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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	2^859433+494711	258716	Makoto Morimoto	10/2013
1753	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
1752	(2^859431-11)/3	258715	Stefano Morozzi	08/2022
1754	(13*10^258710-43)/3	258711	Robert Price	08/2023
1755	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
1756	2^859240+1875271	258658	Enzo Doria	06/2016
1757	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
1758	2^858812+30421	258529	Enzo Doria	03/2024
1759	(23*10^258494-47)/3	258495	Robert Price	09/2023
1760	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
1761	2^857608+105	258166	Stefano Morozzi	05/2021
1762	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
1763	2^857016-633113	257988	Enzo Doria	12/2013
1764	2^855732-113969	257602	Enzo Doria	10/2014
1765	(5*10^257431+91)/3	257432	Robert Price	08/2023
1766	2^853682-3911	256984	Enzo Doria	05/2014
1767	11^246668-90	256879	Enzo Doria	12/2012
1768	2^853181+30287	256834	Enzo Doria	03/2024
1769	5*2^852698+3	256689	Jon Grantham	07/2023
1770	(23*10^256654+7)/3	256655	Robert Price	05/2023
1771	2^851904-113939	256449	Enzo Doria	10/2014
1772	2^851725-851725^2	256395	Henri Lifchitz	03/2019
1773	11^246167-90	256357	Enzo Doria	12/2012
1774	(85*10^256301-1)/3	256303	Robert Price	12/2022
1775	(10^256187+7)/63443/148782853	256175	Alfred Reich	10/2021
1776	2^850700-569049	256087	Enzo Doria	11/2013
1777	2^850675+153	256079	Stefano Morozzi	05/2021
1778	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
1779	(37^163193+1)/38	255918	Paul Bourdelais	07/2019
1780	(14*10^255805-83)/3	255806	Robert Price	11/2022
1781	2^849316+25861	255670	Enzo Doria	12/2023
1782	2^849177-114025	255628	Enzo Doria	12/2014
1783	2*10^255442-21	255443	Robert Price	08/2023
1784	2^848502-3173	255425	Yves Minet	07/2016
1785	2^848178-140291	255328	Enzo Doria	01/2014
1786	7*10^255167+87	255168	Robert Price	11/2022
1787	2^847622-2441	255160	Yves Minet	02/2016
1788	2^847291+182843	255061	Enzo Doria	11/2016
1789	2^847174+1879429	255025	Enzo Doria	09/2016
1790	2^846881+215837	254937	Enzo Doria	12/2023
1791	24*29^174239+13361	254809	Curtis Bright	04/2015
1792	22*10^254639+7	254641	Robert Price	10/2022
1793	2^845633-933075	254561	Paul Bourdelais	11/2021
1794	2^845610-1868591	254554	Enzo Doria	04/2016
1795	2^845484+81931	254517	Enzo Doria	08/2016
1796	2^845402-114761	254492	Enzo Doria	05/2015
1797	98*10^254173-9	254175	Robert Price	05/2023
1798	2^844334-2792441	254170	Enzo Doria	02/2016
1799	2*10^254162+69	254163	Robert Price	08/2023
1800	(4*10^254107+11)/3	254108	Tyler Busby	02/2023
1801	11^243796-90	253888	Enzo Doria	12/2012
1802	(10^253891+7)/44777/79843/16940711	253875	Alfred Reich	10/2021
1803	30^171733-29^171733	253671	Jean-Louis Charton	10/2018
1804	2^842325+25907	253566	Enzo Doria	11/2023
1805	2^842209+1876037	253531	Enzo Doria	07/2016
1806	2^842123-59197	253505	Enzo Doria	10/2015
1807	(8*10^253313-53)/9	253313	Serge Batalov	11/2022
1808	(28*10^253210+191)/3	253211	Robert Price	07/2023
1809	2^840797-3	253106	Paul Bourdelais	06/2019
1810	2^840716-2969	253081	Yves Minet	05/2016
1811	2^840358-462491	252973	Enzo Doria	08/2015
