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	(17*10^157705+67)/3	157706	Robert Price	01/2019
1752	(46^94841+1)/47	157696	Robert Price	01/2014
1753	2^523774+77839	157672	Enzo Doria	05/2016
1754	2^523587+2799143	157616	Enzo Doria	04/2016
1755	2^523371+1872113	157551	Enzo Doria	05/2016
1756	(8*10^157368+49)/3	157369	Robert Price	05/2020
1757	(82*10^157319+449)/9	157320	Robert Price	11/2019
1758	2^522535-351457	157299	Enzo Doria	07/2015
1759	2^522226+2799079	157206	Enzo Doria	04/2016
1760	2^522134-1849451	157178	Enzo Doria	08/2015
1761	9*10^157152+71	157153	Robert Price	08/2020
1762	4*10^157150+93	157151	Robert Price	08/2018
1763	2^521401-29593	156958	Enzo Doria	08/2015
1764	7*10^156956+87	156957	Robert Price	07/2019
1765	2^521348-23397	156942	Enzo Doria	08/2013
1766	10^156902-80000001	156902	Robert Price	04/2021
1767	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
1768	65^86522+64	156857	Lelio R Paula	04/2016
1769	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
1770	2^520977-1858183	156830	Enzo Doria	10/2015
1771	(8*10^156718-101)/3	156719	Robert Price	08/2018
1772	2^520314-1849481	156631	Enzo Doria	08/2015
1773	(13*10^156522+89)/3	156523	Robert Price	09/2018
1774	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
1775	3*10^156435-97	156436	Robert Price	07/2018
1776	(8*10^156371-77)/3	156372	Robert Price	07/2018
1777	53^90679-52^90679	156356	Robert Price	01/2013
1778	2^519106-59141	156267	Enzo Doria	10/2015
1779	2^519053+6077	156251	Enzo Doria	02/2016
1780	2^518968-1860989	156225	Enzo Doria	11/2015
1781	(25*10^156221-7)/9	156222	Robert Price	05/2018
1782	2^518931-2782297	156214	Enzo Doria	09/2015
1783	2^518608-2939	156117	Yves Minet	09/2014
1784	10*27^109005+697	156027	Curtis Bright	05/2015
1785	2^517967-113485	155924	Enzo Doria	08/2014
1786	(103*10^155904+17)/3	155906	Robert Price	08/2020
1787	(8*10^155887-719)/9	155887	Robert Price	03/2021
1788	4*10^155853-39	155854	Robert Price	09/2020
1789	2^517698+4429	155843	Lelio R Paula	01/2013
1790	2^517543-113257	155796	Enzo Doria	07/2014
1791	(14*10^155740-143)/3	155741	Robert Price	11/2018
1792	31^104309-30^104309	155563	Henri Lifchitz	08/2013
1793	2^516742-39851	155555	Enzo Doria	09/2015
1794	(19*10^155504+131)/3	155505	Robert Price	06/2020
1795	7*10^155496+61	155497	Robert Price	08/2019
1796	2^516440+1878421	155464	Enzo Doria	08/2016
1797	2^515863-1867237	155291	Enzo Doria	03/2016
1798	2^515786-461861	155268	Enzo Doria	07/2015
1799	2^515644-113247	155225	Enzo Doria	07/2014
1800	(7*10^155203+107)/3	155204	Robert Price	02/2018
1801	10^155163-40001	155163	Robert Price	01/2021
1802	(17*10^155133-89)/9	155134	Robert Price	07/2018
1803	2^515227-114997	155099	Enzo Doria	06/2015
1805	EPrime(155025)	155025	Eric W. Weisstein	10/2010
1804	(14*10^155024-221)/9	155025	Robert Price	04/2018
1806	(4*10^155022+173)/3	155023	Robert Price	02/2018
1807	(266*10^154897+1)/3	154899	Robert Price	04/2020
1808	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
1809	(86*10^154853-221)/9	154854	Robert Price	09/2019
1810	2^514361+78167	154839	Enzo Doria	05/2016
1811	2^514281-115033	154815	Enzo Doria	06/2015
1812	2^514194-3311	154788	Yves Minet	12/2014
1813	(14*10^154773+37)/3	154774	Robert Price	12/2018
1814	6*10^154742-31	154743	Robert Price	07/2020
