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	2^927429+1882277	279184	Enzo Doria	12/2016
1752	2^926766-11	278985	Stefano Morozzi	07/2022
1753	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
1754	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
1755	(5347*26^197061-297)/25	278839	Eric Chen	12/2025
1756	(166*10^278633-7)/3	278635	Robert Price	02/2023
1757	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
1758	2^925330-1301	278553	Yves Minet	06/2015
1759	(299*10^278546+1)/3	278548	Robert Price	01/2023
1760	2^925299+216053	278543	Enzo Doria	11/2023
1762	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
1761	(79^146749-1)/6395645198026062186	278457	Paul Vanderveen	06/2025
1763	(266*10^278325+1)/3	278327	Robert Price	01/2023
1764	2^923261-69175	277930	Enzo Doria	11/2015
1765	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
1766	2^922301+57	277641	Stefano Morozzi	05/2021
1767	7*10^277478-39	277479	Robert Price	07/2023
1768	((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	277369	Serge Batalov	07/2016
1769	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
1770	2^920318+2792299	277044	Enzo Doria	02/2016
1771	(16*10^276537-31)/3	276538	Robert Price	03/2023
1772	2^918596-2786939	276525	Enzo Doria	11/2015
1773	2^917910+28369	276319	Enzo Doria	01/2024
1774	2^917328+228571	276144	Enzo Doria	11/2024
1775	(6737^72361-1)/(6737^269-1)	276002	Ryan Propper	11/2023
1776	2^916639+60563	275936	Enzo Doria	04/2016
1777	(2*10^275922+1)/3	275922	Serge Batalov	11/2022
1778	2^916385-2786383	275860	Enzo Doria	11/2015
1779	2^915928+82081	275722	Enzo Doria	09/2016
1780	(4*10^275671+11)/3	275672	Tyler Busby	02/2023
1781	2^915576-114137	275616	Enzo Doria	01/2015
1782	2^914828+1876741	275391	Enzo Doria	07/2016
1783	2^914757-2203	275370	Yves Minet	12/2015
1784	7*10^275157-27	275158	Robert Price	11/2022
1785	2^912744+20011	274764	Enzo Doria	06/2023
1786	2^911900+1871245	274510	Enzo Doria	05/2016
1787	(16*10^274251-91)/3	274252	Robert Price	11/2022
1788	2^910999+9	274239	Stefano Morozzi	05/2021
1789	(2^910869-7)/5	274199	Stefano Morozzi	08/2022
1790	2^910490+283429	274085	Enzo Doria	01/2017
1791	7*10^273983+39	273984	Robert Price	01/2023
1792	2^909988-1862249	273934	Enzo Doria	12/2015
1793	2^909901+378567	273908	Boyan Hu	08/2024
1794	2^909297+1879157	273726	Enzo Doria	08/2016
1795	2^909257-1864423	273714	Enzo Doria	01/2016
1796	2^909254+31309	273713	Enzo Doria	03/2024
1797	2^908739-7	273558	Stefano Morozzi	07/2022
1798	2^908579-1861747	273510	Enzo Doria	12/2015
1799	3*2^908005-5	273338	Jon Grantham	07/2023
1800	2^907635-2791597	273226	Enzo Doria	01/2016
1801	2^907059+211193	273052	Enzo Doria	08/2023
1802	(53^158341+1)/54	273022	Paul Bourdelais	07/2019
1803	2^906594-113201	272912	Enzo Doria	08/2014
1804	9*10^272800+91	272801	Robert Price	05/2023
1805	2*10^272710-49	272711	Robert Price	05/2023
1806	2*10^272403-91	272404	Robert Price	02/2023
1807	2^904773+1872167	272364	Enzo Doria	06/2016
1808	6^349903+5	272278	Paul Bourdelais	02/2021
1809	2^904149-1862473	272176	Enzo Doria	12/2015
1810	2^902926+227839	271808	Enzo Doria	10/2024
1811	(7*10^271757-61)/9	271757	Erik Branger	03/2012
1812	2^902497+1880117	271679	Enzo Doria	09/2016
1813	2^901858+77689	271487	Enzo Doria	06/2016
1814	2^901372+1875301	271341	Enzo Doria	06/2016
