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	4*10^168788-47	168789	Robert Price	10/2021
1752	(29*10^168711+691)/9	168712	Robert Price	08/2021
1753	2^560405-39943	168699	Enzo Doria	09/2015
1754	89*10^168614-7	168616	Robert Price	04/2020
1755	(23*10^168608-83)/3	168609	Robert Price	08/2019
1756	(94*10^168541+11)/3	168543	Robert Price	04/2020
1757	2^559686-350471	168483	Enzo Doria	06/2015
1758	2^559672-1855889	168479	Enzo Doria	09/2015
1759	(5*10^168379-473)/9	168379	Robert Price	01/2018
1760	2^559000-59939	168276	Enzo Doria	11/2015
1761	(16*10^168181+41)/3	168182	Robert Price	03/2019
1762	(19*10^168173+77)/3	168174	Robert Price	05/2019
1763	2^558640-114149	168168	Enzo Doria	12/2014
1764	2^558498-1849277	168125	Enzo Doria	08/2015
1765	2^558476-1850249	168119	Enzo Doria	08/2015
1766	(7*10^168067+71)/3	168068	Robert Price	05/2018
1767	2^558150-1852211	168020	Enzo Doria	08/2015
1768	2^558125-113661	168013	Enzo Doria	09/2014
1769	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
1770	(13*10^167911+179)/3	167912	Robert Price	11/2018
1771	(26*10^167861-167)/3	167862	Robert Price	10/2019
1772	39^105456+2	167788	Robert Price	04/2015
1773	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
1774	10^167639+121911	167640	Patrick De Geest	07/2018
1775	10^167639-8001	167639	Robert Price	03/2018
1776	2^556504-462059	167525	Enzo Doria	07/2015
1777	(88*10^167522-637)/9	167523	Robert Price	11/2020
1778	5*10^167510+9	167511	Robert Price	08/2015
1779	7*10^167437-93	167438	Robert Price	08/2020
1780	11^160663+6	167314	Paul Bourdelais	02/2021
1781	(7*10^167308-493)/9	167308	Robert Price	04/2021
1782	2^555343+1874333	167175	Enzo Doria	06/2016
1783	2^555210-461261	167135	Enzo Doria	07/2015
1784	9*10^166996+59	166997	Robert Price	01/2020
1785	(68*10^166976-329)/9	166977	Robert Price	03/2021
1786	2^554372+1880527	166883	Enzo Doria	11/2016
1787	2^554299+72173	166861	Enzo Doria	04/2016
1788	(185*10^166837+7)/3	166839	Robert Price	03/2020
1789	(14*10^166813+139)/9	166814	Robert Price	11/2021
1790	2^554037-2797063	166782	Enzo Doria	03/2016
1791	(49*10^166721-139)/9	166722	Robert Price	03/2019
1792	2*10^166646+69	166647	Robert Price	06/2020
1793	2^553484-29819	166616	Enzo Doria	08/2015
1794	(188*10^166611+7)/3	166613	Robert Price	03/2020
1795	2^553383-2784217	166585	Enzo Doria	10/2015
1796	2^553069+76427	166491	Enzo Doria	05/2016
1797	2*10^166458+51	166459	Robert Price	05/2018
1798	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
1799	11^159756-2424	166369	Mike Oakes	06/2010
1800	2^552649-361275	166364	Enzo Doria	05/2014
1801	2^552628-113669	166358	Enzo Doria	09/2014
1802	10^166324+550603	166325	Patrick De Geest	07/2018
1803	10^166324-801	166324	Robert Price	02/2018
1804	(85*10^166297-1)/3	166299	Robert Price	02/2020
1805	8*10^166227+87	166228	Robert Price	10/2019
1806	2^552137+1879397	166210	Enzo Doria	09/2016
1807	(103*10^166126+11)/3	166128	Robert Price	01/2021
1808	(23^121949-1)/22	166061	Paul Bourdelais	10/2017
1809	2^551542+19249	166031	Payam Samidoost	08/2002
1810	2^551535-23821	166029	Enzo Doria	08/2013
1811	2^551507-23557	166021	Enzo Doria	08/2013
1812	10^165947-7000000001	165947	Robert Price	12/2021
1813	4*10^165938-47	165939	Robert Price	10/2021
