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 (> 30000)	Who ?	When ?
1751	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
1752	2^410206-113081	123485	Enzo Doria	07/2014
1753	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
1754	2^409909-189	123395	Enzo Doria	05/2014
1755	2^409896-109043	123391	Enzo Doria	04/2014
1756	2^409890+75409	123390	Enzo Doria	04/2016
1757	F(590041)	123311	Henri Lifchitz	01/2005
1758	2^409566-113501	123292	Enzo Doria	08/2014
1759	2^409533+77747	123282	Enzo Doria	05/2016
1760	2^409436-112799	123253	Enzo Doria	06/2014
1761	2^409225+1873787	123189	Enzo Doria	06/2016
1762	2^409174+73009	123174	Enzo Doria	04/2016
1763	2^409058-112685	123139	Enzo Doria	06/2014
1764	2^408778+77689	123055	Enzo Doria	05/2016
1765	2^408690-75	123028	Lelio R Paula	11/2013
1766	2^408574-2787341	122994	Enzo Doria	03/2016
1767	Phi(157825,10)	122961	Maksym Voznyy	06/2015
1768	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
1769	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
1770	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
1771	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
1772	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
1773	(73*10^122592-1)/9	122593	Robert Price	01/2015
1774	2^407179-112075	122574	Enzo Doria	06/2014
1775	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
1776	2^407008-1867919	122522	Enzo Doria	04/2016
1777	11^117642-300	122512	Enzo Doria	10/2012
1778	2^406949+72197	122504	Enzo Doria	04/2016
1779	2^406826-65	122467	Lelio R Paula	11/2013
1780	2^406821-2797363	122466	Enzo Doria	04/2016
1781	2^406758-17	122447	Lelio R Paula	11/2013
1782	(30^82883-1)/29	122427	Robert Price	12/2011
1783	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
1784	97^61575-2	122336	Lelio R Paula	12/2014
1785	2^406298+2799109	122308	Enzo Doria	04/2016
1786	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
1787	2^406229-1849993	122288	Enzo Doria	08/2015
1788	3*10^122274+7	122275	Robert Price	07/2015
1789	2^406117+1876577	122254	Enzo Doria	07/2016
1790	3^256199-2^256199	122238	Mike Oakes	06/2005
1791	2^405774+179149	122151	Enzo Doria	06/2016
1792	2^405514-3311	122072	Yves Minet	12/2014
1793	2^405514-115511	122072	Enzo Doria	07/2015
1794	2^405422-113261	122045	Enzo Doria	07/2014
1795	2^405173+71237	121970	Enzo Doria	04/2016
1796	(2^405016+1)/257	121920	Lelio R Paula	04/2014
1797	2^404858+71329	121875	Enzo Doria	04/2016
1798	2^404813-114703	121861	Enzo Doria	04/2015
1799	2^404764+77791	121847	Enzo Doria	05/2016
1800	317^48694+48694^317	121787	Norbert Schneider	08/2015
1801	2^404536-115259	121778	Enzo Doria	06/2015
1802	2^404501-631	121767	Yves Minet	07/2012
1803	63^67620+2	121672	Lelio R Paula	08/2015
1804	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
1805	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
1806	2^403676+76831	121519	Enzo Doria	05/2016
1807	2^403363-113635	121425	Enzo Doria	08/2014
1808	2^403336-1861469	121417	Enzo Doria	03/2016
1809	p(24442)#/2-64	121381	Robert Price	04/2017
1810	11^116555-720	121380	Enzo Doria	11/2012
1811	2^403100-461267	121346	Enzo Doria	07/2015
1812	2^403093-112213	121344	Enzo Doria	06/2014
1813	2^403004+1866361	121317	Enzo Doria	03/2016
1814	2^402953+89	121301	Lelio R Paula	10/2013
1815	2^402944-2788319	121299	Enzo Doria	03/2016
1816	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
1817	2^402828-113183	121264	Enzo Doria	07/2014
1818	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
1819	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
1820	2^402715+1874223	121230	Enzo Doria	06/2016
1821	7*10^121144+9	121145	Robert Price	09/2015
1822	2^401725-113251	120932	Enzo Doria	07/2014
1823	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
1824	2^401652+73711	120910	Enzo Doria	04/2016
1825	(2^401632+3)/79	120902	Lelio R Paula	04/2014
1826	2^401406-2791331	120836	Enzo Doria	03/2016
1827	(28^83497+1)/29	120832	Robert Price	07/2013
1828	2^401369+1867367	120825	Enzo Doria	03/2016
1829	(10^120782+29)/3	120782	Serge Batalov	12/2014
1830	2^401215-1657	120778	Yves Minet	07/2014
1831	2^401159+53	120761	Lelio R Paula	10/2013
1832	2^401031-113047	120723	Enzo Doria	07/2014
1833	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
1834	2^400571-15	120584	Lelio R Paula	10/2013