1815	2^901146+219049	271272	Enzo Doria	02/2024
1816	(8*10^271039-77)/3	271040	Robert Price	04/2023
1817	2^899999+1144031	270927	Norman Luhn	09/2023
1818	2*10^270802-91	270803	Robert Price	02/2023
1819	23*10^270799-7	270801	Robert Price	10/2022
1820	(710^(2135371+1)-9*10^135371-7)/9	270743	Robert Price	06/2026
1821	2^899121-115033	270663	Enzo Doria	07/2015
1822	2^898900+883021	270596	Enzo Doria	12/2016
1823	2^898762-251511	270555	Enzo Doria	12/2013
1824	2^898589+47	270503	Lelio R Paula	03/2016
1825	(939628*10^270345-93962791)/9	270351	Danilo Nitsche	03/2026
1826	1447184*10^270344-14471839	270351	Danilo Nitsche	03/2026
1827	(3178852*10^270344-31788517)/3	270351	Danilo Nitsche	06/2026
1828	269048*10^270344-2690479	270350	Danilo Nitsche	02/2026
1829	172249*10^270344-1722489	270350	Danilo Nitsche	02/2026
1830	(288964*10^270345-28896397)/3	270350	Danilo Nitsche	02/2026
1831	661681*10^270344-6616809	270350	Danilo Nitsche	02/2026
1832	184489*10^270344-1844889	270350	Danilo Nitsche	02/2026
1833	58552*10^270345-5855199	270350	Danilo Nitsche	02/2026
1834	(245662*10^270345-24566197)/3	270350	Danilo Nitsche	02/2026
1835	371745*10^270344-3717449	270350	Danilo Nitsche	02/2026
1836	(1366645*10^270344-13666441)/9	270350	Danilo Nitsche	03/2026
1837	(1648732*10^270344-16487317)/3	270350	Danilo Nitsche	03/2026
1838	(1386601*10^270344-13866001)/9	270350	Danilo Nitsche	03/2026
1839	(1631944*10^270344-16319431)/9	270350	Danilo Nitsche	03/2026
1840	922284*10^270344-9222839	270350	Danilo Nitsche	03/2026
1841	992761*10^270344-9927609	270350	Danilo Nitsche	03/2026
1842	(2241127*10^270344-22411267)/3	270350	Danilo Nitsche	04/2026
1843	(2466128*10^270344-24661277)/3	270350	Danilo Nitsche	04/2026
1844	2366042*10^270343-2366041	270350	Danilo Nitsche	04/2026
1845	(2878615*10^270344-28786147)/3	270350	Danilo Nitsche	04/2026
1846	(2026252*10^270344-20262517)/3	270350	Danilo Nitsche	04/2026
1847	1967284*10^270343-1967283	270350	Danilo Nitsche	04/2026
1848	2629838*10^270343-2629837	270350	Danilo Nitsche	04/2026
1849	(2737132*10^270344-27371317)/3	270350	Danilo Nitsche	04/2026
1850	(4295404*10^270343-4295401)/3	270350	Danilo Nitsche	06/2026
1851	(3080173*10^270344-30801721)/9	270350	Danilo Nitsche	06/2026
1852	4452574*10^270343-4452573	270350	Danilo Nitsche	06/2026
1854	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
1853	(4004452*10^270343-4004443)/9	270349	Danilo Nitsche	06/2026
1855	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
1856	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
1857	2^897867-3217	270285	Yves Minet	12/2016
1858	2^897849-115273	270280	Enzo Doria	07/2015
1859	2^897367+26289	270135	Enzo Doria	03/2024
1860	2^896616-114179	269909	Enzo Doria	12/2014
1861	(12648^66049-1)/(12648^257-1)	269881	Ryan Propper	11/2023
1862	(10^(2134811+1)+610^134811-1)/3	269623	Robert Price	08/2024
1863	(22*10^269517-19)/3	269518	Robert Price	07/2023
1864	10^(2134739+1)-710^134739-1	269479	Robert Price	07/2023
1865	2^894928+583561	269401	Enzo Doria	04/2017
1866	2^894673-39343	269324	Enzo Doria	08/2015
1867	2^893836+23221	269072	Enzo Doria	10/2023
1868	2^892718+29539	268735	Enzo Doria	03/2024
1869	2^892660+213901	268718	Enzo Doria	10/2023
1870	F(1285607)	268676	Henri Lifchitz	11/2008
1871	2^892234+22189	268590	Enzo Doria	09/2023
