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	2^901146+219049	271272	Enzo Doria	02/2024
1752	(8*10^271039-77)/3	271040	Robert Price	04/2023
1753	2^899999+1144031	270927	Norman Luhn	09/2023
1754	2*10^270802-91	270803	Robert Price	02/2023
1755	23*10^270799-7	270801	Robert Price	10/2022
1756	2^899121-115033	270663	Enzo Doria	07/2015
1757	2^898900+883021	270596	Enzo Doria	12/2016
1758	2^898762-251511	270555	Enzo Doria	12/2013
1759	2^898589+47	270503	Lelio R Paula	03/2016
1760	(939628*10^270345-93962791)/9	270351	Danilo Nitsche	03/2026
1761	1447184*10^270344-14471839	270351	Danilo Nitsche	03/2026
1762	269048*10^270344-2690479	270350	Danilo Nitsche	02/2026
1763	172249*10^270344-1722489	270350	Danilo Nitsche	02/2026
1764	(288964*10^270345-28896397)/3	270350	Danilo Nitsche	02/2026
1765	661681*10^270344-6616809	270350	Danilo Nitsche	02/2026
1766	184489*10^270344-1844889	270350	Danilo Nitsche	02/2026
1767	58552*10^270345-5855199	270350	Danilo Nitsche	02/2026
1768	(245662*10^270345-24566197)/3	270350	Danilo Nitsche	02/2026
1769	371745*10^270344-3717449	270350	Danilo Nitsche	02/2026
1770	(1366645*10^270344-13666441)/9	270350	Danilo Nitsche	03/2026
1771	(1648732*10^270344-16487317)/3	270350	Danilo Nitsche	03/2026
1772	(1386601*10^270344-13866001)/9	270350	Danilo Nitsche	03/2026
1773	(1631944*10^270344-16319431)/9	270350	Danilo Nitsche	03/2026
1774	922284*10^270344-9222839	270350	Danilo Nitsche	03/2026
1775	992761*10^270344-9927609	270350	Danilo Nitsche	03/2026
1776	(2241127*10^270344-22411267)/3	270350	Danilo Nitsche	04/2026
1777	(2466128*10^270344-24661277)/3	270350	Danilo Nitsche	04/2026
1778	2366042*10^270343-2366041	270350	Danilo Nitsche	04/2026
1779	(2878615*10^270344-28786147)/3	270350	Danilo Nitsche	04/2026
1780	(2026252*10^270344-20262517)/3	270350	Danilo Nitsche	04/2026
1781	1967284*10^270343-1967283	270350	Danilo Nitsche	04/2026
1782	2629838*10^270343-2629837	270350	Danilo Nitsche	04/2026
1783	(2737132*10^270344-27371317)/3	270350	Danilo Nitsche	04/2026
1784	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
1785	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
1786	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
1787	2^897867-3217	270285	Yves Minet	12/2016
1788	2^897849-115273	270280	Enzo Doria	07/2015
1789	2^897367+26289	270135	Enzo Doria	03/2024
1790	2^896616-114179	269909	Enzo Doria	12/2014
1791	(12648^66049-1)/(12648^257-1)	269881	Ryan Propper	11/2023
1792	(10^(2134811+1)+610^134811-1)/3	269623	Robert Price	08/2024
1793	(22*10^269517-19)/3	269518	Robert Price	07/2023
1794	10^(2134739+1)-710^134739-1	269479	Robert Price	07/2023
1795	2^894928+583561	269401	Enzo Doria	04/2017
1796	2^894673-39343	269324	Enzo Doria	08/2015
1797	2^893836+23221	269072	Enzo Doria	10/2023
1798	2^892718+29539	268735	Enzo Doria	03/2024
1799	2^892660+213901	268718	Enzo Doria	10/2023
1800	F(1285607)	268676	Henri Lifchitz	11/2008
1801	2^892234+22189	268590	Enzo Doria	09/2023
1802	2^892151+24863	268565	Enzo Doria	11/2023
1803	2^892112+187663	268553	Enzo Doria	08/2016
1804	(266*10^268407-17)/3	268409	Robert Price	02/2023
1805	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
1806	2^890957-69583	268205	Enzo Doria	12/2015
1807	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