1815	5*10^154618-79	154619	Robert Price	03/2021
1816	2^513437+1879337	154560	Enzo Doria	09/2016
1817	2^513306-113201	154521	Enzo Doria	07/2014
1818	(10^154494-13)/3	154494	Robert Price	12/2017
1819	2^513042-113787	154442	Enzo Doria	09/2014
1820	(151*10^154434-7)/9	154436	Robert Price	01/2020
1821	2^512628-114053	154317	Enzo Doria	11/2014
1822	2^512529-49783	154287	Enzo Doria	10/2015
1823	(355573#+6991)/(6991*2031599)	154285	Makoto Morimoto	06/2019
1824	2^512315-115297	154223	Enzo Doria	06/2015
1825	2^512168+79561	154178	Enzo Doria	06/2016
1826	4*10^154078-57	154079	Robert Price	10/2018
1827	(355049#+1859)/(111310148891*62587751)	154051	Makoto Morimoto	06/2019
1828	7*10^154038-57	154039	Robert Price	06/2020
1829	2^511658-114371	154025	Enzo Doria	02/2015
1830	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
1831	2^511580-1846679	154001	Enzo Doria	07/2015
1832	(259*10^153998-1)/3	154000	Robert Price	12/2020
1833	2^511541-113713	153990	Enzo Doria	09/2014
1834	49958^32768+49957^32768	153965	Kellen Shenton	11/2020
1835	10^153935-1000001	153935	Robert Price	08/2020
1836	(16*10^153868-73)/3	153869	Robert Price	07/2020
1837	9*10^153851-67	153852	Robert Price	11/2020
1838	2^511077-112723	153850	Enzo Doria	06/2014
1839	69^83653-68^83653	153826	Robert Price	12/2013
1840	2^510963-113707	153816	Enzo Doria	09/2014
1841	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
1842	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
1843	2*10^153746-3	153747	Robert Price	07/2015
1844	2^510626+1179379	153714	Enzo Doria	05/2016
1845	(7*10^153664+113)/3	153665	Robert Price	02/2018
1846	2^510420+81121	153652	Enzo Doria	07/2016
1847	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
1848	2^509894-459161	153494	Enzo Doria	05/2015
1849	2^509841+71657	153478	Enzo Doria	04/2016
1850	9*10^153446+41	153447	Robert Price	08/2020
1851	2^509533-1846723	153385	Enzo Doria	07/2015
1852	2^509468-39989	153366	Enzo Doria	09/2015
1853	70^83117-69^83117	153360	Robert Price	01/2014
1854	(112*10^153025-1)/3	153027	Serge Batalov	12/2014
1855	(19*10^153010+131)/3	153011	Robert Price	06/2020
1856	2^508174-1855151	152976	Enzo Doria	09/2015
1857	181^67757-2	152974	Lelio R Paula	12/2017
1858	2^508160-1864829	152972	Enzo Doria	01/2016
1859	10^152960-50000000001	152960	Robert Price	12/2020
1860	2^507857-1848199	152881	Enzo Doria	07/2015
1861	2^507638-115361	152815	Enzo Doria	07/2015
1862	2^507551-114025	152789	Enzo Doria	11/2014
1863	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
1864	(22*10^152670-13)/9	152671	Robert Price	06/2018
1865	2^506451-22339	152457	Enzo Doria	07/2013
1866	2^505995-113185	152320	Enzo Doria	07/2014
1867	(4*10^152253+149)/9	152253	Robert Price	04/2018
1868	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
1869	2^505431-505431	152150	Henri Lifchitz	04/2005
1870	(203*10^152143+1)/3	152145	Robert Price	03/2020
1871	2^505053+73097	152037	Enzo Doria	04/2016
1872	22*10^151998+3	152000	Robert Price	01/2020
1873	(238*10^151979-1)/3	151981	Robert Price	04/2020
1874	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
1875	350377#+797581	151937	Nicolas PALAU	08/2017
1876	2^504618-343991	151906	Enzo Doria	07/2015
1877	2^504212-461939	151783	Enzo Doria	07/2015
1878	2^504054-2231	151736	Yves Minet	10/2011
1879	(28*10^151682+191)/3	151683	Robert Price	02/2020
