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	7*10^273983+39	273984	Robert Price	01/2023
1752	2^909988-1862249	273934	Enzo Doria	12/2015
1753	2^909901+378567	273908	Boyan Hu	08/2024
1754	2^909297+1879157	273726	Enzo Doria	08/2016
1755	2^909257-1864423	273714	Enzo Doria	01/2016
1756	2^909254+31309	273713	Enzo Doria	03/2024
1757	2^908739-7	273558	Stefano Morozzi	07/2022
1758	2^908579-1861747	273510	Enzo Doria	12/2015
1759	3*2^908005-5	273338	Jon Grantham	07/2023
1760	2^907635-2791597	273226	Enzo Doria	01/2016
1761	2^907059+211193	273052	Enzo Doria	08/2023
1762	(53^158341+1)/54	273022	Paul Bourdelais	07/2019
1763	2^906594-113201	272912	Enzo Doria	08/2014
1764	9*10^272800+91	272801	Robert Price	05/2023
1765	2*10^272710-49	272711	Robert Price	05/2023
1766	2*10^272403-91	272404	Robert Price	02/2023
1767	2^904773+1872167	272364	Enzo Doria	06/2016
1768	6^349903+5	272278	Paul Bourdelais	02/2021
1769	2^904149-1862473	272176	Enzo Doria	12/2015
1770	2^902926+227839	271808	Enzo Doria	10/2024
1771	(7*10^271757-61)/9	271757	Erik Branger	03/2012
1772	2^902497+1880117	271679	Enzo Doria	09/2016
1773	2^901858+77689	271487	Enzo Doria	06/2016
1774	2^901372+1875301	271341	Enzo Doria	06/2016
1775	2^901146+219049	271272	Enzo Doria	02/2024
1776	(8*10^271039-77)/3	271040	Robert Price	04/2023
1777	2^899999+1144031	270927	Norman Luhn	09/2023
1778	2*10^270802-91	270803	Robert Price	02/2023
1779	23*10^270799-7	270801	Robert Price	10/2022
1780	2^899121-115033	270663	Enzo Doria	07/2015
1781	2^898900+883021	270596	Enzo Doria	12/2016
1782	2^898762-251511	270555	Enzo Doria	12/2013
1783	2^898589+47	270503	Lelio R Paula	03/2016
1784	(939628*10^270345-93962791)/9	270351	Danilo Nitsche	03/2026
1785	1447184*10^270344-14471839	270351	Danilo Nitsche	03/2026
1786	(3178852*10^270344-31788517)/3	270351	Danilo Nitsche	06/2026
1787	269048*10^270344-2690479	270350	Danilo Nitsche	02/2026
1788	172249*10^270344-1722489	270350	Danilo Nitsche	02/2026
1789	(288964*10^270345-28896397)/3	270350	Danilo Nitsche	02/2026
1790	661681*10^270344-6616809	270350	Danilo Nitsche	02/2026
1791	184489*10^270344-1844889	270350	Danilo Nitsche	02/2026
1792	58552*10^270345-5855199	270350	Danilo Nitsche	02/2026
1793	(245662*10^270345-24566197)/3	270350	Danilo Nitsche	02/2026
1794	371745*10^270344-3717449	270350	Danilo Nitsche	02/2026
1795	(1366645*10^270344-13666441)/9	270350	Danilo Nitsche	03/2026
1796	(1648732*10^270344-16487317)/3	270350	Danilo Nitsche	03/2026
1797	(1386601*10^270344-13866001)/9	270350	Danilo Nitsche	03/2026
1798	(1631944*10^270344-16319431)/9	270350	Danilo Nitsche	03/2026
1799	922284*10^270344-9222839	270350	Danilo Nitsche	03/2026
1800	992761*10^270344-9927609	270350	Danilo Nitsche	03/2026
1801	(2241127*10^270344-22411267)/3	270350	Danilo Nitsche	04/2026
1802	(2466128*10^270344-24661277)/3	270350	Danilo Nitsche	04/2026
1803	2366042*10^270343-2366041	270350	Danilo Nitsche	04/2026
1804	(2878615*10^270344-28786147)/3	270350	Danilo Nitsche	04/2026
1805	(2026252*10^270344-20262517)/3	270350	Danilo Nitsche	04/2026
1806	1967284*10^270343-1967283	270350	Danilo Nitsche	04/2026
1807	2629838*10^270343-2629837	270350	Danilo Nitsche	04/2026
1808	(2737132*10^270344-27371317)/3	270350	Danilo Nitsche	04/2026
