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	350377#+797581	151937	Nicolas PALAU	08/2017
1752	2^504618-343991	151906	Enzo Doria	07/2015
1753	2^504212-461939	151783	Enzo Doria	07/2015
1754	2^504054-2231	151736	Yves Minet	10/2011
1755	(28*10^151682+191)/3	151683	Robert Price	02/2020
1756	2^503361-39883	151527	Enzo Doria	09/2015
1757	2^503225+382667	151486	Enzo Doria	10/2016
1758	(26*10^151391-503)/9	151392	Robert Price	07/2018
1759	2^502769+1877567	151349	Enzo Doria	08/2016
1760	2^502576-4019	151291	Yves Minet	10/2011
1761	5*10^151257+41	151258	Robert Price	03/2019
1762	2^502290-2792501	151205	Enzo Doria	02/2016
1763	2^502181+1868417	151172	Enzo Doria	04/2016
1764	2^501781-1850503	151052	Enzo Doria	08/2015
1765	(5*10^151007+37)/3	151008	Robert Price	03/2018
1766	2^501627-991	151005	Yves Minet	02/2014
1767	2^501577-115333	150990	Enzo Doria	07/2015
1768	8*10^150975+3	150976	Robert Price	08/2015
1769	2^501512-113669	150971	Enzo Doria	09/2014
1770	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
1771	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
1772	2^500899-500899	150786	Henri Lifchitz	04/2005
1773	2^500832+1876801	150766	Enzo Doria	07/2016
1774	(23*10^150763-59)/9	150764	Robert Price	05/2018
1775	2^500699+1884953	150726	Enzo Doria	02/2017
1776	(13*10^150675-37)/3	150676	Robert Price	01/2019
1777	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
1779	2^500337-71101	150617	Enzo Doria	04/2016
1778	(74*10^150616+133)/9	150617	Robert Price	06/2019
1780	4*10^150577+91	150578	Robert Price	08/2018
1781	2^500160+80071	150564	Enzo Doria	06/2016
1782	(2^500120+5)/9	150551	Lelio R Paula	12/2017
1783	(43*10^150515-421)/9	150516	Robert Price	01/2019
1785	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
1784	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
1786	2^499861-29503	150474	Enzo Doria	08/2015
1787	2^499653-113533	150411	Enzo Doria	08/2014
1788	2^499534-221	150375	Yves Minet	06/2012
1789	2^499225+49727	150282	Enzo Doria	09/2016
1790	2^499054-29261	150231	Enzo Doria	07/2015
1791	(2^498898-7)/9	150183	Lelio R Paula	10/2015
1792	3*10^150182+17	150183	Robert Price	07/2018
1793	5*10^150175+63	150176	Robert Price	09/2020
1794	2^498623+1866983	150101	Enzo Doria	03/2016
1795	numbpart(18140942830)	150033	Serge Batalov	04/2017
1796	10^150029+4381	150030	Patrick De Geest	05/2016
1797	10^150029-41	150029	Serge Batalov	12/2014
1798	10^150000+1158603	150001	Patrick De Geest	09/2018
1799	10^150000-245703	150000	Patrick De Geest	09/2018
1800	(38*10^149999+691)/9	150000	Robert Price	10/2018
1801	2^498238-53	149985	Lelio R Paula	12/2017
1802	5*10^149907+23	149908	Robert Price	03/2019
1803	39347^6442+6442^39347	149874	Hans Havermann	09/2020
1804	2^497850+81049	149868	Enzo Doria	07/2016
1805	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
1806	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
1807	(2*10^149803-143)/3	149803	Robert Price	03/2018
1808	33845^26604+26604^33845	149763	Hans Havermann	09/2020
1809	2^497434-2784191	149743	Enzo Doria	10/2015
1810	(865*10^149737-1)/9	149739	Robert Price	04/2020
1811	38237^8214+8214^38237	149681	Hans Havermann	09/2020
1812	(23*10^149655+19)/3	149656	Robert Price	07/2019
1813	2^497068-113579	149633	Enzo Doria	08/2014