1880	2^503361-39883	151527	Enzo Doria	09/2015
1881	2^503225+382667	151486	Enzo Doria	10/2016
1882	(26*10^151391-503)/9	151392	Robert Price	07/2018
1883	2^502769+1877567	151349	Enzo Doria	08/2016
1884	2^502576-4019	151291	Yves Minet	10/2011
1885	5*10^151257+41	151258	Robert Price	03/2019
1886	2^502290-2792501	151205	Enzo Doria	02/2016
1887	2^502181+1868417	151172	Enzo Doria	04/2016
1888	2^501781-1850503	151052	Enzo Doria	08/2015
1889	(5*10^151007+37)/3	151008	Robert Price	03/2018
1890	2^501627-991	151005	Yves Minet	02/2014
1891	2^501577-115333	150990	Enzo Doria	07/2015
1892	8*10^150975+3	150976	Robert Price	08/2015
1893	2^501512-113669	150971	Enzo Doria	09/2014
1894	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
1895	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
1896	2^500899-500899	150786	Henri Lifchitz	04/2005
1897	2^500832+1876801	150766	Enzo Doria	07/2016
1898	(23*10^150763-59)/9	150764	Robert Price	05/2018
1899	2^500699+1884953	150726	Enzo Doria	02/2017
1900	(13*10^150675-37)/3	150676	Robert Price	01/2019
1901	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
1903	2^500337-71101	150617	Enzo Doria	04/2016
1902	(74*10^150616+133)/9	150617	Robert Price	06/2019
1904	4*10^150577+91	150578	Robert Price	08/2018
1905	2^500160+80071	150564	Enzo Doria	06/2016
1906	(2^500120+5)/9	150551	Lelio R Paula	12/2017
1907	(43*10^150515-421)/9	150516	Robert Price	01/2019
1909	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
1908	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
1910	2^499861-29503	150474	Enzo Doria	08/2015
1911	2^499653-113533	150411	Enzo Doria	08/2014
1912	(14*10^150391-191)/3	150392	Robert Price	10/2020
1913	2^499534-221	150375	Yves Minet	06/2012
1914	2^499225+49727	150282	Enzo Doria	09/2016
1915	2^499054-29261	150231	Enzo Doria	07/2015
1916	(2^498898-7)/9	150183	Lelio R Paula	10/2015
1917	3*10^150182+17	150183	Robert Price	07/2018
1918	5*10^150175+63	150176	Robert Price	09/2020
1919	2^498623+1866983	150101	Enzo Doria	03/2016
1920	(25*10^150050-403)/9	150051	Robert Price	12/2020
1921	numbpart(18140942830)	150033	Serge Batalov	04/2017
1922	10^150029+4381	150030	Patrick De Geest	05/2016
1923	10^150029-41	150029	Serge Batalov	12/2014
1924	10^150000+1158603	150001	Patrick De Geest	09/2018
1925	10^150000-245703	150000	Patrick De Geest	09/2018
1926	(38*10^149999+691)/9	150000	Robert Price	10/2018
1927	2^498238-53	149985	Lelio R Paula	12/2017
1928	45728^1905+1905^45728	149984	Hans Havermann	10/2020
1929	5*10^149907+23	149908	Robert Price	03/2019
1930	39347^6442+6442^39347	149874	Hans Havermann	09/2020
1931	2^497850+81049	149868	Enzo Doria	07/2016
1932	37228^10575+10575^37228	149816	Hans Havermann	10/2020
1933	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
1934	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
1935	(2*10^149803-143)/3	149803	Robert Price	03/2018
1936	33845^26604+26604^33845	149763	Hans Havermann	09/2020
1937	2^497434-2784191	149743	Enzo Doria	10/2015
1938	(865*10^149737-1)/9	149739	Robert Price	04/2020
1939	38237^8214+8214^38237	149681	Hans Havermann	09/2020
1940	(23*10^149655+19)/3	149656	Robert Price	07/2019
1941	2^497068-113579	149633	Enzo Doria	08/2014
1942	2^497037+73727	149624	Enzo Doria	04/2016
1943	34942^19067+19067^34942	149562	Hans Havermann	09/2020