1814	7*10^165916-3	165917	Robert Price	08/2015
1815	(29*10^165796+67)/3	165797	Robert Price	12/2019
1816	81^86837-80^86837	165728	Robert Price	01/2015
1817	(71*10^165663-539)/9	165664	Robert Price	07/2019
1818	2^550270-69551	165648	Enzo Doria	12/2015
1819	(202*10^165569-13)/9	165571	Robert Price	01/2020
1820	2^550000-23625	165567	Enzo Doria	08/2013
1821	2^549675-1852057	165469	Enzo Doria	08/2015
1822	(529*10^165394-7)/9	165396	Robert Price	08/2021
1823	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
1824	(28*10^165358-1)/9	165359	Serge Batalov	10/2014
1825	2^549278+1879669	165350	Enzo Doria	09/2016
1826	(7*10^165350-439)/9	165350	Robert Price	02/2018
1827	2^549252-351269	165342	Enzo Doria	06/2015
1828	67*10^165327-9	165329	Robert Price	03/2021
1829	(14*10^165282+73)/3	165283	Robert Price	12/2018
1830	2^549049+2797607	165281	Enzo Doria	04/2016
1831	(7*10^165239+107)/3	165240	Robert Price	02/2018
1832	(44^100511-1)/43	165184	Paul Bourdelais	11/2017
1833	(7*10^165134+107)/3	165135	Robert Price	02/2018
1834	(301*10^165082+23)/9	165084	Robert Price	06/2021
1835	(23*10^165060-83)/3	165061	Robert Price	08/2019
1836	(76*10^164984+77)/9	164985	Robert Price	10/2019
1837	9*10^164791-89	164792	Robert Price	04/2020
1838	2^547178-1856501	164717	Enzo Doria	10/2015
1839	11^158160-60	164707	Enzo Doria	07/2012
1840	(26*10^164643-167)/3	164644	Robert Price	10/2019
1841	(10^164643+83)/3	164643	Robert Price	08/2021
1842	2^546398-59201	164483	Enzo Doria	10/2015
1843	2^546332-114893	164463	Enzo Doria	05/2015
1844	(65*10^164427+277)/9	164428	Robert Price	08/2021
1845	2^545958+1876189	164350	Enzo Doria	07/2016
1846	2^545878-49841	164326	Enzo Doria	10/2015
1847	(10^164284+77)/3	164284	Robert Price	01/2018
1848	2^545668-4019	164263	Yves Minet	04/2017
1849	10^164216+780639	164217	Patrick De Geest	08/2021
1851	10^164216-50000000001	164216	Robert Price	12/2020
1850	10^164216-891051	164216	Patrick De Geest	08/2021
1852	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
1853	(16*10^164122+197)/3	164123	Robert Price	04/2019
1854	2^545185+76757	164118	Enzo Doria	05/2016
1855	2^545076-114329	164085	Enzo Doria	01/2015
1856	(2*10^164043-143)/3	164043	Robert Price	03/2018
1857	(29^112153+1)/30	164011	Lelio R Paula	03/2017
1858	2^544757+1874777	163989	Enzo Doria	06/2016
1859	2^544444-457199	163894	Enzo Doria	01/2015
1860	2^544264-343529	163840	Enzo Doria	07/2015
1861	7*10^163780+9	163781	Robert Price	09/2015
1862	2^543989+2793047	163758	Enzo Doria	02/2016
1863	(28*10^163709+113)/3	163710	Robert Price	03/2020
1864	(23*10^163523+301)/9	163524	Robert Price	06/2021
1865	(68*10^163521-329)/9	163522	Robert Price	03/2021
1866	35820^35899+35899^35820	163489	Norbert Schneider	11/2021
1867	2^542870-69551	163421	Enzo Doria	12/2015
1868	2^542395+72533	163278	Enzo Doria	04/2016
1869	2^542072-3683	163180	Yves Minet	03/2017
1870	(682*10^163106-7)/9	163108	Robert Price	08/2021
1871	2^541779-1867357	163092	Enzo Doria	04/2016
1872	(29*10^163056+313)/9	163057	Robert Price	04/2021
1873	8*10^162924+9	162925	Robert Price	12/2015
1874	2^540905+81557	162829	Enzo Doria	08/2016
1875	2^540628-2939	162746	Yves Minet	09/2014
1876	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