1812	2^840310+1878379	252959	Enzo Doria	08/2016
1813	2^840203-21	252927	Stefano Morozzi	07/2022
1814	11^242579-60	252620	Enzo Doria	10/2012
1815	45^152659+2	252378	Robert Price	09/2015
1816	(95^127583+1)/96	252322	Paul Bourdelais	07/2019
1817	7*10^252209-17	252210	Robert Price	12/2022
1818	2^837725+1869377	252181	Enzo Doria	05/2016
1819	2^837536-311039	252124	Enzo Doria	06/2015
1820	21^190632-2	252058	Robert Price	07/2015
1821	2^837242+1873297	252035	Enzo Doria	06/2016
1822	2^836995+226575	251961	Enzo Doria	10/2024
1823	2^836656-2787929	251859	Enzo Doria	11/2015
1824	2^836548+219061	251827	Enzo Doria	02/2024
1825	2^836380+1875541	251776	Enzo Doria	07/2016
1826	(359^98327-1)/358	251233	Alexander Zhirkov	11/2017
1827	tau(41^28288)	250924	Nik Lygeros / Olivier Rozier	10/2013
1828	(28*10^250655+113)/3	250656	Robert Price	06/2023
1829	2^832511-461197	250611	Enzo Doria	07/2015
1830	2^832505+1881137	250609	Enzo Doria	11/2016
1831	2^832363+583295	250567	Enzo Doria	12/2016
1832	2^832244-403635	250531	Enzo Doria	01/2014
1833	(14*10^250336-41)/9	250337	Serge Batalov	01/2023
1834	2^831528+24811	250315	Enzo Doria	11/2023
1835	2^831157+1880657	250204	Enzo Doria	11/2016
1836	2^831088-7200899	250183	Enzo Doria	01/2015
1837	2^830956-1349	250143	Yves Minet	07/2015
1838	2^830699+220583	250066	Enzo Doria	03/2024
1839	2^830037+282317	249867	Enzo Doria	09/2016
1840	2^829589-113653	249732	Enzo Doria	09/2014
1841	(4*10^249550-7)/3	249551	Serge Batalov	01/2023
1842	(103*10^249399+17)/3	249401	Robert Price	04/2023
1843	2^828281-3193	249338	Yves Minet	08/2016
1844	(2^828140-19)/3	249295	Stefano Morozzi	08/2022
1845	2^828064-2785619	249273	Enzo Doria	10/2015
1846	2^827602+60409	249134	Enzo Doria	03/2016
1847	2^827306+212419	249044	Enzo Doria	09/2023
1848	10^249010+348861	249011	Patrick De Geest	04/2016
1849	10^249010-21	249010	Serge Batalov	12/2014
1850	2^826733+1882907	248872	Enzo Doria	12/2016
1851	2^825800+22441	248591	Enzo Doria	10/2023
1852	2^825682+1876549	248556	Enzo Doria	07/2016
1853	2^824991-114121	248348	Enzo Doria	12/2014
1854	2^824642-362727	248242	Enzo Doria	12/2013
1855	2^824565-114265	248219	Enzo Doria	01/2015
1856	2^824325-25	248147	Boyan Hu	12/2024
1857	(73*10^248145-1)/9	248146	Robert Price	01/2015
1858	2^823321+219407	247845	Enzo Doria	02/2024
1859	(2^823337+1)/(3*362268281)	247841	Gord Palameta	08/2018
1860	(13*10^247793-43)/3	247794	Robert Price	08/2023
1861	(2^822971-1)/6583769/28211445881/21255852651726486149207	247700	Robert Kinser	09/2016
1862	2^822296+76501	247536	Enzo Doria	05/2016
1863	2^821590-114167	247324	Enzo Doria	12/2014
1864	2^821512-2790659	247300	Enzo Doria	12/2015
1865	(21996^57121-1)/(21996^239-1)	247002	Ryan Propper	11/2023
1866	2^820356+7	246952	Jon Grantham	08/2023
1867	2^820077+382847	246868	Enzo Doria	11/2016
1868	2^820008+81	246848	Henri Lifchitz	01/2025
1869	2^820001+81269	246845	Enzo Doria	07/2016
1870	2^819463-59197	246683	Enzo Doria	10/2015
1871	2^819296+80581	246633	Enzo Doria	07/2016
1872	2^818764+21573	246473	Enzo Doria	11/2023
1873	2^817852+215491	246198	Enzo Doria	11/2023
1874	2^817160-350369	245990	Enzo Doria	06/2015
1875	2^816039-19	245653	Stefano Morozzi	07/2022