1814	2^497037+73727	149624	Enzo Doria	04/2016
1815	34942^19067+19067^34942	149562	Hans Havermann	09/2020
1816	33696^27449+27449^33696	149561	Hans Havermann	09/2020
1817	2^496773+77747	149544	Enzo Doria	05/2016
1818	(206*10^149459+7)/3	149461	Robert Price	07/2020
1819	34589^20940+20940^34589	149459	Hans Havermann	09/2020
1820	2^496477-113485	149455	Enzo Doria	08/2014
1821	((10^74703-1)10000/9+7481)10^74703+(10^74703-1)/9	149410	Hans Havermann	09/2019
1822	2^496270-49451	149393	Enzo Doria	10/2015
1823	2^496238-1865081	149383	Enzo Doria	01/2016
1824	33831^26030+26030^33831	149380	Hans Havermann	09/2020
1825	34131^23780+23780^34131	149365	Hans Havermann	09/2020
1826	(5*10^149335-53)/3	149336	Robert Price	09/2020
1827	2^495968-1853699	149302	Enzo Doria	09/2015
1828	2^495935-4117	149292	Yves Minet	02/2018
1829	35816^14709+14709^35816	149267	Hans Havermann	09/2020
1830	2^495712-396765	149225	Enzo Doria	07/2013
1831	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
1832	2^495420+1880701	149137	Enzo Doria	10/2016
1833	2^495337-1847293	149112	Enzo Doria	07/2015
1834	(2^495193-7)/5	149068	Lelio R Paula	10/2015
1835	33282^30097+30097^33282	149055	Hans Havermann	09/2020
1836	37384^9705+9705^37384	149050	Hans Havermann	09/2020
1837	34808^19143+19143^34808	149049	Hans Havermann	09/2020
1838	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
1839	47^89113-46^89113	149006	Robert Price	10/2012
1840	2^494916+87855	148985	Lelio R Paula	01/2016
1841	6*10^148982+73	148983	Robert Price	04/2019
1842	2^494586-2791991	148886	Enzo Doria	02/2016
1843	8*10^148860-3	148861	Ray Chandler	04/2011
1844	2^494333-286183	148810	Enzo Doria	06/2015
1845	2^494144-264119	148753	Enzo Doria	05/2014
1846	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
1847	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
1848	(151*10^148601-1)/3	148603	Robert Price	03/2020
1849	2^493636+82081	148600	Enzo Doria	09/2016
1850	((((((((((((((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
1851	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
1852	(2*10^148460-23)/3	148460	Robert Price	04/2018
1853	(28*10^148445+101)/3	148446	Robert Price	09/2020
1854	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
1855	(71*10^148306-539)/9	148307	Robert Price	07/2019
1856	5^211959-12874	148153	Enzo Doria	05/2014
1857	(16*10^148071+41)/3	148072	Robert Price	03/2019
1858	187^65175-2	148068	Lelio R Paula	11/2017
1859	2^491851+1871453	148062	Enzo Doria	05/2016
1860	(68*10^148060-257)/9	148061	Robert Price	07/2019
1861	(151*10^148020-1)/3	148022	Robert Price	03/2020
1862	(26*10^147973-23)/3	147974	Robert Price	12/2019
1863	2^491521-1865323	147963	Enzo Doria	02/2016
1864	(2^491476+7)/71	147948	Lelio R Paula	10/2015
1865	2^491391-7807	147924	Lelio R Paula	01/2013
1866	2^491370-113297	147918	Enzo Doria	07/2014
1867	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
1868	(17*10^147890+79)/3	147891	Robert Price	04/2019
1869	94*10^147871-3	147873	Robert Price	05/2020
1870	2^490660-17	147704	Lelio R Paula	12/2017
1871	(229*10^147699-1)/3	147701	Robert Price	07/2020
1872	2^490550+1179439	147671	Enzo Doria	06/2016
1873	(23*10^147649-59)/9	147650	Robert Price	05/2018
1874	2^490303+2793653	147596	Enzo Doria	03/2016