1877	(203*10^162689+1)/3	162691	Robert Price	03/2020
1878	3*10^162620-59	162621	Robert Price	09/2018
1879	3^340694-112960	162553	Enzo Doria	07/2014
1880	2^539807-114081	162499	Enzo Doria	12/2014
1881	2^539654-114893	162453	Enzo Doria	05/2015
1882	9*10^162449-71	162450	Robert Price	11/2020
1883	2^539617-1851583	162441	Enzo Doria	08/2015
1884	(91*10^162410+11)/3	162412	Robert Price	02/2020
1885	2^539346+81049	162360	Enzo Doria	07/2016
1886	2^539220-115499	162322	Enzo Doria	07/2015
1887	2^539217-113713	162321	Enzo Doria	09/2014
1888	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
1889	4*10^162263-39	162264	Robert Price	09/2020
1890	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
1891	(10^162138+11)/3	162138	Serge Batalov	07/2015
1892	(61*10^162100-403)/9	162101	Robert Price	10/2021
1893	2^538473-112723	162097	Enzo Doria	06/2014
1894	2^538157+79337	162002	Enzo Doria	06/2016
1895	2^538136-114749	161996	Enzo Doria	05/2015
1896	2^538104+1531	161986	Lelio R Paula	01/2013
1897	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
1898	2^537815-22737	161899	Enzo Doria	07/2013
1899	2^537804-39839	161896	Enzo Doria	09/2015
1900	(754*10^161816-7)/9	161818	Robert Price	05/2020
1901	2^537458-59201	161791	Enzo Doria	10/2015
1902	2*10^161766+51	161767	Robert Price	05/2018
1903	(7*10^161760+131)/3	161761	Robert Price	06/2020
1904	2^537209-49849	161717	Enzo Doria	10/2015
1905	(58*10^161691+329)/9	161692	Robert Price	05/2019
1906	23*10^161668-3	161670	Robert Price	10/2021
1907	2^536937+1879397	161635	Enzo Doria	09/2016
1908	34*10^161593-9	161595	Robert Price	06/2020
1909	(31*10^161582-1)/3	161584	Robert Price	02/2020
1910	2^536569-22881	161524	Enzo Doria	07/2013
1911	10^161253+573493	161254	Patrick De Geest	07/2018
1912	10^161253-8001	161253	Robert Price	03/2018
1913	97*10^161247-3	161249	Robert Price	05/2020
1914	7*10^161192-9	161193	Robert Price	10/2015
1915	2^535269-113803	161133	Enzo Doria	09/2014
1916	2^535205-23295	161113	Enzo Doria	08/2013
1917	(49*10^161105+437)/9	161106	Robert Price	09/2021
1918	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
1919	2^534359-23229	160859	Enzo Doria	08/2013
1920	457^60454+60454^457	160803	Norbert Schneider	07/2021
1921	8*10^160782+53	160783	Robert Price	08/2020
1922	67^88037-66^88037	160763	Robert Price	10/2013
1923	(88*10^160761-637)/9	160762	Robert Price	11/2020
1924	2^533948-1852559	160735	Enzo Doria	08/2015
1925	2^533665-23335	160650	Enzo Doria	08/2013
1926	(19*10^160619+77)/3	160620	Robert Price	05/2019
1927	3^336353-2^336353	160482	Mike Oakes	10/2007
1928	2*10^160339-63	160340	Robert Price	01/2022
1929	(91*10^160249+11)/3	160251	Robert Price	02/2020
1930	2^532253+1868417	160225	Enzo Doria	04/2016
1931	2^532108-291989	160181	Enzo Doria	07/2015
1932	(28*10^160171-79)/3	160172	Robert Price	02/2021
1933	(26*10^160166-131)/3	160167	Robert Price	10/2019
1934	(17*10^160143+67)/3	160144	Robert Price	01/2019
1935	(19*10^159921-49)/3	159922	Robert Price	05/2019
1936	2^531110-1853771	159881	Enzo Doria	09/2015
1937	(275^65536+53^65536)/2	159864	Kellen Shenton	11/2020
1938	2^530992-1845299	159845	Enzo Doria	07/2015
1939	2^530810+25	159790	Stefano Morozzi	04/2021