1876	2^816029+219407	245650	Enzo Doria	02/2024
1877	(71*10^245558-17)/9	245559	Serge Batalov	01/2023
1878	5*3^514648+2^514648	245551	Jon Grantham	08/2023
1879	88093#+(653879#)/(88093#)	245374	Makoto Morimoto	11/2017
1880	2^815111-113857	245373	Enzo Doria	10/2014
1881	(34555^54289-1)/(34555^233-1)	245334	Ryan Propper	11/2023
1882	2^814914-4001	245314	Yves Minet	05/2017
1883	846^83761-845^83761	245200	Jean-Louis Charton	12/2012
1884	2^814356-2790449	245146	Enzo Doria	12/2015
1885	2^814276-459029	245122	Enzo Doria	04/2015
1886	2^814023+180923	245046	Enzo Doria	07/2016
1887	2^813496+216751	244887	Enzo Doria	12/2023
1888	(3^513059-2^513059)/(1026119*5430216457)	244776	Mike Oakes	03/2017
1889	3^513007+16	244767	Robert Price	04/2020
1890	(46^147197-31^147197)/15	244752	Aurel Gibier	06/2024
1891	2^811882+27289	244401	Enzo Doria	12/2023
1892	2^811842-113675	244389	Enzo Doria	09/2014
1893	2^811132-2787929	244176	Enzo Doria	11/2015
1894	2^809746-2790971	243758	Enzo Doria	01/2016
1895	(14*10^243724-197)/3	243725	Robert Price	03/2023
1896	2^808767-3295	243464	Yves Minet	12/2016
1897	2^808621-113809	243420	Enzo Doria	09/2014
1898	2^808199+29693	243293	Enzo Doria	03/2024
1899	2^807724+1879621	243150	Enzo Doria	09/2016
1900	2^807417+217787	243057	Enzo Doria	01/2024
1901	(23*10^242909+91)/3	242910	Robert Price	03/2023
1902	2^806708+20371	242844	Enzo Doria	08/2023
1903	2*10^242822-91	242823	Robert Price	02/2023
1904	20^186554-3	242713	Paul Bourdelais	12/2020
1905	2^805843-113611	242583	Enzo Doria	08/2014
1906	2^805745-459763	242554	Enzo Doria	05/2015
1907	2^805353+782687	242436	Enzo Doria	11/2016
1908	(19*10^242362-7)/3	242363	Robert Price	12/2023
1909	2^804895+29963	242298	Enzo Doria	03/2024
1910	2^804725+28229	242247	Enzo Doria	01/2024
1911	6^311257+5	242206	Paul Bourdelais	02/2021
1912	(21^242194)%(10^242194)	242194	Henri Lifchitz	06/2025
1913	2^804277-417933	242112	Enzo Doria	01/2014
1914	2^803468-269039	241868	Enzo Doria	10/2013
1915	2^803172+80851	241779	Enzo Doria	07/2016
1916	2^803011+220073	241731	Enzo Doria	03/2024
1917	3^506233-2	241535	Robert Price	11/2013
1918	2^802025-25999	241434	Enzo Doria	10/2013
1919	(3^505823+3^252912+1)/7	241339	Serge Batalov	03/2014
1920	2^801575+25073	241299	Enzo Doria	11/2023
1921	2^801303+1872923	241217	Enzo Doria	05/2016
1922	2^801105+216977	241157	Enzo Doria	12/2023
1923	(23*10^241048-143)/3	241049	Robert Price	12/2023
1924	2^800579-1862947	240999	Enzo Doria	12/2015
1925	2^799999+16205	240824	Norman Luhn	09/2023
1926	3^504206+2	240568	Luke W. Richards	03/2018
1927	2^798973-26283	240515	Enzo Doria	10/2013
1928	2^798671-69487	240424	Enzo Doria	12/2015
1929	2^797220+79831	239988	Enzo Doria	06/2016
1930	2^796910-26001	239894	Enzo Doria	10/2013
1931	(97^120721-1)/811245216	239837	Paul Vanderveen	06/2025
1932	2^796598+653119	239800	Enzo Doria	12/2016
1933	2^796432-1859729	239750	Enzo Doria	11/2015
1934	2^796002-1852211	239621	Enzo Doria	08/2015
1935	2^795884+214081	239585	Enzo Doria	10/2023
1936	2^795709+75767	239533	Enzo Doria	04/2016
1937	2^795708+81721	239532	Enzo Doria	08/2016
1938	2^795468-2786249	239460	Enzo Doria	10/2015
1939	2^795442+80779	239452	Enzo Doria	07/2016