1875	199^64181-2	147543	Lelio R Paula	11/2017
1876	2^489871-286987	147466	Enzo Doria	07/2015
1877	2^489864-351899	147464	Enzo Doria	07/2015
1878	175^65724-2	147422	Lelio R Paula	11/2017
1879	2^489712+1874851	147419	Enzo Doria	06/2016
1880	63^81896-2	147359	Lelio R Paula	10/2017
1881	(11*10^147313-107)/3	147314	Robert Price	09/2018
1882	2^489305-59815	147296	Enzo Doria	10/2015
1883	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
1884	2^489125+80357	147242	Enzo Doria	06/2016
1885	(148*10^147139-1)/3	147141	Robert Price	03/2020
1886	2^488648-112799	147098	Enzo Doria	07/2014
1887	2^488627-350317	147092	Enzo Doria	06/2015
1888	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
1889	2^488280-2165	146987	Yves Minet	07/2014
1890	2^488278+45	146987	Lelio R Paula	12/2017
1891	2^487927-39	146881	Lelio R Paula	12/2017
1892	(7*10^146860-13)/3	146861	Robert Price	07/2018
1893	(26*10^146856-77)/3	146857	Robert Price	11/2019
1894	2^487726-1863341	146821	Enzo Doria	12/2015
1895	((10^73362-1)10000/9+6701)10^73362+(10^73362-1)/9	146728	Hans Havermann	09/2019
1896	(22*10^146661-19)/3	146662	Robert Price	04/2019
1897	2^487121-39523	146639	Enzo Doria	09/2015
1898	(7*2^486967+1)/39	146591	Lelio R Paula	09/2015
1899	2^486893-79	146570	Yves Minet	09/2017
1900	2^486840+1879141	146554	Enzo Doria	08/2016
1901	2^486774-87	146534	Lelio R Paula	12/2017
1902	96^73877-95^73877	146445	Robert Price	10/2015
1903	8*10^146421+81	146422	Robert Price	08/2019
1904	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
1905	179^64935+2	146290	Lelio R Paula	10/2017
1906	(19*10^146181-49)/3	146182	Robert Price	05/2019
1907	2^485531-114621	146160	Enzo Doria	05/2015
1908	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
1909	2^485389+81887	146117	Enzo Doria	08/2016
1910	(10^146063+71)/9	146063	Serge Batalov	07/2015
1911	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
1912	(22*10^146029+257)/9	146030	Robert Price	06/2018
1913	7*10^145982-53	145983	Robert Price	06/2020
1914	2^484743+1872923	145923	Enzo Doria	05/2016
1915	2^484341+1879157	145802	Enzo Doria	08/2016
1916	2*10^145784-91	145785	Robert Price	04/2020
1917	2^484271-51	145781	Lelio R Paula	11/2017
1918	70^78989-69^78989	145743	Robert Price	01/2014
1919	51^85334+2	145714	Robert Price	07/2015
1920	2^483886-1857101	145665	Enzo Doria	10/2015
1921	(19*10^145585+131)/3	145586	Robert Price	06/2020
1922	2^483563-1863457	145567	Enzo Doria	12/2015
1923	2^483516-1861409	145553	Enzo Doria	11/2015
1924	2^483384-115019	145514	Enzo Doria	06/2015
1925	(19*10^145499-61)/3	145500	Robert Price	05/2019
1926	2^483302-3221	145489	Lelio R Paula	12/2012
1927	2^483046+1874029	145412	Enzo Doria	06/2016
1928	2^482991-2789317	145395	Enzo Doria	12/2015
1929	2^482978-2789711	145391	Enzo Doria	12/2015
1930	2^482966-2789711	145388	Enzo Doria	12/2015
1931	2^482817-1858843	145343	Enzo Doria	10/2015
1932	2^482751-113635	145323	Enzo Doria	08/2014
1933	2^482705-459763	145309	Enzo Doria	05/2015
1934	(4^241306+11)/3	145281	Robert Price	03/2017
1935	(238*10^145276-1)/3	145278	Robert Price	04/2020
1936	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
1937	53^84239-52^84239	145252	Robert Price	01/2013
1938	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