1940	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
1941	2^530417-113833	159672	Enzo Doria	09/2014
1942	2^530406-69701	159669	Enzo Doria	02/2016
1943	5*10^159656+41	159657	Robert Price	03/2019
1944	8*10^159614+29	159615	Robert Price	11/2021
1945	7^188858-188858^7	159604	Norbert Schneider	05/2018
1946	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
1947	(17*10^159438-377)/9	159439	Robert Price	03/2018
1948	(203*10^159381+1)/3	159383	Robert Price	03/2020
1949	89*10^159258-9	159260	Robert Price	05/2020
1950	2^528944-461315	159229	Enzo Doria	07/2015
1951	(13*10^159147+161)/3	159148	Robert Price	11/2018
1952	2^528620-113879	159131	Enzo Doria	10/2014
1953	2^528000-23307	158944	Enzo Doria	08/2013
1954	(29*10^158909+61)/9	158910	Robert Price	08/2018
1955	2^527817+1876817	158889	Enzo Doria	07/2016
1956	2^527774-49451	158876	Enzo Doria	10/2015
1957	2^527745-291553	158868	Enzo Doria	07/2015
1958	(91*10^158862+11)/3	158864	Robert Price	02/2020
1959	2^527644-1856999	158837	Enzo Doria	10/2015
1960	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
1961	2^527573-1863253	158816	Enzo Doria	12/2015
1962	2^527553-23401	158810	Enzo Doria	08/2013
1963	(49*10^158783+437)/9	158784	Robert Price	09/2021
1964	10^158755+310207	158756	Patrick De Geest	08/2021
1965	10^158755-50001	158755	Robert Price	08/2020
1966	11^152420-210	158730	Enzo Doria	09/2012
1967	(13*10^158694+401)/9	158695	Robert Price	01/2018
1968	2^527052-69059	158659	Enzo Doria	11/2015
1969	2^526849-113233	158598	Enzo Doria	07/2014
1970	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016
1971	(299*10^158544-17)/3	158546	Robert Price	04/2020
1972	2^526658-3551	158540	Yves Minet	03/2017
1973	7*10^158465-11	158466	Robert Price	06/2019
1974	2^526375-23115	158455	Enzo Doria	08/2013
1975	(77*10^158407-293)/9	158408	Robert Price	09/2019
1976	2^526028-112793	158351	Enzo Doria	07/2014
1977	(229*10^158339-1)/3	158341	Robert Price	07/2020
1978	2^525690-9221	158249	Lelio R Paula	01/2013
1979	2*10^158242-7	158243	Robert Price	10/2015
1980	2^525667-525667^2	158242	Henri Lifchitz	12/2017
1981	(56*10^158230+187)/9	158231	Robert Price	10/2021
1982	10^158209-7000000001	158209	Robert Price	12/2021
1983	2^525186-1857431	158097	Enzo Doria	10/2015
1984	2^524515-23245	157895	Enzo Doria	08/2013
1985	2^524499-109087	157890	Enzo Doria	04/2014
1986	2^18067*(2^506221+1)-1	157827	Makoto Morimoto	05/2014
1987	2^524288+189093	157827	Makoto Morimoto	01/2016
1988	2^524288-164073	157827	Matthias Baur	03/2020
1989	(2^(2^19)-9333)/(1923463121331973)	157814	Makoto Morimoto	09/2017
1990	(10^157792+359)/9	157792	Serge Batalov	12/2014
1991	2^524154+25	157787	Stefano Morozzi	04/2021
1992	2^523924+1876591	157717	Enzo Doria	07/2016
1993	(17*10^157705+67)/3	157706	Robert Price	01/2019
1994	(46^94841+1)/47	157696	Robert Price	01/2014
1995	2^523774+77839	157672	Enzo Doria	05/2016
1996	2^523587+2799143	157616	Enzo Doria	04/2016
1997	2^523371+1872113	157551	Enzo Doria	05/2016
1998	8*10^157477+27	157478	Robert Price	09/2021
1999	(8*10^157368+49)/3	157369	Robert Price	05/2020
2000	(82*10^157319+449)/9	157320	Robert Price	11/2019

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PRP Records

Probable Primes Top 10000

(288949 PRPs in the top)