1944	33696^27449+27449^33696	149561	Hans Havermann	09/2020
1945	2^496773+77747	149544	Enzo Doria	05/2016
1946	(206*10^149459+7)/3	149461	Robert Price	07/2020
1947	34589^20940+20940^34589	149459	Hans Havermann	09/2020
1948	2^496477-113485	149455	Enzo Doria	08/2014
1949	((10^74703-1)10000/9+7481)10^74703+(10^74703-1)/9	149410	Hans Havermann	09/2019
1950	2^496270-49451	149393	Enzo Doria	10/2015
1951	2^496238-1865081	149383	Enzo Doria	01/2016
1952	33831^26030+26030^33831	149380	Hans Havermann	09/2020
1953	34131^23780+23780^34131	149365	Hans Havermann	09/2020
1954	(5*10^149335-53)/3	149336	Robert Price	09/2020
1955	2^495968-1853699	149302	Enzo Doria	09/2015
1956	2^495935-4117	149292	Yves Minet	02/2018
1957	35816^14709+14709^35816	149267	Hans Havermann	09/2020
1958	2^495712-396765	149225	Enzo Doria	07/2013
1959	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
1960	2^495420+1880701	149137	Enzo Doria	10/2016
1961	2^495337-1847293	149112	Enzo Doria	07/2015
1962	(2^495193-7)/5	149068	Lelio R Paula	10/2015
1963	33282^30097+30097^33282	149055	Hans Havermann	09/2020
1964	37384^9705+9705^37384	149050	Hans Havermann	09/2020
1965	34808^19143+19143^34808	149049	Hans Havermann	09/2020
1966	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
1967	47^89113-46^89113	149006	Robert Price	10/2012
1968	2^494916+87855	148985	Lelio R Paula	01/2016
1969	6*10^148982+73	148983	Robert Price	04/2019
1970	10^148934+1530019	148935	Patrick De Geest	02/2021
1971	10^148934-1000000001	148934	Robert Price	11/2020
1972	10^148934-512057	148934	Patrick De Geest	02/2021
1973	39000^6571+6571^39000	148888	Hans Havermann	10/2020
1974	2^494586-2791991	148886	Enzo Doria	02/2016
1975	8*10^148860-3	148861	Ray Chandler	04/2011
1976	38262^7769+7769^38262	148854	Hans Havermann	10/2020
1977	2^494333-286183	148810	Enzo Doria	06/2015
1978	2^494144-264119	148753	Enzo Doria	05/2014
1979	36502^11823+11823^36502	148663	Hans Havermann	11/2020
1980	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
1981	64239^206+206^64239	148641	Hans Havermann	10/2020
1982	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
1983	(151*10^148601-1)/3	148603	Robert Price	03/2020
1984	2^493636+82081	148600	Enzo Doria	09/2016
1985	((((((((((((((34251^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	148593	Serge Batalov	07/2016
1986	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
1987	(2*10^148460-23)/3	148460	Robert Price	04/2018
1988	(28*10^148445+101)/3	148446	Robert Price	09/2020
1989	36203^12556+12556^36203	148391	Hans Havermann	10/2020
1990	33912^23749+23749^33912	148387	Hans Havermann	10/2020
1991	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
1992	34294^21117+21117^34294	148309	Hans Havermann	10/2020
1993	(71*10^148306-539)/9	148307	Robert Price	07/2019
1994	38042^7875+7875^38042	148222	Hans Havermann	10/2020
1995	5^211959-12874	148153	Enzo Doria	05/2014
1996	34142^21831+21831^34142	148145	Hans Havermann	10/2020
1997	10^148112-70000001	148112	Robert Price	03/2021
1998	36303^12016+12016^36303	148108	Hans Havermann	10/2020
1999	(16*10^148071+41)/3	148072	Robert Price	03/2019
2000	187^65175-2	148068	Lelio R Paula	11/2017

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Probable Primes Top 10000

(280928 PRPs in the top)