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	2^609846-1834251	183582	Enzo Doria	07/2015
1752	10^183546+1547323	183547	Patrick De Geest	02/2021
1754	10^183546-800000001	183546	Robert Price	09/2020
1753	10^183546-584297	183546	Patrick De Geest	02/2021
1755	7*10^183511+39	183512	Robert Price	01/2023
1756	(23*10^183477-71)/3	183478	Robert Price	07/2020
1757	11^176176-240	183469	Enzo Doria	11/2012
1758	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
1759	6*10^183429+53	183430	Robert Price	05/2020
1760	(28*10^183403+191)/3	183404	Robert Price	02/2020
1761	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
1762	2^608965-113989	183317	Enzo Doria	10/2014
1763	A005165(43592)	183312	Serge Batalov	07/2017
1764	(61*10^183294+119)/9	183295	Robert Price	05/2019
1765	2^608814-461261	183272	Enzo Doria	06/2015
1766	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
1767	2^608541-608541^2	183190	Henri Lifchitz	02/2018
1768	2^608293+143807	183115	Enzo Doria	10/2016
1769	2^608164-462419	183076	Enzo Doria	08/2015
1770	2^607950-1862303	183012	Enzo Doria	12/2015
1771	(46*10^182896+683)/9	182897	Robert Price	03/2019
1772	(2*10^182787+73)/3	182787	Robert Price	09/2020
1773	2^607101+1871987	182756	Enzo Doria	05/2016
1774	2^606869-69175	182686	Enzo Doria	11/2015
1775	8*10^182671+71	182672	Robert Price	05/2022
1776	(23*10^182666-71)/3	182667	Robert Price	07/2020
1777	3*10^182614-11	182615	Robert Price	07/2018
1778	2^606560-357	182593	Enzo Doria	05/2014
1779	66*10^182420+7	182422	Robert Price	07/2020
1780	2^605687+1866983	182330	Enzo Doria	03/2016
1781	2^605655-114445	182321	Enzo Doria	02/2015
1782	94*10^182291-3	182293	Robert Price	05/2020
1783	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
1784	(14*10^182177-221)/9	182178	Robert Price	04/2018
1785	2^605174-112751	182176	Enzo Doria	06/2014
1786	2^604761+1874507	182052	Enzo Doria	06/2016
1787	2^604705+1871957	182035	Enzo Doria	05/2016
1788	(14*10^182000+229)/9	182001	Robert Price	03/2018
1789	(10^181996+41)/3	181996	Robert Price	12/2017
1790	(17*10^181979+91)/9	181980	Robert Price	02/2022
1791	(5*10^181950-101)/3	181951	Robert Price	04/2018
1792	2^603915+75233	181797	Enzo Doria	04/2016
1793	39470^39537+39537^39470	181723	Norbert Schneider	12/2022
1794	(10^181710+7)/563747/2019847	181698	Alfred Reich	08/2021
1795	7*10^181594-57	181595	Robert Price	06/2020
1796	8*10^181580+29	181581	Robert Price	11/2021
1797	(83*10^181544+61)/9	181545	Serge Batalov	01/2023
1798	(2*10^181457+7)/9	181457	Rytis Slatkevicius	01/2023
1799	3*10^181445+23	181446	Robert Price	03/2022
1800	(194*10^181369-11)/3	181371	Robert Price	09/2020
1801	11^174145-360	181354	Enzo Doria	10/2012
1802	2^602351-396765	181326	Enzo Doria	08/2013
1803	6*10^181306+17	181307	Robert Price	04/2019
1804	(286*10^181220-1)/3	181222	Robert Price	11/2020
1805	2^601957-113833	181208	Enzo Doria	09/2014
1806	66^99581-65^99581	181193	Robert Price	09/2013
1807	10^181182+383973	181183	Patrick De Geest	04/2016
1808	10^181182-21	181182	Serge Batalov	12/2014
1809	(797*10^181171-41)/9	181173	Robert Price	04/2022
1810	(5*10^181127-29)/3	181128	Robert Price	03/2018
1811	2^601521-29143	181076	Enzo Doria	07/2015
1812	2^601442-2797811	181053	Enzo Doria	04/2016
1813	44*10^181029+3	181031	Robert Price	04/2020