1835	(10^120574+359)/9	120574	Serge Batalov	12/2014
1836	2^400424-216413	120540	Enzo Doria	04/2013
1837	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
1838	2^400166+1874899	120462	Enzo Doria	06/2016
1839	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
1840	2^399966+73759	120402	Enzo Doria	04/2016
1841	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
1842	2^399918-95	120388	Lelio R Paula	04/2013
1843	2^399792-1849259	120350	Enzo Doria	08/2015
1844	9*10^120342-7	120343	Robert Price	09/2015
1845	2^399526-1861721	120270	Enzo Doria	11/2015
1846	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
1847	2^399322-2798111	120208	Enzo Doria	04/2016
1848	72^64693-71^64693	120157	Robert Price	03/2014
1849	2^399111-28489	120145	Enzo Doria	08/2015
1851	2^398877+105	120074	Donovan Johnson	01/2006
1850	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
1852	2^398710+57	120024	Lelio R Paula	04/2013
1853	2^398691-115057	120018	Enzo Doria	06/2015
1854	L(574219)	120005	Renaud Lifchitz	03/2004
1855	2^398571+60413	119982	Yves Minet	03/2011
1856	p(24179)#/2-64	119949	Robert Price	04/2017
1857	2^398448+1872001	119945	Enzo Doria	05/2016
1858	8*10^119930-3	119931	Ray Chandler	04/2011
1859	(10^119880+179)/9	119880	Serge Batalov	12/2014
1860	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
1861	2^398029+1872527	119819	Enzo Doria	05/2016
1862	2^397897-113541	119779	Enzo Doria	08/2014
1863	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
1864	2^397426+73849	119638	Enzo Doria	04/2016
1865	2^396933-112723	119489	Enzo Doria	06/2014
1866	11^114738-150	119488	Enzo Doria	10/2012
1867	2^396790-21	119446	Lelio R Paula	04/2013
1868	(2^396633-7)/5	119398	Lelio R Paula	04/2014
1869	105^59050+104	119352	Norbert Schneider	11/2016
1870	2^396374+73729	119321	Enzo Doria	04/2016
1871	2^396258-459491	119286	Enzo Doria	05/2015
1872	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
1873	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
1874	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
1875	(30^80599+1)/31	119054	Robert Price	07/2013
1876	2^395062-109121	118926	Enzo Doria	04/2014
1877	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
1878	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
1879	2^394266+71389	118686	Enzo Doria	04/2016
1880	5^169727+2	118635	Lelio R Paula	08/2013
1881	2^394034-3	118617	M. Frind & P. Underwood	09/2002
1882	3^248572-6242	118599	Enzo Doria	05/2014
1883	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
1884	7^140303-6	118570	Robert Price	11/2014
1885	2^393427+75683	118434	Enzo Doria	04/2016
1886	2^393376-114749	118418	Enzo Doria	04/2015
1887	2^393180+73	118359	Lelio R Paula	04/2013
1888	p(23881)#/2+256	118328	Robert Price	05/2017
1889	(10^118324+359)/9	118324	Serge Batalov	12/2014
1890	p(23879)#/2+64	118317	Robert Price	03/2017
1891	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
1892	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
1893	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
1894	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
1895	2^392516-29219	118160	Enzo Doria	07/2015
1896	Phi(177231,10)	118152	Maksym Voznyy	09/2015
1897	2^392413-112123	118129	Enzo Doria	06/2014
1898	(2^392342+5)/27	118106	Lelio R Paula	04/2014
1899	2^392300-1841429	118095	Enzo Doria	06/2015
1900	2^392220+75241	118070	Enzo Doria	04/2016
1901	2^391933+5897	117984	Yves Minet	02/2011
1902	2^391912-1849259	117978	Enzo Doria	08/2015
1903	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
1904	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
1905	2^391324+90901	117801	Yves Minet	02/2011
1906	2^391301-1859923	117794	Enzo Doria	03/2016
1907	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
1908	2^390960+1880881	117691	Enzo Doria	11/2016
1909	2^390897-1860553	117672	Enzo Doria	11/2015
1910	2^390889-115003	117670	Enzo Doria	06/2015
1911	2^390779-30337	117637	Paul Bourdelais	02/2012
1912	11^112916-780	117590	Enzo Doria	12/2012
1913	(16^97613-5^97613)/11	117537	Robert Price	07/2013
1914	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
1915	31^78759-30	117459	Theodore Burton	02/2007
1916	2^389998+37	117402	Lelio R Paula	03/2013
1917	2^389478+43	117245	Lelio R Paula	03/2013