1872	2^892151+24863	268565	Enzo Doria	11/2023
1873	2^892112+187663	268553	Enzo Doria	08/2016
1874	(266*10^268407-17)/3	268409	Robert Price	02/2023
1875	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
1876	2^890957-69583	268205	Enzo Doria	12/2015
1877	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
1878	2^890122-351401	267954	Enzo Doria	07/2015
1879	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
1880	2^888852+229051	267572	Enzo Doria	11/2024
1881	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
1882	(1005^89087-1)/1004	267451	Jinyuan Wang	01/2024
1883	(485^99523-1)/484	267291	Michael Stocker	05/2020
1884	2^886324+77791	266811	Enzo Doria	06/2016
1885	7*10^266731+87	266732	Robert Price	11/2022
1886	2^886040+213901	266725	Enzo Doria	10/2023
1887	2^885242+217909	266485	Enzo Doria	01/2024
1888	2^884738+26809	266333	Enzo Doria	12/2023
1889	2^884714+1880527	266326	Enzo Doria	10/2016
1890	7*10^266024-47	266025	Robert Price	08/2023
1891	11^255426+255426^11	265999	Serge Batalov	05/2014
1892	2^883462-343421	265949	Enzo Doria	07/2015
1893	2^883442+1875019	265943	Enzo Doria	06/2016
1894	2^883333-291583	265910	Enzo Doria	07/2015
1895	2^883132+30421	265850	Enzo Doria	03/2024
1896	10^265566+3593037	265567	Paul Bourdelais	08/2023
1897	(2*10^265321-17)/3	265321	Serge Batalov	11/2022
1898	(16*10^265052-91)/3	265053	Robert Price	11/2022
1899	2^880411+1882673	265031	Enzo Doria	12/2016
1900	2^880101+228917	264937	Enzo Doria	11/2024
1901	(14*10^264791-11)/3	264792	Robert Price	08/2022
1902	2^879530-2788031	264765	Enzo Doria	12/2015
1903	2^879292+25171	264694	Enzo Doria	11/2023
1904	(2*10^264539+61)/9	264539	Serge Batalov	11/2022
1905	2^878118+2793079	264340	Enzo Doria	02/2016
1906	(2^878073-7)/5	264326	Stefano Morozzi	08/2022
1907	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
1908	5^377865+3^377865-1	264117	Jon Grantham	08/2023
1909	(19*10^263971+131)/3	263972	Robert Price	08/2023
1910	2^876202-17	263764	Stefano Morozzi	07/2022
1911	(14*10^263720-11)/3	263721	Robert Price	08/2022
1912	2^875748-461129	263627	Enzo Doria	07/2015
1913	2^875518-15	263558	Stefano Morozzi	07/2022
1914	(29*10^263523-17)/3	263524	Robert Price	01/2023
1915	2^875181-2789923	263456	Enzo Doria	12/2015
1916	2^875101-350083	263432	Enzo Doria	08/2015
1917	2^874684+1883587	263307	Enzo Doria	01/2017
1918	2^874616+1872211	263286	Enzo Doria	05/2016
1919	2^874566+30049	263271	Enzo Doria	03/2024
1920	3^551491+16	263129	Robert Price	04/2020
1921	2^874073+2792957	263123	Enzo Doria	02/2016
1922	(7*10^263006-19)/3	263007	Robert Price	10/2023
1923	2^873628+1878751	262989	Enzo Doria	08/2016
1924	2^873497+20837	262949	Enzo Doria	08/2023
1925	2^873288-269	262886	Yves Minet	01/2015
1926	(2*10^262874+7)/9	262874	Rytis Slatkevicius	01/2023
1927	(28*10^262655-43)/3	262656	Robert Price	04/2023
1928	(2*10^262603-11)/9	262603	Serge Batalov	11/2022
1929	2^871991-4207	262496	Yves Minet	03/2021
1930	(23*10^262324+7)/3	262325	Robert Price	05/2023
1931	2^871146-3173	262242	Yves Minet	07/2016
1932	(10^(2131020+1)+6310^131020-1)/9	262041	Robert Price	08/2024
1933	2^869601-163	261776	Yves Minet	01/2015
1934	(2*10^261704+61)/9	261704	Serge Batalov	11/2022
1935	2^869326+282859	261694	Enzo Doria	11/2016
1936	2^869035-114181	261606	Enzo Doria	12/2014
1937	2^868817+26777	261540	Enzo Doria	12/2023