1809	(4295404*10^270343-4295401)/3	270350	Danilo Nitsche	06/2026
1810	(3080173*10^270344-30801721)/9	270350	Danilo Nitsche	06/2026
1811	4452574*10^270343-4452573	270350	Danilo Nitsche	06/2026
1813	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
1812	(4004452*10^270343-4004443)/9	270349	Danilo Nitsche	06/2026
1814	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
1815	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
1816	2^897867-3217	270285	Yves Minet	12/2016
1817	2^897849-115273	270280	Enzo Doria	07/2015
1818	2^897367+26289	270135	Enzo Doria	03/2024
1819	2^896616-114179	269909	Enzo Doria	12/2014
1820	(12648^66049-1)/(12648^257-1)	269881	Ryan Propper	11/2023
1821	(10^(2134811+1)+610^134811-1)/3	269623	Robert Price	08/2024
1822	(22*10^269517-19)/3	269518	Robert Price	07/2023
1823	10^(2134739+1)-710^134739-1	269479	Robert Price	07/2023
1824	2^894928+583561	269401	Enzo Doria	04/2017
1825	2^894673-39343	269324	Enzo Doria	08/2015
1826	2^893836+23221	269072	Enzo Doria	10/2023
1827	2^892718+29539	268735	Enzo Doria	03/2024
1828	2^892660+213901	268718	Enzo Doria	10/2023
1829	F(1285607)	268676	Henri Lifchitz	11/2008
1830	2^892234+22189	268590	Enzo Doria	09/2023
1831	2^892151+24863	268565	Enzo Doria	11/2023
1832	2^892112+187663	268553	Enzo Doria	08/2016
1833	(266*10^268407-17)/3	268409	Robert Price	02/2023
1834	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
1835	2^890957-69583	268205	Enzo Doria	12/2015
1836	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
1837	2^890122-351401	267954	Enzo Doria	07/2015
1838	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
1839	2^888852+229051	267572	Enzo Doria	11/2024
1840	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
1841	(1005^89087-1)/1004	267451	Jinyuan Wang	01/2024
1842	(485^99523-1)/484	267291	Michael Stocker	05/2020
1843	2^886324+77791	266811	Enzo Doria	06/2016
1844	7*10^266731+87	266732	Robert Price	11/2022
1845	2^886040+213901	266725	Enzo Doria	10/2023
1846	2^885242+217909	266485	Enzo Doria	01/2024
1847	2^884738+26809	266333	Enzo Doria	12/2023
1848	2^884714+1880527	266326	Enzo Doria	10/2016
1849	7*10^266024-47	266025	Robert Price	08/2023
1850	11^255426+255426^11	265999	Serge Batalov	05/2014
1851	2^883462-343421	265949	Enzo Doria	07/2015
1852	2^883442+1875019	265943	Enzo Doria	06/2016
1853	2^883333-291583	265910	Enzo Doria	07/2015
1854	2^883132+30421	265850	Enzo Doria	03/2024
1855	10^265566+3593037	265567	Paul Bourdelais	08/2023
1856	(2*10^265321-17)/3	265321	Serge Batalov	11/2022
1857	(16*10^265052-91)/3	265053	Robert Price	11/2022
1858	2^880411+1882673	265031	Enzo Doria	12/2016
1859	2^880101+228917	264937	Enzo Doria	11/2024
1860	(14*10^264791-11)/3	264792	Robert Price	08/2022
1861	2^879530-2788031	264765	Enzo Doria	12/2015
1862	2^879292+25171	264694	Enzo Doria	11/2023
1863	(2*10^264539+61)/9	264539	Serge Batalov	11/2022
1864	2^878118+2793079	264340	Enzo Doria	02/2016
1865	(2^878073-7)/5	264326	Stefano Morozzi	08/2022
1866	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
1867	5^377865+3^377865-1	264117	Jon Grantham	08/2023
1868	(19*10^263971+131)/3	263972	Robert Price	08/2023
1869	2^876202-17	263764	Stefano Morozzi	07/2022
1870	(14*10^263720-11)/3	263721	Robert Price	08/2022
1871	2^875748-461129	263627	Enzo Doria	07/2015