1939	2^482087+72623	145123	Enzo Doria	04/2016
1940	2^482016-286565	145102	Enzo Doria	07/2015
1941	(19*10^145093+101)/3	145094	Robert Price	09/2019
1942	2^481840+15	145049	Robert Price	09/2015
1943	2^481801-481801	145037	Henri Lifchitz	03/2005
1944	2^481775+1869083	145029	Enzo Doria	05/2016
1945	29^99167+2	145022	Ray Chandler	08/2011
1946	2^481663+1875653	144996	Enzo Doria	07/2016
1947	2^481149-459073	144841	Enzo Doria	05/2015
1948	2^481045-113215	144809	Enzo Doria	07/2014
1949	(64*10^144797+287)/9	144798	Robert Price	04/2019
1950	2^480859-113695	144753	Enzo Doria	09/2014
1951	2^480766-2787191	144725	Enzo Doria	11/2015
1952	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
1953	2^480678+1874239	144699	Enzo Doria	06/2016
1954	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
1955	L(692147)	144651	Henri Lifchitz	10/2008
1956	(76*10^144648+77)/9	144649	Robert Price	10/2019
1957	2^480417+35	144620	Robert Price	11/2015
1958	2^480296-59879	144584	Enzo Doria	10/2015
1959	2^479844+3	144448	Donovan Johnson	06/2006
1960	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
1961	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
1962	2^479348-2792219	144299	Enzo Doria	02/2016
1963	3^302389-6242	144277	Enzo Doria	05/2014
1964	2*10^144220-3	144221	Robert Price	07/2015
1965	2^478904-109109	144165	Enzo Doria	04/2014
1966	2^478337-115333	143994	Enzo Doria	07/2015
1967	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
1968	88^74047-87^74047	143984	Robert Price	05/2015
1969	(19*10^143963+467)/9	143964	Robert Price	02/2018
1970	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
1971	2^478088+27	143919	Robert Price	11/2015
1972	7*10^143857-93	143858	Robert Price	08/2020
1973	3*10^143844+61	143845	Robert Price	09/2020
1974	2^477475-22071	143735	Enzo Doria	07/2013
1975	2^477417-22123	143717	Enzo Doria	07/2013
1976	2^477359-3577	143700	Yves Minet	03/2017
1977	(14*10^143662-71)/3	143663	Robert Price	12/2018
1978	2^476936-396765	143573	Enzo Doria	07/2013
1979	2^476888-2791229	143558	Enzo Doria	01/2016
1980	2^476868-1859939	143552	Enzo Doria	11/2015
1981	755^49878+49878^755	143547	Norbert Schneider	04/2019
1982	2^476558-113627	143459	Enzo Doria	08/2014
1983	2^476478-45	143435	Lelio R Paula	11/2017
1984	(2^475854+9)/73	143245	Lelio R Paula	08/2015
1985	2^475813-113239	143234	Enzo Doria	07/2014
1986	2^475624-114059	143178	Enzo Doria	11/2014
1987	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
1988	2^475480-2786129	143134	Enzo Doria	10/2015
1989	(19*10^143129-43)/3	143130	Robert Price	05/2019
1990	(14*10^143097+73)/3	143098	Robert Price	12/2018
1991	2^475299-111937	143080	Enzo Doria	05/2014
1992	2^475160-2797859	143038	Enzo Doria	04/2016
1993	(2^475069+3)/395	143008	Lelio R Paula	08/2015
1994	2^475027-461437	142998	Enzo Doria	07/2015
1995	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
1996	(8*10^142932+43)/3	142933	Robert Price	06/2018
1997	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
1998	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
1999	2^474417-59923	142814	Enzo Doria	10/2015
2000	4*10^142810-21	142811	Robert Price	09/2018

Find by discoverer :

PRP Records

Probable Primes Top 10000

(271067 PRPs in the top)