1938	3^547850+9000004	261391	Enzo Doria	10/2023
1939	Phi(156793,2^7)	261261	Henri Lifchitz	10/2025
1940	4*10^261248+91	261249	Robert Price	11/2022
1941	55083^55083+1282^1282	261150	Henri Lifchitz	10/2024
1942	2^866908+34891	260966	Enzo Doria	07/2024
1943	2^865715+80303	260607	Enzo Doria	07/2016
1944	2^865474+23209	260534	Enzo Doria	10/2023
1945	2^865238+214759	260463	Enzo Doria	11/2023
1946	2^865048+1882411	260406	Enzo Doria	12/2016
1947	2^864899-113871	260361	Enzo Doria	10/2014
1948	(16*10^260256-91)/3	260257	Robert Price	11/2022
1949	(7*10^260198-61)/9	260198	Erik Branger	11/2011
1950	2^864298-2788421	260180	Enzo Doria	12/2015
1951	2^864039-2791357	260102	Enzo Doria	01/2016
1952	2^863621-113833	259976	Enzo Doria	10/2014
1953	10^259945-11	259945	Mischa Rodermond	04/2023
1954	2^863433+34877	259920	Enzo Doria	07/2024
1955	(28*10^259897+113)/3	259898	Robert Price	06/2023
1956	2^862837+75767	259740	Enzo Doria	05/2016
1957	2^862637-31	259680	Jorge Menendez	05/2019
1958	2^862088+1874941	259515	Enzo Doria	06/2016
1959	2^861987-134557	259484	Hans Havermann	10/2018
1960	(14*10^259431-143)/3	259432	Robert Price	05/2023
1961	2^861516-1854029	259343	Enzo Doria	09/2015
1962	2^860975-1853977	259180	Enzo Doria	09/2015
1963	3^543128+16	259138	Robert Price	04/2020
1964	2^860625-1858843	259074	Enzo Doria	10/2015
1965	2^860110+77689	258919	Enzo Doria	05/2016
1966	2^859600+1880371	258766	Enzo Doria	10/2016
1967	2^859433+494711	258716	Makoto Morimoto	10/2013
1969	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
1968	(2^859431-11)/3	258715	Stefano Morozzi	08/2022
1970	(13*10^258710-43)/3	258711	Robert Price	08/2023
1971	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
1972	2^859240+1875271	258658	Enzo Doria	06/2016
1973	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
1974	2^858812+30421	258529	Enzo Doria	03/2024
1975	(23*10^258494-47)/3	258495	Robert Price	09/2023
1976	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
1977	2^857608+105	258166	Stefano Morozzi	05/2021
1978	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
1979	2^857016-633113	257988	Enzo Doria	12/2013
1980	2^855732-113969	257602	Enzo Doria	10/2014
1981	(5*10^257431+91)/3	257432	Robert Price	08/2023
1982	2^853682-3911	256984	Enzo Doria	05/2014
1983	11^246668-90	256879	Enzo Doria	12/2012
1984	2^853181+30287	256834	Enzo Doria	03/2024
1985	5*2^852698+3	256689	Jon Grantham	07/2023
1986	(23*10^256654+7)/3	256655	Robert Price	05/2023
1987	2^851904-113939	256449	Enzo Doria	10/2014
1988	2^851725-851725^2	256395	Henri Lifchitz	03/2019
1989	11^246167-90	256357	Enzo Doria	12/2012
1990	(85*10^256301-1)/3	256303	Robert Price	12/2022
1991	(10^256187+7)/63443/148782853	256175	Alfred Reich	10/2021
1992	2^850700-569049	256087	Enzo Doria	11/2013
1993	2^850675+153	256079	Stefano Morozzi	05/2021
1994	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
1995	(37^163193+1)/38	255918	Paul Bourdelais	07/2019
1996	(14*10^255805-83)/3	255806	Robert Price	11/2022
1997	2^849316+25861	255670	Enzo Doria	12/2023
1998	2^849177-114025	255628	Enzo Doria	12/2014
1999	2*10^255442-21	255443	Robert Price	08/2023
2000	2^848502-3173	255425	Yves Minet	07/2016

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Probable Primes Top 10000

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