo Doria	07/2015
1769	2^883132+30421	265850	Enzo Doria	03/2024
1770	10^265566+3593037	265567	Paul Bourdelais	08/2023
1771	(2*10^265321-17)/3	265321	Serge Batalov	11/2022
1772	(16*10^265052-91)/3	265053	Robert Price	11/2022
1773	2^880411+1882673	265031	Enzo Doria	12/2016
1774	2^880101+228917	264937	Enzo Doria	11/2024
1775	(14*10^264791-11)/3	264792	Robert Price	08/2022
1776	2^879530-2788031	264765	Enzo Doria	12/2015
1777	2^879292+25171	264694	Enzo Doria	11/2023
1778	(2*10^264539+61)/9	264539	Serge Batalov	11/2022
1779	2^878118+2793079	264340	Enzo Doria	02/2016
1780	(2^878073-7)/5	264326	Stefano Morozzi	08/2022
1781	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
1782	5^377865+3^377865-1	264117	Jon Grantham	08/2023
1783	(19*10^263971+131)/3	263972	Robert Price	08/2023
1784	2^876202-17	263764	Stefano Morozzi	07/2022
1785	(14*10^263720-11)/3	263721	Robert Price	08/2022
1786	2^875748-461129	263627	Enzo Doria	07/2015
1787	2^875518-15	263558	Stefano Morozzi	07/2022
1788	(29*10^263523-17)/3	263524	Robert Price	01/2023
1789	2^875181-2789923	263456	Enzo Doria	12/2015
1790	2^875101-350083	263432	Enzo Doria	08/2015
1791	2^874684+1883587	263307	Enzo Doria	01/2017
1792	2^874616+1872211	263286	Enzo Doria	05/2016
1793	2^874566+30049	263271	Enzo Doria	03/2024
1794	3^551491+16	263129	Robert Price	04/2020
1795	2^874073+2792957	263123	Enzo Doria	02/2016
1796	(7*10^263006-19)/3	263007	Robert Price	10/2023
1797	2^873628+1878751	262989	Enzo Doria	08/2016
1798	2^873497+20837	262949	Enzo Doria	08/2023
1799	2^873288-269	262886	Yves Minet	01/2015
1800	(2*10^262874+7)/9	262874	Rytis Slatkevicius	01/2023
1801	(28*10^262655-43)/3	262656	Robert Price	04/2023
1802	(2*10^262603-11)/9	262603	Serge Batalov	11/2022
1803	2^871991-4207	262496	Yves Minet	03/2021
1804	(23*10^262324+7)/3	262325	Robert Price	05/2023
1805	2^871146-3173	262242	Yves Minet	07/2016
1806	(10^(2131020+1)+6310^131020-1)/9	262041	Robert Price	08/2024
1807	2^869601-163	261776	Yves Minet	01/2015
1808	(2*10^261704+61)/9	261704	Serge Batalov	11/2022
1809	2^869326+282859	261694	Enzo Doria	11/2016
1810	2^869035-114181	261606	Enzo Doria	12/2014
1811	2^868817+26777	261540	Enzo Doria	12/2023
1812	3^547850+9000004	261391	Enzo Doria	10/2023
1813	Phi(156793,2^7)	261261	Henri Lifchitz	10/2025
1814	4*10^261248+91	261249	Robert Price	11/2022
1815	55083^55083+1282^1282	261150	Henri Lifchitz	10/2024
1816	2^866908+34891	260966	Enzo Doria	07/2024
1817	2^865715+80303	260607	Enzo Doria	07/2016
1818	2^865474+23209	260534	Enzo Doria	10/2023
1819	2^865238+214759	260463	Enzo Doria	11/2023
1820	2^865048+1882411	260406	Enzo Doria	12/2016
1821	2^864899-113871	260361	Enzo Doria	10/2014
1822	(16*10^260256-91)/3	260257	Robert Price	11/2022
1823	(7*10^260198-61)/9	260198	Erik Branger	11/2011
1824	2^864298-2788421	260180	Enzo Doria	12/2015
1825	2^864039-2791357	260102	Enzo Doria	01/2016
1826	2^863621-113833	259976	Enzo Doria	10/2014
1827	10^259945-11	259945	Mischa Rodermond	04/2023