1872	2^875518-15	263558	Stefano Morozzi	07/2022
1873	(29*10^263523-17)/3	263524	Robert Price	01/2023
1874	2^875181-2789923	263456	Enzo Doria	12/2015
1875	2^875101-350083	263432	Enzo Doria	08/2015
1876	2^874684+1883587	263307	Enzo Doria	01/2017
1877	2^874616+1872211	263286	Enzo Doria	05/2016
1878	2^874566+30049	263271	Enzo Doria	03/2024
1879	3^551491+16	263129	Robert Price	04/2020
1880	2^874073+2792957	263123	Enzo Doria	02/2016
1881	(7*10^263006-19)/3	263007	Robert Price	10/2023
1882	2^873628+1878751	262989	Enzo Doria	08/2016
1883	2^873497+20837	262949	Enzo Doria	08/2023
1884	2^873288-269	262886	Yves Minet	01/2015
1885	(2*10^262874+7)/9	262874	Rytis Slatkevicius	01/2023
1886	(28*10^262655-43)/3	262656	Robert Price	04/2023
1887	(2*10^262603-11)/9	262603	Serge Batalov	11/2022
1888	2^871991-4207	262496	Yves Minet	03/2021
1889	(23*10^262324+7)/3	262325	Robert Price	05/2023
1890	2^871146-3173	262242	Yves Minet	07/2016
1891	(10^(2131020+1)+6310^131020-1)/9	262041	Robert Price	08/2024
1892	2^869601-163	261776	Yves Minet	01/2015
1893	(2*10^261704+61)/9	261704	Serge Batalov	11/2022
1894	2^869326+282859	261694	Enzo Doria	11/2016
1895	2^869035-114181	261606	Enzo Doria	12/2014
1896	2^868817+26777	261540	Enzo Doria	12/2023
1897	3^547850+9000004	261391	Enzo Doria	10/2023
1898	Phi(156793,2^7)	261261	Henri Lifchitz	10/2025
1899	4*10^261248+91	261249	Robert Price	11/2022
1900	55083^55083+1282^1282	261150	Henri Lifchitz	10/2024
1901	2^866908+34891	260966	Enzo Doria	07/2024
1902	2^865715+80303	260607	Enzo Doria	07/2016
1903	2^865474+23209	260534	Enzo Doria	10/2023
1904	2^865238+214759	260463	Enzo Doria	11/2023
1905	2^865048+1882411	260406	Enzo Doria	12/2016
1906	2^864899-113871	260361	Enzo Doria	10/2014
1907	(16*10^260256-91)/3	260257	Robert Price	11/2022
1908	(7*10^260198-61)/9	260198	Erik Branger	11/2011
1909	2^864298-2788421	260180	Enzo Doria	12/2015
1910	2^864039-2791357	260102	Enzo Doria	01/2016
1911	2^863621-113833	259976	Enzo Doria	10/2014
1912	10^259945-11	259945	Mischa Rodermond	04/2023
1913	2^863433+34877	259920	Enzo Doria	07/2024
1914	(28*10^259897+113)/3	259898	Robert Price	06/2023
1915	2^862837+75767	259740	Enzo Doria	05/2016
1916	2^862637-31	259680	Jorge Menendez	05/2019
1917	2^862088+1874941	259515	Enzo Doria	06/2016
1918	2^861987-134557	259484	Hans Havermann	10/2018
1919	(14*10^259431-143)/3	259432	Robert Price	05/2023
1920	2^861516-1854029	259343	Enzo Doria	09/2015
1921	2^860975-1853977	259180	Enzo Doria	09/2015
1922	3^543128+16	259138	Robert Price	04/2020
1923	2^860625-1858843	259074	Enzo Doria	10/2015
1924	2^860110+77689	258919	Enzo Doria	05/2016
1925	2^859600+1880371	258766	Enzo Doria	10/2016
1926	2^859433+494711	258716	Makoto Morimoto	10/2013
1928	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
1927	(2^859431-11)/3	258715	Stefano Morozzi	08/2022
1929	(13*10^258710-43)/3	258711	Robert Price	08/2023
1930	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
1931	2^859240+1875271	258658	Enzo Doria	06/2016
1932	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
1933	2^858812+30421	258529	Enzo Doria	03/2024
1934	(23*10^258494-47)/3	258495	Robert Price	09/2023
1935	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
