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	(29*10^175236+31)/3	175237	Robert Price	04/2021
1752	2^582072-1848599	175222	Enzo Doria	08/2015
1753	(404267#+465)/(3^45^231)	175208	Makoto Morimoto	06/2019
1754	(2^581871-15)/7	175160	Stefano Morozzi	08/2022
1755	(5*10^175117-311)/9	175117	Robert Price	12/2021
1756	(220221^32768+1)/2	175075	Serge Batalov	03/2018
1757	2^581560+1874911	175068	Enzo Doria	06/2016
1758	(25*10^174987-97)/9	174988	Robert Price	01/2022
1759	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
1760	(47*10^174790+493)/9	174791	Robert Price	03/2019
1761	2^580528-114035	174757	Enzo Doria	11/2014
1762	(19*10^174754+737)/9	174755	Robert Price	07/2018
1763	(35*10^174704-377)/9	174705	Robert Price	07/2018
1764	(49*10^174681+293)/9	174682	Robert Price	03/2021
1765	6*10^174681+11	174682	Robert Price	07/2022
1766	3*10^174665-97	174666	Robert Price	07/2018
1767	2^580046-459161	174612	Enzo Doria	05/2015
1768	2^579992-39779	174595	Enzo Doria	09/2015
1769	(29*10^174481-149)/3	174482	Robert Price	08/2022
1770	(4*10^174423+101)/3	174424	Robert Price	11/2021
1771	(2^579371-17)/3	174408	Stefano Morozzi	08/2022
1772	(2*10^174301-71)/3	174301	Robert Price	12/2017
1773	14^152048+3	174267	Paul Bourdelais	12/2020
1774	(2^578696+1)/257	174203	Lelio R Paula	09/2015
1775	2^578656-1851809	174193	Enzo Doria	08/2015
1776	2^578583-113917	174171	Enzo Doria	10/2014
1777	2^578434-83	174126	Yves Minet	07/2017
1778	15^148048-2	174118	Robert Price	06/2015
1779	5*10^174101+81	174102	Robert Price	03/2019
1780	2^578346+2794249	174100	Enzo Doria	03/2016
1781	10^173947+1372429	173948	Patrick De Geest	08/2021
1783	10^173947-500000001	173947	Robert Price	12/2020
1782	10^173947-286391	173947	Patrick De Geest	08/2021
1784	5*10^173904-13	173905	Robert Price	01/2019
1785	(8*10^173862-59)/3	173863	Robert Price	08/2021
1786	(71*10^173854-287)/9	173855	Robert Price	09/2019
1787	(43*10^173826+101)/9	173827	Robert Price	11/2018
1788	2*10^173809-87	173810	Robert Price	04/2018
1789	(2^577372-23)/7	173806	Stefano Morozzi	08/2022
1790	(L!41532)/2	173772	Serge Batalov	07/2017
1791	2^577146-49877	173739	Enzo Doria	10/2015
1792	2^576889+49727	173661	Enzo Doria	09/2016
1793	(167*10^173571-17)/3	173573	Robert Price	03/2020
1794	37803^37916+37916^37803	173562	Norbert Schneider	06/2022
1795	5*10^173534+29	173535	Robert Price	12/2020
1796	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
1797	4*10^173509+99	173510	Robert Price	12/2020
1798	(13*10^173467-37)/3	173468	Robert Price	01/2019
1799	2^576016-113919	173399	Enzo Doria	11/2014
1800	2^575911-1849387	173367	Enzo Doria	08/2015
1801	2^575614+9	173278	Stefano Morozzi	04/2021
1802	(16*10^173251+107)/3	173252	Robert Price	03/2019
1803	2^575196-114053	173152	Enzo Doria	11/2014
1804	7*10^173135-53	173136	Robert Price	06/2020
1805	(301*10^173047+23)/9	173049	Robert Price	06/2021
1806	2^574591-115387	172970	Enzo Doria	07/2015
1807	(202*10^172940-13)/9	172942	Robert Price	01/2020
1808	45^104608+104608^45	172940	Norbert Schneider	06/2021
1809	2^574328+81121	172890	Enzo Doria	07/2016
1810	(115*10^172862-1)/3	172864	Serge Batalov	12/2014
1811	3*10^172812+13	172813	Robert Price	07/2018
1812	4*5^247217-9	172798	Lelio R Paula	10/2015
1813	6*10^172772-31	172773	Robert Price	07/2020