1814	5*10^180992-9	180993	Robert Price	05/2015
1815	10^180979+79477	180980	Patrick De Geest	04/2016
1816	10^180979+107739	180980	Patrick De Geest	04/2016
1817	10^180979-11	180979	Serge Batalov	12/2014
1818	2^601023-113851	180926	Enzo Doria	10/2014
1819	(23*10^180862-143)/3	180863	Robert Price	12/2019
1820	3*10^180852+29	180853	Robert Price	05/2018
1821	(277*10^180782-7)/9	180784	Robert Price	02/2022
1822	(8*10^180725-629)/9	180725	Robert Price	01/2022
1823	(79*10^180710-1)/3	180712	Robert Price	02/2020
1824	2^600300-1852559	180709	Enzo Doria	08/2015
1825	(2*10^180706-77)/3	180706	Robert Price	02/2021
1826	(10^180689+71)/9	180689	Serge Batalov	07/2015
1827	2^600209+76487	180681	Enzo Doria	05/2016
1828	(8*10^180536-269)/9	180536	Robert Price	09/2021
1829	2^599702-369885	180529	Enzo Doria	11/2013
1830	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
1831	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
1832	(29*10^180432-17)/3	180433	Robert Price	09/2019
1833	4*10^180360+93	180361	Robert Price	08/2018
1834	2^598942+80779	180300	Enzo Doria	07/2016
1835	(38*10^180296+403)/9	180297	Robert Price	10/2018
1836	(85*10^180241+77)/9	180242	Robert Price	07/2022
1837	2^598591-1844797	180194	Enzo Doria	06/2015
1838	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
1839	(29*10^180072+691)/9	180073	Robert Price	08/2021
1840	(59*10^180038+157)/9	180039	Robert Price	12/2021
1841	95*10^180019-9	180021	Robert Price	01/2022
1842	6*10^179970+91	179971	Robert Price	05/2019
1843	(4*10^179963-79)/3	179964	Robert Price	02/2018
1844	(403*10^179944-43)/9	179946	Robert Price	06/2021
1845	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
1846	2^597424-1859729	179843	Enzo Doria	11/2015
1847	Phi(180683,10)	179760	Maksym Voznyy	09/2015
1848	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
1849	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
1850	(29*10^179697+223)/9	179698	Robert Price	09/2018
1851	2^596884+73	179680	Stefano Morozzi	04/2021
1852	(11*10^179679+13)/3	179680	Robert Price	03/2022
1853	(68*10^179656+7)/3	179658	Robert Price	01/2020
1854	(10^179643+173)/3	179643	Robert Price	05/2021
1855	2^596690-461261	179622	Enzo Doria	07/2015
1856	2^596684-113939	179620	Enzo Doria	10/2014
1857	2*10^179602+63	179603	Robert Price	05/2018
1858	(25*10^179488-403)/9	179489	Robert Price	01/2021
1859	7*10^179460+99	179461	Robert Price	05/2021
1860	3^375887-112696	179344	Enzo Doria	07/2014
1861	4*10^179265-71	179266	Robert Price	12/2018
1862	2*10^179193+83	179194	Robert Price	12/2021
1863	2^595144-1850429	179157	Enzo Doria	08/2015
1864	2^595122-5	179150	Stefano Morozzi	07/2022
1865	3*10^179138+89	179139	Robert Price	10/2018
1866	(52*10^179062-133)/9	179063	Robert Price	09/2021
1867	2^594531+82253	178972	Enzo Doria	09/2016
1868	(664*10^178939-61)/9	178941	Robert Price	09/2021
1869	2^594260-2787899	178891	Enzo Doria	11/2015
1870	(14*10^178822+67)/9	178823	Robert Price	05/2022
1871	(29*10^178732-119)/9	178733	Robert Price	12/2021
1872	2^593631+101381	178701	Jorge Menendez	04/2018
1873	10^178695+136719	178696	Patrick De Geest	05/2016
1874	10^178695-71	178695	Serge Batalov	12/2014
1875	(2*10^178649-161)/3	178649	Robert Price	12/2020
1876	(691^62903-1)/690	178609	Michael Stocker	05/2020
