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	(1648732*10^270344-16487317)/3	270350	Danilo Nitsche	03/2026
1752	(1386601*10^270344-13866001)/9	270350	Danilo Nitsche	03/2026
1753	(1631944*10^270344-16319431)/9	270350	Danilo Nitsche	03/2026
1754	922284*10^270344-9222839	270350	Danilo Nitsche	03/2026
1755	992761*10^270344-9927609	270350	Danilo Nitsche	03/2026
1756	(2241127*10^270344-22411267)/3	270350	Danilo Nitsche	04/2026
1757	(2466128*10^270344-24661277)/3	270350	Danilo Nitsche	04/2026
1758	2366042*10^270343-2366041	270350	Danilo Nitsche	04/2026
1759	(2878615*10^270344-28786147)/3	270350	Danilo Nitsche	04/2026
1760	(2026252*10^270344-20262517)/3	270350	Danilo Nitsche	04/2026
1761	1967284*10^270343-1967283	270350	Danilo Nitsche	04/2026
1762	2629838*10^270343-2629837	270350	Danilo Nitsche	04/2026
1763	(2737132*10^270344-27371317)/3	270350	Danilo Nitsche	04/2026
1764	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
1765	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
1766	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
1767	2^897867-3217	270285	Yves Minet	12/2016
1768	2^897849-115273	270280	Enzo Doria	07/2015
1769	2^897367+26289	270135	Enzo Doria	03/2024
1770	2^896616-114179	269909	Enzo Doria	12/2014
1771	(12648^66049-1)/(12648^257-1)	269881	Ryan Propper	11/2023
1772	(10^(2134811+1)+610^134811-1)/3	269623	Robert Price	08/2024
1773	(22*10^269517-19)/3	269518	Robert Price	07/2023
1774	10^(2134739+1)-710^134739-1	269479	Robert Price	07/2023
1775	2^894928+583561	269401	Enzo Doria	04/2017
1776	2^894673-39343	269324	Enzo Doria	08/2015
1777	2^893836+23221	269072	Enzo Doria	10/2023
1778	2^892718+29539	268735	Enzo Doria	03/2024
1779	2^892660+213901	268718	Enzo Doria	10/2023
1780	F(1285607)	268676	Henri Lifchitz	11/2008
1781	2^892234+22189	268590	Enzo Doria	09/2023
1782	2^892151+24863	268565	Enzo Doria	11/2023
1783	2^892112+187663	268553	Enzo Doria	08/2016
1784	(266*10^268407-17)/3	268409	Robert Price	02/2023
1785	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
1786	2^890957-69583	268205	Enzo Doria	12/2015
1787	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
1788	2^890122-351401	267954	Enzo Doria	07/2015
1789	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
1790	2^888852+229051	267572	Enzo Doria	11/2024
1791	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
1792	(1005^89087-1)/1004	267451	Jinyuan Wang	01/2024
1793	(485^99523-1)/484	267291	Michael Stocker	05/2020
1794	2^886324+77791	266811	Enzo Doria	06/2016
1795	7*10^266731+87	266732	Robert Price	11/2022
1796	2^886040+213901	266725	Enzo Doria	10/2023
1797	2^885242+217909	266485	Enzo Doria	01/2024
1798	2^884738+26809	266333	Enzo Doria	12/2023
1799	2^884714+1880527	266326	Enzo Doria	10/2016
1800	7*10^266024-47	266025	Robert Price	08/2023
1801	11^255426+255426^11	265999	Serge Batalov	05/2014
1802	2^883462-343421	265949	Enzo Doria	07/2015
1803	2^883442+1875019	265943	Enzo Doria	06/2016
1804	2^883333-291583	265910	Enzo Doria	07/2015
1805	2^883132+30421	265850	Enzo Doria	03/2024
1806	10^265566+3593037	265567	Paul Bourdelais	08/2023
1807	(2*10^265321-17)/3	265321	Serge Batalov	11/2022
1808	(16*10^265052-91)/3	265053	Robert Price	11/2022