1814	69061#+(467617#)/(69061#)	172766	Makoto Morimoto	10/2017
1815	(34*10^172693-547)/9	172694	Robert Price	03/2021
1816	5*10^172692+57	172693	Robert Price	12/2018
1817	2^573668-2782319	172692	Enzo Doria	09/2015
1818	2^573444-1855109	172624	Enzo Doria	09/2015
1819	(14*10^172532-29)/3	172533	Robert Price	09/2021
1820	3^361608+2	172531	Robert Price	08/2014
1821	(54^99563+1)/55	172481	Paul Bourdelais	11/2017
1822	2^572592-114893	172368	Enzo Doria	05/2015
1823	4*10^172354-39	172355	Robert Price	09/2020
1824	37535^37674+37674^37535	172338	Norbert Schneider	05/2022
1825	(11*10^172322-119)/9	172323	Robert Price	11/2021
1826	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
1827	(38^109037-1)/37	172254	Paul Bourdelais	10/2017
1828	(4*10^172241+89)/3	172242	Robert Price	08/2021
1829	3*10^172219+73	172220	Robert Price	08/2018
1830	A352736(15)	172032	Kellen Shenton	05/2022
1831	(36^110503+1)/37	171975	Lelio R Paula	04/2017
1832	8*10^171934+71	171935	Robert Price	05/2022
1833	(11*10^171933+601)/9	171934	Robert Price	02/2022
1834	(22*10^171929-73)/3	171930	Robert Price	04/2019
1835	(49*10^171892-319)/9	171893	Robert Price	10/2021
1836	4*10^171891-63	171892	Robert Price	10/2018
1837	67*10^171882-9	171884	Robert Price	03/2021
1838	2^570980-2782289	171883	Enzo Doria	09/2015
1839	(25*10^171849-37)/3	171850	Robert Price	10/2019
1840	10^171832+387909	171833	Patrick De Geest	08/2021
1841	10^171832-10001	171832	Robert Price	02/2021
1843	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
1842	(2^570769-9)/7	171818	Stefano Morozzi	08/2022
1844	(74*10^171651-29)/9	171652	Robert Price	06/2022
1845	(536*10^171601-23)/9	171603	Robert Price	02/2020
1846	7*10^171535-99	171536	Robert Price	06/2019
1847	(28*10^171534+101)/3	171535	Robert Price	09/2020
1848	2^569563-1854607	171456	Enzo Doria	09/2015
1849	3*10^171391+59	171392	Robert Price	08/2018
1850	(13*10^171306-37)/3	171307	Robert Price	01/2019
1851	8*10^171296+87	171297	Robert Price	10/2019
1852	(55^98419-1)/54	171284	Paul Bourdelais	12/2017
1853	(29*10^171275+67)/3	171276	Robert Price	12/2019
1854	(457*10^171248-7)/9	171250	Robert Price	09/2022
1855	(194*10^171193+1)/3	171195	Robert Price	01/2022
1856	2^568642+1876129	171179	Enzo Doria	07/2016
1857	4*10^171146-47	171147	Robert Price	10/2021
1858	(19*10^170970+131)/3	170971	Robert Price	06/2020
1859	(46*10^170932+143)/9	170933	Robert Price	01/2019
1860	(79*10^170901-1)/3	170903	Robert Price	02/2020
1861	(58*10^170842+221)/9	170843	Robert Price	02/2017
1862	(29*10^170830+583)/9	170831	Robert Price	06/2021
1863	3*10^170800+73	170801	Robert Price	08/2018
1864	(29*10^170799-119)/9	170800	Robert Price	12/2021
1865	11^164009-270	170798	Enzo Doria	10/2012
1866	2*10^170767+41	170768	Robert Price	05/2018
1867	3^357706-112358	170670	Enzo Doria	07/2014
1868	TheodorusPrime(170657)	170657	Eric W. Weisstein	08/2013
1869	2^566871+1876163	170646	Enzo Doria	07/2016
1870	(10657#+(404267#)/(10657#))/(1675379)	170624	Makoto Morimoto	10/2017
1871	2^566496+7	170533	Donovan Johnson	07/2006
1872	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
1873	7*10^170348+33	170349	Robert Price	06/2020
1874	2^565183-352021	170138	Enzo Doria	07/2015
1875	2^565143-114457	170125	Enzo Doria	02/2015