1877	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
1878	2^593222-14145	178578	Jorge Menendez	10/2017
1879	7*10^178566+33	178567	Robert Price	06/2020
1880	2^593178+1867219	178565	Enzo Doria	03/2016
1881	(38*10^178456+151)/9	178457	Robert Price	03/2022
1882	(302*10^178369+13)/9	178371	Robert Price	02/2020
1883	(26*10^178296-113)/3	178297	Robert Price	06/2020
1884	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
1885	(13*10^178233+137)/3	178234	Robert Price	06/2021
1886	(5*10^178206+91)/3	178207	Robert Price	04/2018
1887	2^591872-291929	178172	Enzo Doria	07/2015
1888	2^591682-286871	178115	Enzo Doria	07/2015
1889	4*10^178091+9	178092	Robert Price	05/2015
1890	410747#+478483	178007	Makoto Morimoto	02/2016
1891	3*10^177872+73	177873	Robert Price	08/2018
1892	2^590762-396765	177838	Enzo Doria	08/2013
1893	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
1895	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
1894	Smr(37765)	177719	Eric W. Weisstein	12/2021
1896	(266*10^177577-11)/3	177579	Robert Price	04/2020
1897	(11*10^177466-113)/3	177467	Robert Price	10/2018
1898	3*10^177373-97	177374	Robert Price	07/2018
1899	2^589204+1881151	177369	Enzo Doria	11/2016
1900	2^589132-69479	177347	Enzo Doria	01/2016
1901	(101*10^177302-17)/3	177304	Robert Price	02/2020
1902	2^588912-113519	177281	Enzo Doria	08/2014
1903	(682*10^177266-7)/9	177268	Robert Price	08/2021
1904	15^150706+2	177245	Robert Price	06/2015
1905	2^588194-1861001	177065	Enzo Doria	11/2015
1906	5*10^177016-37	177017	Robert Price	11/2021
1907	(23*10^176964-47)/3	176965	Robert Price	09/2019
1908	20530^41031+41031^20530	176942	Norbert Schneider	07/2022
1909	(19*10^176932+521)/9	176933	Robert Price	05/2018
1910	(8*10^176908+43)/3	176909	Robert Price	06/2018
1911	(85*10^176900+203)/9	176901	Robert Price	09/2020
1912	2^587560-113699	176874	Enzo Doria	09/2014
1913	20596^40995+40995^20596	176844	Norbert Schneider	07/2022
1914	(101*10^176815-17)/3	176817	Robert Price	02/2020
1915	(25*10^176715-37)/3	176716	Robert Price	10/2019
1916	5^252763-12862	176674	Enzo Doria	05/2014
1917	38442^38531+38531^38442	176658	Norbert Schneider	09/2022
1918	2^586804+81721	176646	Enzo Doria	08/2016
1919	(10^176584+77)/3	176584	Robert Price	01/2018
1920	2^586570+1874419	176576	Enzo Doria	06/2016
1921	(157*10^176482-1)/3	176484	Robert Price	01/2022
1922	2^585994-3311	176402	Yves Minet	12/2014
1923	8*10^176383-81	176384	Robert Price	02/2021
1924	(23*10^176357+61)/3	176358	Robert Price	01/2022
1925	2^585832-112799	176354	Enzo Doria	07/2014
1926	(29*10^176240+49)/3	176241	Robert Price	09/2021
1927	(2^585387-11)/3	176219	Stefano Morozzi	08/2022
1928	2^585336-461039	176204	Enzo Doria	06/2015
1929	(25*10^176164+143)/3	176165	Robert Price	08/2020
1930	2^585095-1848127	176132	Enzo Doria	08/2015
1931	(5*10^176101-311)/9	176101	Robert Price	12/2021
1932	6*10^176092+77	176093	Robert Price	06/2020
1933	2^584950-115451	176088	Enzo Doria	07/2015
1934	(646*10^176044+11)/9	176046	Robert Price	10/2021
1935	2^584671-3697	176004	Yves Minet	03/2017
1936	(13*10^175965-37)/3	175966	Robert Price	01/2019
1937	2*10^175860-87	175861	Robert Price	04/2018
1938	(86*10^175774-221)/9	175775	Robert Price	09/2019
1939	9*10^175654+47	175655	Robert Price	01/2022