1809	2^880411+1882673	265031	Enzo Doria	12/2016
1810	2^880101+228917	264937	Enzo Doria	11/2024
1811	(14*10^264791-11)/3	264792	Robert Price	08/2022
1812	2^879530-2788031	264765	Enzo Doria	12/2015
1813	2^879292+25171	264694	Enzo Doria	11/2023
1814	(2*10^264539+61)/9	264539	Serge Batalov	11/2022
1815	2^878118+2793079	264340	Enzo Doria	02/2016
1816	(2^878073-7)/5	264326	Stefano Morozzi	08/2022
1817	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
1818	5^377865+3^377865-1	264117	Jon Grantham	08/2023
1819	(19*10^263971+131)/3	263972	Robert Price	08/2023
1820	2^876202-17	263764	Stefano Morozzi	07/2022
1821	(14*10^263720-11)/3	263721	Robert Price	08/2022
1822	2^875748-461129	263627	Enzo Doria	07/2015
1823	2^875518-15	263558	Stefano Morozzi	07/2022
1824	(29*10^263523-17)/3	263524	Robert Price	01/2023
1825	2^875181-2789923	263456	Enzo Doria	12/2015
1826	2^875101-350083	263432	Enzo Doria	08/2015
1827	2^874684+1883587	263307	Enzo Doria	01/2017
1828	2^874616+1872211	263286	Enzo Doria	05/2016
1829	2^874566+30049	263271	Enzo Doria	03/2024
1830	3^551491+16	263129	Robert Price	04/2020
1831	2^874073+2792957	263123	Enzo Doria	02/2016
1832	(7*10^263006-19)/3	263007	Robert Price	10/2023
1833	2^873628+1878751	262989	Enzo Doria	08/2016
1834	2^873497+20837	262949	Enzo Doria	08/2023
1835	2^873288-269	262886	Yves Minet	01/2015
1836	(2*10^262874+7)/9	262874	Rytis Slatkevicius	01/2023
1837	(28*10^262655-43)/3	262656	Robert Price	04/2023
1838	(2*10^262603-11)/9	262603	Serge Batalov	11/2022
1839	2^871991-4207	262496	Yves Minet	03/2021
1840	(23*10^262324+7)/3	262325	Robert Price	05/2023
1841	2^871146-3173	262242	Yves Minet	07/2016
1842	(10^(2131020+1)+6310^131020-1)/9	262041	Robert Price	08/2024
1843	2^869601-163	261776	Yves Minet	01/2015
1844	(2*10^261704+61)/9	261704	Serge Batalov	11/2022
1845	2^869326+282859	261694	Enzo Doria	11/2016
1846	2^869035-114181	261606	Enzo Doria	12/2014
1847	2^868817+26777	261540	Enzo Doria	12/2023
1848	3^547850+9000004	261391	Enzo Doria	10/2023
1849	Phi(156793,2^7)	261261	Henri Lifchitz	10/2025
1850	4*10^261248+91	261249	Robert Price	11/2022
1851	55083^55083+1282^1282	261150	Henri Lifchitz	10/2024
1852	2^866908+34891	260966	Enzo Doria	07/2024
1853	2^865715+80303	260607	Enzo Doria	07/2016
1854	2^865474+23209	260534	Enzo Doria	10/2023
1855	2^865238+214759	260463	Enzo Doria	11/2023
1856	2^865048+1882411	260406	Enzo Doria	12/2016
1857	2^864899-113871	260361	Enzo Doria	10/2014
1858	(16*10^260256-91)/3	260257	Robert Price	11/2022
1859	(7*10^260198-61)/9	260198	Erik Branger	11/2011
1860	2^864298-2788421	260180	Enzo Doria	12/2015
1861	2^864039-2791357	260102	Enzo Doria	01/2016
1862	2^863621-113833	259976	Enzo Doria	10/2014
1863	10^259945-11	259945	Mischa Rodermond	04/2023
1864	2^863433+34877	259920	Enzo Doria	07/2024
1865	(28*10^259897+113)/3	259898	Robert Price	06/2023
1866	2^862837+75767	259740	Enzo Doria	05/2016
1867	2^862637-31	259680	Jorge Menendez	05/2019
1868	2^862088+1874941	259515	Enzo Doria	06/2016
1869	2^861987-134557	259484	Hans Havermann	10/2018
1870	(14*10^259431-143)/3	259432	Robert Price	05/2023
1871	2^861516-1854029	259343	Enzo Doria	09/2015
1872	2^860975-1853977	259180	Enzo Doria	09/2015
1873	3^543128+16	259138	Robert Price	04/2020