1876	2^564976-49869	170075	Enzo Doria	10/2015
1877	(7*10^169944+23)/3	169945	Robert Price	06/2020
1878	(37*10^169943+251)/9	169944	Robert Price	09/2021
1879	2^564526-351401	169940	Enzo Doria	07/2015
1880	4*10^169759+19	169760	Robert Price	10/2018
1881	(2^563903-13)/5	169752	Stefano Morozzi	08/2022
1882	21^128327-20^128327	169677	Jean-Louis Charton	11/2014
1883	2^563583+89	169656	Stefano Morozzi	04/2021
1884	(4*10^169559+83)/3	169560	Robert Price	02/2018
1885	(194*10^169461-17)/3	169463	Robert Price	09/2020
1886	2^562749+2793047	169405	Enzo Doria	02/2016
1887	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
1888	(109*10^169337+11)/3	169339	Robert Price	06/2022
1889	(56*10^169311+691)/9	169312	Robert Price	05/2019
1890	2^562369-29503	169290	Enzo Doria	08/2015
1891	(17*10^169283+19)/9	169284	Robert Price	03/2021
1892	10^169074-5000000001	169074	Robert Price	09/2022
1893	8*10^169071+59	169072	Robert Price	11/2021
1894	(10^169044+173)/3	169044	Robert Price	05/2021
1895	(22*10^169019+383)/9	169020	Robert Price	05/2018
1896	(64*10^168935+143)/9	168936	Robert Price	05/2021
1897	(22*10^168906+47)/3	168907	Robert Price	06/2021
1898	5*10^168807+87	168808	Robert Price	02/2019
1899	(77*10^168803-149)/9	168804	Robert Price	03/2022
1900	4*10^168788-47	168789	Robert Price	10/2021
1901	(154*10^168781+17)/9	168783	Robert Price	06/2022
1902	(418*10^168751-31)/9	168753	Robert Price	05/2022
1903	(29*10^168711+691)/9	168712	Robert Price	08/2021
1904	2^560405-39943	168699	Enzo Doria	09/2015
1905	(397*10^168634+17)/9	168636	Robert Price	03/2022
1906	89*10^168614-7	168616	Robert Price	04/2020
1907	(23*10^168608-83)/3	168609	Robert Price	08/2019
1908	(94*10^168541+11)/3	168543	Robert Price	04/2020
1909	2^559686-350471	168483	Enzo Doria	06/2015
1910	2^559672-1855889	168479	Enzo Doria	09/2015
1911	(5*10^168379-473)/9	168379	Robert Price	01/2018
1912	2^559000-59939	168276	Enzo Doria	11/2015
1913	(16*10^168181+41)/3	168182	Robert Price	03/2019
1914	(19*10^168173+77)/3	168174	Robert Price	05/2019
1915	(74*10^168170+529)/9	168171	Robert Price	02/2022
1916	2^558640-114149	168168	Enzo Doria	12/2014
1917	2^558498-1849277	168125	Enzo Doria	08/2015
1918	2^558476-1850249	168119	Enzo Doria	08/2015
1919	(7*10^168067+71)/3	168068	Robert Price	05/2018
1920	2^558150-1852211	168020	Enzo Doria	08/2015
1921	2^558125-113661	168013	Enzo Doria	09/2014
1922	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
1923	(13*10^167911+179)/3	167912	Robert Price	11/2018
1924	(26*10^167861-167)/3	167862	Robert Price	10/2019
1925	39^105456+2	167788	Robert Price	04/2015
1926	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
1927	6*10^167662-13	167663	Robert Price	07/2022
1928	10^167639+121911	167640	Patrick De Geest	07/2018
1929	10^167639-8001	167639	Robert Price	03/2018
1930	2^556504-462059	167525	Enzo Doria	07/2015
1931	(88*10^167522-637)/9	167523	Robert Price	11/2020
1932	5*10^167510+9	167511	Robert Price	08/2015
1933	7*10^167437-93	167438	Robert Price	08/2020
1934	11^160663+6	167314	Paul Bourdelais	02/2021
1935	(7*10^167308-493)/9	167308	Robert Price	04/2021
1936	2^555343+1874333	167175	Enzo Doria	06/2016
1937	2^555210-461261	167135	Enzo Doria	07/2015
1938	9*10^166996+59	166997	Robert Price	01/2020
1939	(68*10^166976-329)/9	166977	Robert Price	03/2021