1940	10^175608+2971	175609	Mike Oakes	05/2010
1941	10^175608-55829	175608	Patrick De Geest	09/2013
1942	2^583051+1879793	175516	Enzo Doria	09/2016
1943	(76*10^175514+491)/9	175515	Robert Price	10/2021
1944	2^582860-23829	175459	Enzo Doria	08/2013
1945	(8*10^175428-53)/9	175428	Serge Batalov	11/2022
1946	(28*10^175417-67)/3	175418	Robert Price	10/2020
1947	2^582670-23913	175402	Enzo Doria	08/2013
1948	2^582573-29563	175372	Enzo Doria	08/2015
1949	2^582435-1862767	175331	Enzo Doria	12/2015
1950	10^175295-40000001	175295	Robert Price	07/2022
1951	(11*10^175250-149)/3	175251	Robert Price	09/2018
1952	(29*10^175236+31)/3	175237	Robert Price	04/2021
1953	2^582072-1848599	175222	Enzo Doria	08/2015
1954	(404267#+465)/(3^45^231)	175208	Makoto Morimoto	06/2019
1955	Phi(262767,10)/259613797	175168	Makoto Kamada	12/2022
1956	(2^581871-15)/7	175160	Stefano Morozzi	08/2022
1957	(5*10^175117-311)/9	175117	Robert Price	12/2021
1958	(220221^32768+1)/2	175075	Serge Batalov	03/2018
1959	2^581560+1874911	175068	Enzo Doria	06/2016
1960	(25*10^174987-97)/9	174988	Robert Price	01/2022
1961	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
1962	(47*10^174790+493)/9	174791	Robert Price	03/2019
1963	2^580528-114035	174757	Enzo Doria	11/2014
1964	(19*10^174754+737)/9	174755	Robert Price	07/2018
1965	(35*10^174704-377)/9	174705	Robert Price	07/2018
1967	(49*10^174681+293)/9	174682	Robert Price	03/2021
1966	6*10^174681+11	174682	Robert Price	07/2022
1968	3*10^174665-97	174666	Robert Price	07/2018
1969	2^580046-459161	174612	Enzo Doria	05/2015
1970	2^579992-39779	174595	Enzo Doria	09/2015
1971	(29*10^174481-149)/3	174482	Robert Price	08/2022
1972	(4*10^174423+101)/3	174424	Robert Price	11/2021
1973	(2^579371-17)/3	174408	Stefano Morozzi	08/2022
1974	(2*10^174301-71)/3	174301	Robert Price	12/2017
1975	14^152048+3	174267	Paul Bourdelais	12/2020
1976	(2^578696+1)/257	174203	Lelio R Paula	09/2015
1977	2^578656-1851809	174193	Enzo Doria	08/2015
1978	2^578583-113917	174171	Enzo Doria	10/2014
1979	2^578434-83	174126	Yves Minet	07/2017
1980	15^148048-2	174118	Robert Price	06/2015
1981	5*10^174101+81	174102	Robert Price	03/2019
1982	2^578346+2794249	174100	Enzo Doria	03/2016
1983	10^173947+1372429	173948	Patrick De Geest	08/2021
1985	10^173947-500000001	173947	Robert Price	12/2020
1984	10^173947-286391	173947	Patrick De Geest	08/2021
1986	5*10^173904-13	173905	Robert Price	01/2019
1987	(8*10^173862-59)/3	173863	Robert Price	08/2021
1988	(71*10^173854-287)/9	173855	Robert Price	09/2019
1989	(43*10^173826+101)/9	173827	Robert Price	11/2018
1990	2*10^173809-87	173810	Robert Price	04/2018
1991	(2^577372-23)/7	173806	Stefano Morozzi	08/2022
1992	(L!41532)/2	173772	Serge Batalov	07/2017
1993	2^577146-49877	173739	Enzo Doria	10/2015
1994	2^576889+49727	173661	Enzo Doria	09/2016
1995	(167*10^173571-17)/3	173573	Robert Price	03/2020
1996	37803^37916+37916^37803	173562	Norbert Schneider	06/2022
1997	5*10^173534+29	173535	Robert Price	12/2020
1998	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
1999	4*10^173509+99	173510	Robert Price	12/2020
2000	(13*10^173467-37)/3	173468	Robert Price	01/2019

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Probable Primes Top 10000

(293016 PRPs in the top)