1808	2^890122-351401	267954	Enzo Doria	07/2015
1809	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
1810	2^888852+229051	267572	Enzo Doria	11/2024
1811	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
1812	(1005^89087-1)/1004	267451	Jinyuan Wang	01/2024
1813	(485^99523-1)/484	267291	Michael Stocker	05/2020
1814	2^886324+77791	266811	Enzo Doria	06/2016
1815	7*10^266731+87	266732	Robert Price	11/2022
1816	2^886040+213901	266725	Enzo Doria	10/2023
1817	2^885242+217909	266485	Enzo Doria	01/2024
1818	2^884738+26809	266333	Enzo Doria	12/2023
1819	2^884714+1880527	266326	Enzo Doria	10/2016
1820	7*10^266024-47	266025	Robert Price	08/2023
1821	11^255426+255426^11	265999	Serge Batalov	05/2014
1822	2^883462-343421	265949	Enzo Doria	07/2015
1823	2^883442+1875019	265943	Enzo Doria	06/2016
1824	2^883333-291583	265910	Enzo Doria	07/2015
1825	2^883132+30421	265850	Enzo Doria	03/2024
1826	10^265566+3593037	265567	Paul Bourdelais	08/2023
1827	(2*10^265321-17)/3	265321	Serge Batalov	11/2022
1828	(16*10^265052-91)/3	265053	Robert Price	11/2022
1829	2^880411+1882673	265031	Enzo Doria	12/2016
1830	2^880101+228917	264937	Enzo Doria	11/2024
1831	(14*10^264791-11)/3	264792	Robert Price	08/2022
1832	2^879530-2788031	264765	Enzo Doria	12/2015
1833	2^879292+25171	264694	Enzo Doria	11/2023
1834	(2*10^264539+61)/9	264539	Serge Batalov	11/2022
1835	2^878118+2793079	264340	Enzo Doria	02/2016
1836	(2^878073-7)/5	264326	Stefano Morozzi	08/2022
1837	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
1838	5^377865+3^377865-1	264117	Jon Grantham	08/2023
1839	(19*10^263971+131)/3	263972	Robert Price	08/2023
1840	2^876202-17	263764	Stefano Morozzi	07/2022
1841	(14*10^263720-11)/3	263721	Robert Price	08/2022
1842	2^875748-461129	263627	Enzo Doria	07/2015
1843	2^875518-15	263558	Stefano Morozzi	07/2022
1844	(29*10^263523-17)/3	263524	Robert Price	01/2023
1845	2^875181-2789923	263456	Enzo Doria	12/2015
1846	2^875101-350083	263432	Enzo Doria	08/2015
1847	2^874684+1883587	263307	Enzo Doria	01/2017
1848	2^874616+1872211	263286	Enzo Doria	05/2016
1849	2^874566+30049	263271	Enzo Doria	03/2024
1850	3^551491+16	263129	Robert Price	04/2020
1851	2^874073+2792957	263123	Enzo Doria	02/2016
1852	(7*10^263006-19)/3	263007	Robert Price	10/2023
1853	2^873628+1878751	262989	Enzo Doria	08/2016
1854	2^873497+20837	262949	Enzo Doria	08/2023
1855	2^873288-269	262886	Yves Minet	01/2015
1856	(2*10^262874+7)/9	262874	Rytis Slatkevicius	01/2023
1857	(28*10^262655-43)/3	262656	Robert Price	04/2023
1858	(2*10^262603-11)/9	262603	Serge Batalov	11/2022
1859	2^871991-4207	262496	Yves Minet	03/2021
1860	(23*10^262324+7)/3	262325	Robert Price	05/2023
1861	2^871146-3173	262242	Yves Minet	07/2016
1862	(10^(2131020+1)+6310^131020-1)/9	262041	Robert Price	08/2024
1863	2^869601-163	261776	Yves Minet	01/2015
1864	(2*10^261704+61)/9	261704	Serge Batalov	11/2022
1865	2^869326+282859	261694	Enzo Doria	11/2016
1866	2^869035-114181	261606	Enzo Doria	12/2014
1867	2^868817+26777	261540	Enzo Doria	12/2023
1868	3^547850+9000004	261391	Enzo Doria	10/2023
1869	Phi(156793,2^7)	261261	Henri Lifchitz	10/2025
1870	4*10^261248+91	261249	Robert Price	11/2022
1871	55083^55083+1282^1282	261150	Henri Lifchitz	10/2024