1828	2^863433+34877	259920	Enzo Doria	07/2024
1829	(28*10^259897+113)/3	259898	Robert Price	06/2023
1830	2^862837+75767	259740	Enzo Doria	05/2016
1831	2^862637-31	259680	Jorge Menendez	05/2019
1832	2^862088+1874941	259515	Enzo Doria	06/2016
1833	2^861987-134557	259484	Hans Havermann	10/2018
1834	(14*10^259431-143)/3	259432	Robert Price	05/2023
1835	2^861516-1854029	259343	Enzo Doria	09/2015
1836	2^860975-1853977	259180	Enzo Doria	09/2015
1837	3^543128+16	259138	Robert Price	04/2020
1838	2^860625-1858843	259074	Enzo Doria	10/2015
1839	2^860110+77689	258919	Enzo Doria	05/2016
1840	2^859600+1880371	258766	Enzo Doria	10/2016
1841	2^859433+494711	258716	Makoto Morimoto	10/2013
1843	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
1842	(2^859431-11)/3	258715	Stefano Morozzi	08/2022
1844	(13*10^258710-43)/3	258711	Robert Price	08/2023
1845	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
1846	2^859240+1875271	258658	Enzo Doria	06/2016
1847	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
1848	2^858812+30421	258529	Enzo Doria	03/2024
1849	(23*10^258494-47)/3	258495	Robert Price	09/2023
1850	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
1851	2^857608+105	258166	Stefano Morozzi	05/2021
1852	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
1853	2^857016-633113	257988	Enzo Doria	12/2013
1854	2^855732-113969	257602	Enzo Doria	10/2014
1855	(5*10^257431+91)/3	257432	Robert Price	08/2023
1856	2^853682-3911	256984	Enzo Doria	05/2014
1857	11^246668-90	256879	Enzo Doria	12/2012
1858	2^853181+30287	256834	Enzo Doria	03/2024
1859	5*2^852698+3	256689	Jon Grantham	07/2023
1860	(23*10^256654+7)/3	256655	Robert Price	05/2023
1861	2^851904-113939	256449	Enzo Doria	10/2014
1862	2^851725-851725^2	256395	Henri Lifchitz	03/2019
1863	11^246167-90	256357	Enzo Doria	12/2012
1864	(85*10^256301-1)/3	256303	Robert Price	12/2022
1865	(10^256187+7)/63443/148782853	256175	Alfred Reich	10/2021
1866	2^850700-569049	256087	Enzo Doria	11/2013
1867	2^850675+153	256079	Stefano Morozzi	05/2021
1868	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
1869	(37^163193+1)/38	255918	Paul Bourdelais	07/2019
1870	(14*10^255805-83)/3	255806	Robert Price	11/2022
1871	2^849316+25861	255670	Enzo Doria	12/2023
1872	2^849177-114025	255628	Enzo Doria	12/2014
1873	2*10^255442-21	255443	Robert Price	08/2023
1874	2^848502-3173	255425	Yves Minet	07/2016
1875	2^848178-140291	255328	Enzo Doria	01/2014
1876	7*10^255167+87	255168	Robert Price	11/2022
1877	2^847622-2441	255160	Yves Minet	02/2016
1878	2^847291+182843	255061	Enzo Doria	11/2016
1879	2^847174+1879429	255025	Enzo Doria	09/2016
1880	2^846881+215837	254937	Enzo Doria	12/2023
1881	Phi(475779,2^3)	254889	Henri Lifchitz	12/2025
1882	24*29^174239+13361	254809	Curtis Bright	04/2015
1883	22*10^254639+7	254641	Robert Price	10/2022
1884	2^845633-933075	254561	Paul Bourdelais	11/2021
1885	2^845610-1868591	254554	Enzo Doria	04/2016