1940	2^795075-1852057	239342	Enzo Doria	08/2015
1941	(86^123677+1)/87	239252	Paul Bourdelais	01/2019
1942	2^794043+1875023	239031	Enzo Doria	06/2016
1943	2^793347-69577	238822	Enzo Doria	01/2016
1944	5*2^793288+3	238805	Jon Grantham	07/2023
1945	2^792988-344429	238714	Enzo Doria	08/2015
1946	2^792700-2786369	238627	Enzo Doria	11/2015
1947	2^792663-1844797	238616	Enzo Doria	06/2015
1948	2^792605-291943	238598	Enzo Doria	07/2015
1949	2^792366+218599	238526	Enzo Doria	01/2024
1950	(2^792061-2^396031+1)/5	238434	Thomas Ritschel	03/2014
1951	2^791321+30077	238212	Enzo Doria	03/2024
1952	4*10^238163+21	238164	Robert Price	12/2022
1953	(26*10^238157-77)/3	238158	Robert Price	03/2023
1954	10^237670+9	237671	Robert Price	08/2023
1955	2^789373+1869377	237625	Enzo Doria	05/2016
1956	((10^59387+1)^3(10^59387+1+10^29694)-(10^118774+10^59387)(10^29694-1)+10^178161)/27961	237544	Serge Batalov	04/2015
1957	Phi(1187740M,10)	237544	Anonymous	03/2025
1958	2^789033+218537	237523	Enzo Doria	01/2024
1959	2^788942+1866409	237496	Enzo Doria	02/2016
1960	2^788844-114329	237466	Enzo Doria	01/2015
1961	2^788705-1859713	237424	Enzo Doria	11/2015
1962	2^788325+224789	237310	Enzo Doria	07/2024
1963	15^201475+14	236953	Alfred Reich	10/2023
1964	2^786663+219173	236810	Enzo Doria	02/2024
1965	2^786180+1871971	236664	Enzo Doria	05/2016
1966	11^227092-90	236492	Enzo Doria	11/2012
1967	2^785260+1866361	236387	Enzo Doria	02/2016
1968	2^785220+1880611	236375	Enzo Doria	10/2016
1969	(2^784689-15)/7	236215	Stefano Morozzi	08/2022
1970	19^184650-2	236122	Robert Price	10/2014
1971	10^236059+216513	236060	Patrick De Geest	04/2016
1972	10^236059-20909	236059	Robert Price	09/2015
1973	2^783988+38011	236004	Enzo Doria	10/2024
1974	2^783893-21	235976	Stefano Morozzi	07/2022
1975	(47^140983-1)/2792206142311142462	235719	Paul Vanderveen	06/2025
1976	2^782821+37577	235653	Enzo Doria	10/2024
1977	(87^121487-1)/86	235625	Paul Bourdelais	12/2018
1978	2^782634-113981	235597	Enzo Doria	11/2014
1979	2^782423+1879733	235533	Enzo Doria	09/2016
1980	(10^(2117707+1)+1210^117707-1)/3	235415	Robert Price	10/2023
1981	(2^781970)/(781970^2)	235385	Henri Lifchitz	06/2025
1982	2^781682-2789543	235310	Enzo Doria	12/2015
1983	2^780481+21489	234949	Enzo Doria	05/2024
1984	2^780408-113453	234927	Enzo Doria	08/2014
1985	7*10^234915+9	234916	Robert Price	04/2023
1986	2^780368-1864829	234915	Enzo Doria	01/2016
1987	2^780284+7	234889	Jon Grantham	08/2023
1988	2^779593-1836559	234681	Enzo Doria	05/2015
1989	(8713#+(549391#)/(8713#))/360295171	234487	Makoto Morimoto	11/2017
1990	(5^335429+1)/6	234455	Paul Bourdelais	08/2010
1991	2^778788+22201	234439	Enzo Doria	09/2023
1992	2^778395-113617	234321	Enzo Doria	08/2014
1993	5*2^778090+3	234230	Jon Grantham	07/2023
1994	(21430^54289-1)/(21430^233-1)	234118	Ryan Propper	11/2023
1995	(5*10^234054-101)/3	234055	Robert Price	08/2023
1996	23*10^234025-7	234027	Robert Price	10/2022
1997	2^777170+21489	233952	Enzo Doria	05/2024
1998	Phi(78125,5517)	233857	Anonymous	09/2022
1999	5^334359-3^334359-1	233707	Jon Grantham	08/2023
2000	2^776245-2792353	233674	Enzo Doria	02/2016

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301979 PRPs in the top)