1872	2^866908+34891	260966	Enzo Doria	07/2024
1873	2^865715+80303	260607	Enzo Doria	07/2016
1874	2^865474+23209	260534	Enzo Doria	10/2023
1875	2^865238+214759	260463	Enzo Doria	11/2023
1876	2^865048+1882411	260406	Enzo Doria	12/2016
1877	2^864899-113871	260361	Enzo Doria	10/2014
1878	(16*10^260256-91)/3	260257	Robert Price	11/2022
1879	(7*10^260198-61)/9	260198	Erik Branger	11/2011
1880	2^864298-2788421	260180	Enzo Doria	12/2015
1881	2^864039-2791357	260102	Enzo Doria	01/2016
1882	2^863621-113833	259976	Enzo Doria	10/2014
1883	10^259945-11	259945	Mischa Rodermond	04/2023
1884	2^863433+34877	259920	Enzo Doria	07/2024
1885	(28*10^259897+113)/3	259898	Robert Price	06/2023
1886	2^862837+75767	259740	Enzo Doria	05/2016
1887	2^862637-31	259680	Jorge Menendez	05/2019
1888	2^862088+1874941	259515	Enzo Doria	06/2016
1889	2^861987-134557	259484	Hans Havermann	10/2018
1890	(14*10^259431-143)/3	259432	Robert Price	05/2023
1891	2^861516-1854029	259343	Enzo Doria	09/2015
1892	2^860975-1853977	259180	Enzo Doria	09/2015
1893	3^543128+16	259138	Robert Price	04/2020
1894	2^860625-1858843	259074	Enzo Doria	10/2015
1895	2^860110+77689	258919	Enzo Doria	05/2016
1896	2^859600+1880371	258766	Enzo Doria	10/2016
1897	2^859433+494711	258716	Makoto Morimoto	10/2013
1899	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
1898	(2^859431-11)/3	258715	Stefano Morozzi	08/2022
1900	(13*10^258710-43)/3	258711	Robert Price	08/2023
1901	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
1902	2^859240+1875271	258658	Enzo Doria	06/2016
1903	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
1904	2^858812+30421	258529	Enzo Doria	03/2024
1905	(23*10^258494-47)/3	258495	Robert Price	09/2023
1906	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
1907	2^857608+105	258166	Stefano Morozzi	05/2021
1908	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
1909	2^857016-633113	257988	Enzo Doria	12/2013
1910	2^855732-113969	257602	Enzo Doria	10/2014
1911	(5*10^257431+91)/3	257432	Robert Price	08/2023
1912	2^853682-3911	256984	Enzo Doria	05/2014
1913	11^246668-90	256879	Enzo Doria	12/2012
1914	2^853181+30287	256834	Enzo Doria	03/2024
1915	5*2^852698+3	256689	Jon Grantham	07/2023
1916	(23*10^256654+7)/3	256655	Robert Price	05/2023
1917	2^851904-113939	256449	Enzo Doria	10/2014
1918	2^851725-851725^2	256395	Henri Lifchitz	03/2019
1919	11^246167-90	256357	Enzo Doria	12/2012
1920	(85*10^256301-1)/3	256303	Robert Price	12/2022
1921	(10^256187+7)/63443/148782853	256175	Alfred Reich	10/2021
1922	2^850700-569049	256087	Enzo Doria	11/2013
1923	2^850675+153	256079	Stefano Morozzi	05/2021
1924	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
1925	(37^163193+1)/38	255918	Paul Bourdelais	07/2019
1926	(14*10^255805-83)/3	255806	Robert Price	11/2022
1927	2^849316+25861	255670	Enzo Doria	12/2023
1928	2^849177-114025	255628	Enzo Doria	12/2014
1929	2*10^255442-21	255443	Robert Price	08/2023
1930	2^848502-3173	255425	Yves Minet	07/2016
1931	2^848178-140291	255328	Enzo Doria	01/2014
1932	7*10^255167+87	255168	Robert Price	11/2022
1933	2^847622-2441	255160	Yves Minet	02/2016
1934	2^847291+182843	255061	Enzo Doria	11/2016
1935	2^847174+1879429	255025	Enzo Doria	09/2016
1936	2^846881+215837	254937	Enzo Doria	12/2023