1874	2^860625-1858843	259074	Enzo Doria	10/2015
1875	2^860110+77689	258919	Enzo Doria	05/2016
1876	2^859600+1880371	258766	Enzo Doria	10/2016
1877	2^859433+494711	258716	Makoto Morimoto	10/2013
1879	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
1878	(2^859431-11)/3	258715	Stefano Morozzi	08/2022
1880	(13*10^258710-43)/3	258711	Robert Price	08/2023
1881	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
1882	2^859240+1875271	258658	Enzo Doria	06/2016
1883	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
1884	2^858812+30421	258529	Enzo Doria	03/2024
1885	(23*10^258494-47)/3	258495	Robert Price	09/2023
1886	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
1887	2^857608+105	258166	Stefano Morozzi	05/2021
1888	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
1889	2^857016-633113	257988	Enzo Doria	12/2013
1890	2^855732-113969	257602	Enzo Doria	10/2014
1891	(5*10^257431+91)/3	257432	Robert Price	08/2023
1892	2^853682-3911	256984	Enzo Doria	05/2014
1893	11^246668-90	256879	Enzo Doria	12/2012
1894	2^853181+30287	256834	Enzo Doria	03/2024
1895	5*2^852698+3	256689	Jon Grantham	07/2023
1896	(23*10^256654+7)/3	256655	Robert Price	05/2023
1897	2^851904-113939	256449	Enzo Doria	10/2014
1898	2^851725-851725^2	256395	Henri Lifchitz	03/2019
1899	11^246167-90	256357	Enzo Doria	12/2012
1900	(85*10^256301-1)/3	256303	Robert Price	12/2022
1901	(10^256187+7)/63443/148782853	256175	Alfred Reich	10/2021
1902	2^850700-569049	256087	Enzo Doria	11/2013
1903	2^850675+153	256079	Stefano Morozzi	05/2021
1904	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
1905	(37^163193+1)/38	255918	Paul Bourdelais	07/2019
1906	(14*10^255805-83)/3	255806	Robert Price	11/2022
1907	2^849316+25861	255670	Enzo Doria	12/2023
1908	2^849177-114025	255628	Enzo Doria	12/2014
1909	2*10^255442-21	255443	Robert Price	08/2023
1910	2^848502-3173	255425	Yves Minet	07/2016
1911	2^848178-140291	255328	Enzo Doria	01/2014
1912	7*10^255167+87	255168	Robert Price	11/2022
1913	2^847622-2441	255160	Yves Minet	02/2016
1914	2^847291+182843	255061	Enzo Doria	11/2016
1915	2^847174+1879429	255025	Enzo Doria	09/2016
1916	2^846881+215837	254937	Enzo Doria	12/2023
1917	Phi(475779,2^3)	254889	Henri Lifchitz	12/2025
1918	24*29^174239+13361	254809	Curtis Bright	04/2015
1919	22*10^254639+7	254641	Robert Price	10/2022
1920	2^845633-933075	254561	Paul Bourdelais	11/2021
1921	2^845610-1868591	254554	Enzo Doria	04/2016
1922	2^845484+81931	254517	Enzo Doria	08/2016
1923	2^845402-114761	254492	Enzo Doria	05/2015
1924	Phi(115655,561)	254335	Henri Lifchitz	12/2025
1925	98*10^254173-9	254175	Robert Price	05/2023
1926	2^844334-2792441	254170	Enzo Doria	02/2016
1927	2*10^254162+69	254163	Robert Price	08/2023
1928	(4*10^254107+11)/3	254108	Tyler Busby	02/2023
1929	11^243796-90	253888	Enzo Doria	12/2012
1930	(10^253891+7)/44777/79843/16940711	253875	Alfred Reich	10/2021
1931	30^171733-29^171733	253671	Jean-Louis Charton	10/2018
1932	2^842325+25907	253566	Enzo Doria	11/2023
1933	2^842209+1876037	253531	Enzo Doria	07/2016
1934	2^842123-59197	253505	Enzo Doria	10/2015
1935	(8*10^253313-53)/9	253313	Serge Batalov	11/2022
1936	(28*10^253210+191)/3	253211	Robert Price	07/2023