1886	2^845484+81931	254517	Enzo Doria	08/2016
1887	2^845402-114761	254492	Enzo Doria	05/2015
1888	Phi(115655,561)	254335	Henri Lifchitz	12/2025
1889	98*10^254173-9	254175	Robert Price	05/2023
1890	2^844334-2792441	254170	Enzo Doria	02/2016
1891	2*10^254162+69	254163	Robert Price	08/2023
1892	(4*10^254107+11)/3	254108	Tyler Busby	02/2023
1893	11^243796-90	253888	Enzo Doria	12/2012
1894	(10^253891+7)/44777/79843/16940711	253875	Alfred Reich	10/2021
1895	30^171733-29^171733	253671	Jean-Louis Charton	10/2018
1896	2^842325+25907	253566	Enzo Doria	11/2023
1897	2^842209+1876037	253531	Enzo Doria	07/2016
1898	2^842123-59197	253505	Enzo Doria	10/2015
1899	(8*10^253313-53)/9	253313	Serge Batalov	11/2022
1900	(28*10^253210+191)/3	253211	Robert Price	07/2023
1901	2^840797-3	253106	Paul Bourdelais	06/2019
1902	2^840716-2969	253081	Yves Minet	05/2016
1903	2^840358-462491	252973	Enzo Doria	08/2015
1904	2^840310+1878379	252959	Enzo Doria	08/2016
1905	2^840203-21	252927	Stefano Morozzi	07/2022
1906	11^242579-60	252620	Enzo Doria	10/2012
1907	45^152659+2	252378	Robert Price	09/2015
1908	(95^127583+1)/96	252322	Paul Bourdelais	07/2019
1909	7*10^252209-17	252210	Robert Price	12/2022
1910	2^837725+1869377	252181	Enzo Doria	05/2016
1911	2^837536-311039	252124	Enzo Doria	06/2015
1912	21^190632-2	252058	Robert Price	07/2015
1913	2^837242+1873297	252035	Enzo Doria	06/2016
1914	2^836995+226575	251961	Enzo Doria	10/2024
1915	2^836656-2787929	251859	Enzo Doria	11/2015
1916	2^836548+219061	251827	Enzo Doria	02/2024
1917	2^836380+1875541	251776	Enzo Doria	07/2016
1918	(359^98327-1)/358	251233	Alexander Zhirkov	11/2017
1919	tau(41^28288)	250924	Nik Lygeros / Olivier Rozier	10/2013
1920	Phi(137951,-100)	250801	Henri Lifchitz	12/2025
1921	Phi(74531,11#)	250691	Henri Lifchitz	12/2025
1922	(28*10^250655+113)/3	250656	Robert Price	06/2023
1923	2^832511-461197	250611	Enzo Doria	07/2015
1924	2^832505+1881137	250609	Enzo Doria	11/2016
1925	2^832363+583295	250567	Enzo Doria	12/2016
1926	2^832244-403635	250531	Enzo Doria	01/2014
1927	(14*10^250336-41)/9	250337	Serge Batalov	01/2023
1928	2^831528+24811	250315	Enzo Doria	11/2023
1929	2^831157+1880657	250204	Enzo Doria	11/2016
1930	2^831088-7200899	250183	Enzo Doria	01/2015
1931	2^830956-1349	250143	Yves Minet	07/2015
1932	2^830699+220583	250066	Enzo Doria	03/2024
1933	2^830037+282317	249867	Enzo Doria	09/2016
1934	2^829589-113653	249732	Enzo Doria	09/2014
1935	(4*10^249550-7)/3	249551	Serge Batalov	01/2023
1936	(103*10^249399+17)/3	249401	Robert Price	04/2023
1937	2^828281-3193	249338	Yves Minet	08/2016
1938	(2^828140-19)/3	249295	Stefano Morozzi	08/2022
1939	2^828064-2785619	249273	Enzo Doria	10/2015
1940	2^827602+60409	249134	Enzo Doria	03/2016
1941	2^827306+212419	249044	Enzo Doria	09/2023
1942	10^249010+348861	249011	Patrick De Geest	04/2016
1943	10^249010-21	249010	Serge Batalov	12/2014
1944	2^826733+1882907	248872	Enzo Doria	12/2016
1945	2^825800+22441	248591	Enzo Doria	10/2023