1940	(64*10^166901+683)/9	166902	Robert Price	06/2022
1941	2^554372+1880527	166883	Enzo Doria	11/2016
1942	2^554299+72173	166861	Enzo Doria	04/2016
1943	(185*10^166837+7)/3	166839	Robert Price	03/2020
1944	(14*10^166813+139)/9	166814	Robert Price	11/2021
1945	2^554037-2797063	166782	Enzo Doria	03/2016
1946	(49*10^166721-139)/9	166722	Robert Price	03/2019
1947	2*10^166646+69	166647	Robert Price	06/2020
1948	2^553484-29819	166616	Enzo Doria	08/2015
1949	(188*10^166611+7)/3	166613	Robert Price	03/2020
1950	2^553383-2784217	166585	Enzo Doria	10/2015
1951	2^553069+76427	166491	Enzo Doria	05/2016
1952	2*10^166458+51	166459	Robert Price	05/2018
1953	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
1954	11^159756-2424	166369	Mike Oakes	06/2010
1955	2^552649-361275	166364	Enzo Doria	05/2014
1956	2^552628-113669	166358	Enzo Doria	09/2014
1957	(19*10^166325+137)/3	166326	Robert Price	03/2022
1958	10^166324+550603	166325	Patrick De Geest	07/2018
1959	10^166324-801	166324	Robert Price	02/2018
1960	(85*10^166297-1)/3	166299	Robert Price	02/2020
1961	8*10^166227+87	166228	Robert Price	10/2019
1962	2^552137+1879397	166210	Enzo Doria	09/2016
1963	(103*10^166126+11)/3	166128	Robert Price	01/2021
1964	(22*10^166077+179)/3	166078	Robert Price	02/2022
1965	(23^121949-1)/22	166061	Paul Bourdelais	10/2017
1966	2^551542+19249	166031	Payam Samidoost	08/2002
1967	2^551535-23821	166029	Enzo Doria	08/2013
1968	2^551507-23557	166021	Enzo Doria	08/2013
1969	10^165947-7000000001	165947	Robert Price	12/2021
1970	4*10^165938-47	165939	Robert Price	10/2021
1971	7*10^165916-3	165917	Robert Price	08/2015
1972	(29*10^165796+67)/3	165797	Robert Price	12/2019
1973	81^86837-80^86837	165728	Robert Price	01/2015
1974	(71*10^165663-539)/9	165664	Robert Price	07/2019
1975	2^550270-69551	165648	Enzo Doria	12/2015
1976	(202*10^165569-13)/9	165571	Robert Price	01/2020
1977	2^550000-23625	165567	Enzo Doria	08/2013
1978	2^549675-1852057	165469	Enzo Doria	08/2015
1979	(529*10^165394-7)/9	165396	Robert Price	08/2021
1980	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
1981	(28*10^165358-1)/9	165359	Serge Batalov	10/2014
1982	2^549278+1879669	165350	Enzo Doria	09/2016
1983	(7*10^165350-439)/9	165350	Robert Price	02/2018
1984	2^549252-351269	165342	Enzo Doria	06/2015
1985	67*10^165327-9	165329	Robert Price	03/2021
1987	(14*10^165282+73)/3	165283	Robert Price	12/2018
1986	(8*10^165283-629)/9	165283	Robert Price	01/2022
1988	2^549049+2797607	165281	Enzo Doria	04/2016
1989	(218*10^165258+7)/9	165260	Robert Price	06/2022
1990	(7*10^165239+107)/3	165240	Robert Price	02/2018
1991	(44^100511-1)/43	165184	Paul Bourdelais	11/2017
1992	(7*10^165134+107)/3	165135	Robert Price	02/2018
1993	(301*10^165082+23)/9	165084	Robert Price	06/2021
1994	(23*10^165060-83)/3	165061	Robert Price	08/2019
1995	(76*10^164984+77)/9	164985	Robert Price	10/2019
1996	(4*10^164929-211)/9	164929	Robert Price	03/2022
1997	10^164878-500001	164878	Robert Price	03/2022
1998	9*10^164791-89	164792	Robert Price	04/2020
1999	2^547178-1856501	164717	Enzo Doria	10/2015
2000	11^158160-60	164707	Enzo Doria	07/2012

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Probable Primes Top 10000

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