1937	2^840797-3	253106	Paul Bourdelais	06/2019
1938	2^840716-2969	253081	Yves Minet	05/2016
1939	2^840358-462491	252973	Enzo Doria	08/2015
1940	2^840310+1878379	252959	Enzo Doria	08/2016
1941	2^840203-21	252927	Stefano Morozzi	07/2022
1942	11^242579-60	252620	Enzo Doria	10/2012
1943	45^152659+2	252378	Robert Price	09/2015
1944	(95^127583+1)/96	252322	Paul Bourdelais	07/2019
1945	7*10^252209-17	252210	Robert Price	12/2022
1946	2^837725+1869377	252181	Enzo Doria	05/2016
1947	2^837536-311039	252124	Enzo Doria	06/2015
1948	21^190632-2	252058	Robert Price	07/2015
1949	2^837242+1873297	252035	Enzo Doria	06/2016
1950	2^836995+226575	251961	Enzo Doria	10/2024
1951	2^836656-2787929	251859	Enzo Doria	11/2015
1952	2^836548+219061	251827	Enzo Doria	02/2024
1953	2^836380+1875541	251776	Enzo Doria	07/2016
1954	(359^98327-1)/358	251233	Alexander Zhirkov	11/2017
1955	tau(41^28288)	250924	Nik Lygeros / Olivier Rozier	10/2013
1956	Phi(137951,-100)	250801	Henri Lifchitz	12/2025
1957	Phi(74531,11#)	250691	Henri Lifchitz	12/2025
1958	(28*10^250655+113)/3	250656	Robert Price	06/2023
1959	2^832511-461197	250611	Enzo Doria	07/2015
1960	2^832505+1881137	250609	Enzo Doria	11/2016
1961	2^832363+583295	250567	Enzo Doria	12/2016
1962	2^832244-403635	250531	Enzo Doria	01/2014
1963	(14*10^250336-41)/9	250337	Serge Batalov	01/2023
1964	2^831528+24811	250315	Enzo Doria	11/2023
1965	2^831157+1880657	250204	Enzo Doria	11/2016
1966	2^831088-7200899	250183	Enzo Doria	01/2015
1967	2^830956-1349	250143	Yves Minet	07/2015
1968	2^830699+220583	250066	Enzo Doria	03/2024
1969	2^830037+282317	249867	Enzo Doria	09/2016
1970	2^829589-113653	249732	Enzo Doria	09/2014
1971	(4*10^249550-7)/3	249551	Serge Batalov	01/2023
1972	(103*10^249399+17)/3	249401	Robert Price	04/2023
1973	2^828281-3193	249338	Yves Minet	08/2016
1974	(2^828140-19)/3	249295	Stefano Morozzi	08/2022
1975	2^828064-2785619	249273	Enzo Doria	10/2015
1976	2^827602+60409	249134	Enzo Doria	03/2016
1977	2^827306+212419	249044	Enzo Doria	09/2023
1978	10^249010+348861	249011	Patrick De Geest	04/2016
1979	10^249010-21	249010	Serge Batalov	12/2014
1980	2^826733+1882907	248872	Enzo Doria	12/2016
1981	2^825800+22441	248591	Enzo Doria	10/2023
1982	2^825682+1876549	248556	Enzo Doria	07/2016
1983	2^824991-114121	248348	Enzo Doria	12/2014
1984	2^824642-362727	248242	Enzo Doria	12/2013
1985	2^824565-114265	248219	Enzo Doria	01/2015
1986	2^824325-25	248147	Boyan Hu	12/2024
1987	(73*10^248145-1)/9	248146	Robert Price	01/2015
1988	2^823321+219407	247845	Enzo Doria	02/2024
1989	(2^823337+1)/(3*362268281)	247841	Gord Palameta	08/2018
1990	(13*10^247793-43)/3	247794	Robert Price	08/2023
1991	(2^822971-1)/6583769/28211445881/21255852651726486149207	247700	Robert Kinser	09/2016
1992	2^822296+76501	247536	Enzo Doria	05/2016
1993	2^821590-114167	247324	Enzo Doria	12/2014
1994	2^821512-2790659	247300	Enzo Doria	12/2015
1995	(21996^57121-1)/(21996^239-1)	247002	Ryan Propper	11/2023
1996	2^820356+7	246952	Jon Grantham	08/2023
1997	2^820077+382847	246868	Enzo Doria	11/2016
1998	2^820008+81	246848	Henri Lifchitz	01/2025
1999	2^820001+81269	246845	Enzo Doria	07/2016
2000	2^819463-59197	246683	Enzo Doria	10/2015

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