1946	2^825682+1876549	248556	Enzo Doria	07/2016
1947	2^824991-114121	248348	Enzo Doria	12/2014
1948	2^824642-362727	248242	Enzo Doria	12/2013
1949	2^824565-114265	248219	Enzo Doria	01/2015
1950	2^824325-25	248147	Boyan Hu	12/2024
1951	(73*10^248145-1)/9	248146	Robert Price	01/2015
1952	2^823321+219407	247845	Enzo Doria	02/2024
1953	(2^823337+1)/(3*362268281)	247841	Gord Palameta	08/2018
1954	(13*10^247793-43)/3	247794	Robert Price	08/2023
1955	(2^822971-1)/6583769/28211445881/21255852651726486149207	247700	Robert Kinser	09/2016
1956	2^822296+76501	247536	Enzo Doria	05/2016
1957	2^821590-114167	247324	Enzo Doria	12/2014
1958	2^821512-2790659	247300	Enzo Doria	12/2015
1959	(21996^57121-1)/(21996^239-1)	247002	Ryan Propper	11/2023
1960	2^820356+7	246952	Jon Grantham	08/2023
1961	2^820077+382847	246868	Enzo Doria	11/2016
1962	2^820008+81	246848	Henri Lifchitz	01/2025
1963	2^820001+81269	246845	Enzo Doria	07/2016
1964	2^819463-59197	246683	Enzo Doria	10/2015
1965	2^819296+80581	246633	Enzo Doria	07/2016
1966	2^818764+21573	246473	Enzo Doria	11/2023
1967	2^817852+215491	246198	Enzo Doria	11/2023
1968	2^817160-350369	245990	Enzo Doria	06/2015
1969	2^816039-19	245653	Stefano Morozzi	07/2022
1970	2^816029+219407	245650	Enzo Doria	02/2024
1971	(71*10^245558-17)/9	245559	Serge Batalov	01/2023
1972	5*3^514648+2^514648	245551	Jon Grantham	08/2023
1973	88093#+(653879#)/(88093#)	245374	Makoto Morimoto	11/2017
1974	2^815111-113857	245373	Enzo Doria	10/2014
1975	(34555^54289-1)/(34555^233-1)	245334	Ryan Propper	11/2023
1976	2^814914-4001	245314	Yves Minet	05/2017
1977	846^83761-845^83761	245200	Jean-Louis Charton	12/2012
1978	2^814356-2790449	245146	Enzo Doria	12/2015
1979	2^814276-459029	245122	Enzo Doria	04/2015
1980	2^814023+180923	245046	Enzo Doria	07/2016
1981	2^813496+216751	244887	Enzo Doria	12/2023
1982	(3^513059-2^513059)/(1026119*5430216457)	244776	Mike Oakes	03/2017
1983	3^513007+16	244767	Robert Price	04/2020
1984	(46^147197-31^147197)/15	244752	Aurel Gibier	06/2024
1985	(2543*17^198855-15)/16	244684	Eric Chen	01/2026
1986	2^811882+27289	244401	Enzo Doria	12/2023
1987	2^811842-113675	244389	Enzo Doria	09/2014
1988	2^811132-2787929	244176	Enzo Doria	11/2015
1989	2^809746-2790971	243758	Enzo Doria	01/2016
1990	(14*10^243724-197)/3	243725	Robert Price	03/2023
1991	2^808767-3295	243464	Yves Minet	12/2016
1992	2^808621-113809	243420	Enzo Doria	09/2014
1993	2^808199+29693	243293	Enzo Doria	03/2024
1994	2^807724+1879621	243150	Enzo Doria	09/2016
1995	2^807417+217787	243057	Enzo Doria	01/2024
1996	(23*10^242909+91)/3	242910	Robert Price	03/2023
1997	2^806708+20371	242844	Enzo Doria	08/2023
1998	2*10^242822-91	242823	Robert Price	02/2023
1999	20^186554-3	242713	Paul Bourdelais	12/2020
2000	2^805843-113611	242583	Enzo Doria	08/2014

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Probable Primes Top 10000

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