1918	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
1919	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
1920	2^389033-12797413	117111	Enzo Doria	04/2016
1921	2^388960-109505	117089	Enzo Doria	04/2014
1922	(2^388928-5)/569	117077	Lelio R Paula	03/2014
1923	2^388888-1529	117067	Yves Minet	01/2013
1924	10^117059+28879	117060	Patrick De Geest	05/2016
1925	(10^117059-71)/1	117059	Serge Batalov	12/2014
1926	3^245154-6256	116969	Enzo Doria	05/2014
1927	2^388536-113495	116961	Enzo Doria	08/2014
1928	2^388469-43	116941	Lelio R Paula	03/2013
1929	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
1930	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
1931	2^388180+93	116854	Donovan Johnson	07/2008
1932	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
1933	2^387946-113261	116784	Enzo Doria	07/2014
1934	2^387745+75557	116723	Enzo Doria	04/2016
1935	2^387554+71455	116666	Enzo Doria	04/2016
1936	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
1937	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
1938	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
1939	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
1940	2^386947+1869143	116483	Enzo Doria	05/2016
1941	(30^78857-1)/29	116480	Robert Price	12/2011
1942	(2^386903-3)/5	116469	Lelio R Paula	03/2014
1943	2^386389-1864783	116315	Enzo Doria	03/2016
1944	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
1945	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
1946	2^385969-823	116189	Yves Minet	05/2012
1947	57^66162+2	116173	Lelio R Paula	08/2013
1948	2^385854+75049	116154	Enzo Doria	04/2016
1949	2^385775-109587	116130	Enzo Doria	04/2014
1950	2^385622+71839	116084	Enzo Doria	04/2016
1951	2^385564+781	116067	Lelio R Paula	01/2012
1952	2^385410+71893	116020	Enzo Doria	04/2016
1953	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
1954	2^384953-111943	115883	Paul Bourdelais	02/2012
1955	43^70942-2	115882	Lelio R Paula	04/2014
1956	7*10^115863+3	115864	Robert Price	08/2015
1957	2^384834+93	115847	Donovan Johnson	07/2008
1958	2^384809+71297	115840	Enzo Doria	04/2016
1959	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
1960	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
1961	(97*10^115794-1)/3	115796	Serge Batalov	12/2014
1962	2^384530+1874305	115756	Enzo Doria	06/2016
1963	(3*2^384524-1)/7631	115750	Lelio R Paula	03/2014
1964	2^384312+81091	115690	Yves Minet	02/2010
1965	3^242337-4042	115625	Enzo Doria	05/2014
1966	(11*2^383859-13)/15	115553	Renaud Lifchitz	03/2011
1967	2^383780-3149	115530	Yves Minet	10/2014
1968	2^383560-455	115464	Yves Minet	03/2012
1969	(2^383544+5)/3	115458	Lelio R Paula	03/2014
1970	89^59221-88^59221	115445	Robert Price	06/2015
1971	2^383347+1869413	115399	Enzo Doria	05/2016
1972	(2^383130-7)/131793	115329	Lelio R Paula	03/2014
1973	(12^106859+1)/13	115320	Paul Bourdelais	02/2010
1974	2^383039+1869509	115307	Enzo Doria	05/2016
1975	(13*2^382968+1)/7	115286	Lelio R Paula	04/2014
1976	2^382633+73697	115185	Enzo Doria	04/2016
1977	2^382509-113593	115147	Enzo Doria	08/2014
1978	2^382502-2791721	115145	Enzo Doria	03/2016
1979	9^120590-120590	115073	Robert Price	03/2014
1980	2^382198+9	115054	Lelio R Paula	03/2013
1981	2^381883-59197	114959	Enzo Doria	10/2015
1983	2^381806-4481	114936	Yves Minet	07/2011
1982	2^381808-1851507	114936	Enzo Doria	08/2015
1984	2^381774-112373	114926	Enzo Doria	06/2014
1985	2^381555-109051	114860	Enzo Doria	04/2014
1986	2^381546-113501	114857	Enzo Doria	08/2014
1987	2^381360-110429	114801	Enzo Doria	05/2014
1988	2^381252-115079	114769	Enzo Doria	06/2015
1989	2^381209-29323	114756	Enzo Doria	07/2015
1990	569^41651-568^41651	114754	Jean-Louis Charton	11/2009
1991	2^381201+1873205	114753	Enzo Doria	06/2016
1992	2^380974-112991	114685	Enzo Doria	07/2014
1993	88^58949-87	114626	Norbert Schneider	11/2015
1994	2^380700+91	114603	Lelio R Paula	03/2013
1996	10^114575+3^114576	114576	Mike Oakes	09/2010
1995	10^114575+66561	114576	Patrick De Geest	02/2017
1997	10^114575-581081	114575	Patrick De Geest	02/2017
1998	2^380587-115315	114569	Enzo Doria	06/2015
1999	2^380513-216925	114546	Enzo Doria	05/2014
2000	2^380451-1840087	114528	Enzo Doria	06/2015

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Probable Primes Top 10000

(177649 PRPs in the top)