1936	2^857608+105	258166	Stefano Morozzi	05/2021
1937	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
1938	2^857016-633113	257988	Enzo Doria	12/2013
1939	2^855732-113969	257602	Enzo Doria	10/2014
1940	(5*10^257431+91)/3	257432	Robert Price	08/2023
1941	2^853682-3911	256984	Enzo Doria	05/2014
1942	11^246668-90	256879	Enzo Doria	12/2012
1943	2^853181+30287	256834	Enzo Doria	03/2024
1944	5*2^852698+3	256689	Jon Grantham	07/2023
1945	(23*10^256654+7)/3	256655	Robert Price	05/2023
1946	2^851904-113939	256449	Enzo Doria	10/2014
1947	2^851725-851725^2	256395	Henri Lifchitz	03/2019
1948	11^246167-90	256357	Enzo Doria	12/2012
1949	(85*10^256301-1)/3	256303	Robert Price	12/2022
1950	(10^256187+7)/63443/148782853	256175	Alfred Reich	10/2021
1951	2^850700-569049	256087	Enzo Doria	11/2013
1952	2^850675+153	256079	Stefano Morozzi	05/2021
1953	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
1954	(37^163193+1)/38	255918	Paul Bourdelais	07/2019
1955	(14*10^255805-83)/3	255806	Robert Price	11/2022
1956	2^849316+25861	255670	Enzo Doria	12/2023
1957	2^849177-114025	255628	Enzo Doria	12/2014
1958	2*10^255442-21	255443	Robert Price	08/2023
1959	2^848502-3173	255425	Yves Minet	07/2016
1960	2^848178-140291	255328	Enzo Doria	01/2014
1961	7*10^255167+87	255168	Robert Price	11/2022
1962	2^847622-2441	255160	Yves Minet	02/2016
1963	2^847291+182843	255061	Enzo Doria	11/2016
1964	2^847174+1879429	255025	Enzo Doria	09/2016
1965	2^846881+215837	254937	Enzo Doria	12/2023
1966	Phi(475779,2^3)	254889	Henri Lifchitz	12/2025
1967	24*29^174239+13361	254809	Curtis Bright	04/2015
1968	22*10^254639+7	254641	Robert Price	10/2022
1969	2^845633-933075	254561	Paul Bourdelais	11/2021
1970	2^845610-1868591	254554	Enzo Doria	04/2016
1971	2^845484+81931	254517	Enzo Doria	08/2016
1972	2^845402-114761	254492	Enzo Doria	05/2015
1973	Phi(115655,561)	254335	Henri Lifchitz	12/2025
1974	98*10^254173-9	254175	Robert Price	05/2023
1975	2^844334-2792441	254170	Enzo Doria	02/2016
1976	2*10^254162+69	254163	Robert Price	08/2023
1977	(4*10^254107+11)/3	254108	Tyler Busby	02/2023
1978	11^243796-90	253888	Enzo Doria	12/2012
1979	(10^253891+7)/44777/79843/16940711	253875	Alfred Reich	10/2021
1980	30^171733-29^171733	253671	Jean-Louis Charton	10/2018
1981	2^842325+25907	253566	Enzo Doria	11/2023
1982	2^842209+1876037	253531	Enzo Doria	07/2016
1983	2^842123-59197	253505	Enzo Doria	10/2015
1984	(8*10^253313-53)/9	253313	Serge Batalov	11/2022
1985	(28*10^253210+191)/3	253211	Robert Price	07/2023
1986	2^840797-3	253106	Paul Bourdelais	06/2019
1987	2^840716-2969	253081	Yves Minet	05/2016
1988	2^840358-462491	252973	Enzo Doria	08/2015
1989	2^840310+1878379	252959	Enzo Doria	08/2016
1990	2^840203-21	252927	Stefano Morozzi	07/2022
1991	11^242579-60	252620	Enzo Doria	10/2012
1992	45^152659+2	252378	Robert Price	09/2015
1993	(95^127583+1)/96	252322	Paul Bourdelais	07/2019
1994	7*10^252209-17	252210	Robert Price	12/2022
1995	2^837725+1869377	252181	Enzo Doria	05/2016
1996	2^837536-311039	252124	Enzo Doria	06/2015
1997	21^190632-2	252058	Robert Price	07/2015
1998	2^837242+1873297	252035	Enzo Doria	06/2016
1999	2^836995+226575	251961	Enzo Doria	10/2024
2000	2^836656-2787929	251859	Enzo Doria	11/2015

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