1937	Phi(475779,2^3)	254889	Henri Lifchitz	12/2025
1938	24*29^174239+13361	254809	Curtis Bright	04/2015
1939	22*10^254639+7	254641	Robert Price	10/2022
1940	2^845633-933075	254561	Paul Bourdelais	11/2021
1941	2^845610-1868591	254554	Enzo Doria	04/2016
1942	2^845484+81931	254517	Enzo Doria	08/2016
1943	2^845402-114761	254492	Enzo Doria	05/2015
1944	Phi(115655,561)	254335	Henri Lifchitz	12/2025
1945	98*10^254173-9	254175	Robert Price	05/2023
1946	2^844334-2792441	254170	Enzo Doria	02/2016
1947	2*10^254162+69	254163	Robert Price	08/2023
1948	(4*10^254107+11)/3	254108	Tyler Busby	02/2023
1949	11^243796-90	253888	Enzo Doria	12/2012
1950	(10^253891+7)/44777/79843/16940711	253875	Alfred Reich	10/2021
1951	30^171733-29^171733	253671	Jean-Louis Charton	10/2018
1952	2^842325+25907	253566	Enzo Doria	11/2023
1953	2^842209+1876037	253531	Enzo Doria	07/2016
1954	2^842123-59197	253505	Enzo Doria	10/2015
1955	(8*10^253313-53)/9	253313	Serge Batalov	11/2022
1956	(28*10^253210+191)/3	253211	Robert Price	07/2023
1957	2^840797-3	253106	Paul Bourdelais	06/2019
1958	2^840716-2969	253081	Yves Minet	05/2016
1959	2^840358-462491	252973	Enzo Doria	08/2015
1960	2^840310+1878379	252959	Enzo Doria	08/2016
1961	2^840203-21	252927	Stefano Morozzi	07/2022
1962	11^242579-60	252620	Enzo Doria	10/2012
1963	45^152659+2	252378	Robert Price	09/2015
1964	(95^127583+1)/96	252322	Paul Bourdelais	07/2019
1965	7*10^252209-17	252210	Robert Price	12/2022
1966	2^837725+1869377	252181	Enzo Doria	05/2016
1967	2^837536-311039	252124	Enzo Doria	06/2015
1968	21^190632-2	252058	Robert Price	07/2015
1969	2^837242+1873297	252035	Enzo Doria	06/2016
1970	2^836995+226575	251961	Enzo Doria	10/2024
1971	2^836656-2787929	251859	Enzo Doria	11/2015
1972	2^836548+219061	251827	Enzo Doria	02/2024
1973	2^836380+1875541	251776	Enzo Doria	07/2016
1974	(359^98327-1)/358	251233	Alexander Zhirkov	11/2017
1975	tau(41^28288)	250924	Nik Lygeros / Olivier Rozier	10/2013
1976	Phi(137951,-100)	250801	Henri Lifchitz	12/2025
1977	406^96126+405	250748	Alfred Reich	05/2026
1978	Phi(74531,11#)	250691	Henri Lifchitz	12/2025
1979	(28*10^250655+113)/3	250656	Robert Price	06/2023
1980	2^832511-461197	250611	Enzo Doria	07/2015
1981	2^832505+1881137	250609	Enzo Doria	11/2016
1982	2^832363+583295	250567	Enzo Doria	12/2016
1983	2^832244-403635	250531	Enzo Doria	01/2014
1984	(14*10^250336-41)/9	250337	Serge Batalov	01/2023
1985	2^831528+24811	250315	Enzo Doria	11/2023
1986	2^831157+1880657	250204	Enzo Doria	11/2016
1987	2^831088-7200899	250183	Enzo Doria	01/2015
1988	2^830956-1349	250143	Yves Minet	07/2015
1989	2^830699+220583	250066	Enzo Doria	03/2024
1990	2^830037+282317	249867	Enzo Doria	09/2016
1991	2^829589-113653	249732	Enzo Doria	09/2014
1992	(4*10^249550-7)/3	249551	Serge Batalov	01/2023
1993	(103*10^249399+17)/3	249401	Robert Price	04/2023
1994	2^828281-3193	249338	Yves Minet	08/2016
1995	(2^828140-19)/3	249295	Stefano Morozzi	08/2022
1996	2^828064-2785619	249273	Enzo Doria	10/2015
1997	2^827602+60409	249134	Enzo Doria	03/2016
1998	2^827306+212419	249044	Enzo Doria	09/2023
1999	10^249010+348861	249011	Patrick De Geest	04/2016
2000	10^249010-21	249010	Serge Batalov	12/2014

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