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	2^415290-113591	125015	Enzo Doria	08/2014
1752	2^415276-460919	125011	Enzo Doria	06/2015
1753	2^415259+77243	125006	Enzo Doria	05/2016
1754	2^415144-3683	124971	Yves Minet	10/2011
1755	2^414874+79	124890	Lelio R Paula	01/2015
1756	(2^414765+7)/1389	124854	Lelio R Paula	05/2014
1757	2^414618+79459	124813	Enzo Doria	06/2016
1758	2^414432-1846709	124757	Enzo Doria	07/2015
1759	(13*2^414274-1)/153	124708	Lelio R Paula	05/2014
1760	2^414032-5	124637	Henri Lifchitz	07/2006
1761	2^414032+1872331	124637	Enzo Doria	05/2016
1762	14120^30009-30009^14120	124533	Norbert Schneider	02/2015
1763	64^68909-63^68909	124463	Robert Price	07/2013
1764	2^413387+76253	124442	Enzo Doria	04/2016
1765	287117#+391613	124424	Nicolas PALAU	01/2017
1766	(27*2^413207-1)/108335	124385	Lelio R Paula	05/2014
1767	2^412868-120599	124286	Paul Bourdelais	02/2012
1768	45^75145-2	124231	Lelio R Paula	08/2015
1769	2^412645-112213	124219	Enzo Doria	06/2014
1770	2^412248+74611	124100	Enzo Doria	04/2016
1771	2^412192-3329	124083	Yves Minet	12/2014
1772	(25*2^412191-1)/23	124082	Lelio R Paula	05/2014
1773	F(593689)	124074	Henri Lifchitz	01/2005
1774	(11*2^412161+1)/19	124073	Lelio R Paula	05/2014
1775	2^411884-113279	123990	Enzo Doria	07/2014
1776	(2^411832+1)/257	123972	Lelio R Paula	05/2014
1777	2^411790-1853531	123962	Enzo Doria	08/2015
1778	(5^177337+1)/6	123953	Paul Bourdelais	11/2008
1779	2^411711-113257	123938	Enzo Doria	07/2014
1780	(23*2^411675-1)/3	123928	Lelio R Paula	05/2014
1781	2^411325-351103	123822	Enzo Doria	06/2015
1782	2^411052+1872481	123739	Enzo Doria	05/2016
1783	2^410997+39	123723	Lelio R Paula	05/2014
1784	2^410596-39	123602	Lelio R Paula	05/2014
1785	2^410540-115079	123585	Enzo Doria	06/2015
1786	(3*2^410392-1)/9229	123537	Lelio R Paula	05/2014
1787	2^410206-113081	123485	Enzo Doria	07/2014
1788	(25*2^410192+1)/10397	123478	Lelio R Paula	04/2014
1789	2^409909-189	123395	Enzo Doria	05/2014
1790	2^409896-109043	123391	Enzo Doria	04/2014
1791	2^409890+75409	123390	Enzo Doria	04/2016
1792	F(590041)	123311	Henri Lifchitz	01/2005
1793	2^409566-113501	123292	Enzo Doria	08/2014
1794	2^409533+77747	123282	Enzo Doria	05/2016
1795	2^409436-112799	123253	Enzo Doria	06/2014
1796	2^409225+1873787	123189	Enzo Doria	06/2016
1797	2^409174+73009	123174	Enzo Doria	04/2016
1798	2^409058-112685	123139	Enzo Doria	06/2014
1799	2^408778+77689	123055	Enzo Doria	05/2016
1800	2^408690-75	123028	Lelio R Paula	11/2013
1801	2^408574-2787341	122994	Enzo Doria	03/2016
1802	Phi(157825,10)	122961	Maksym Voznyy	06/2015
1803	(13*2^408283+1)/1665	122904	Lelio R Paula	05/2014
1804	(11*2^408100-1)/35	122850	Lelio R Paula	04/2014
1805	(2^407821-lucasV(1,2,407821)+1)/2	122767	Mike Oakes	11/2016
1806	(21*2^407604-1)/215	122701	Lelio R Paula	04/2014
1807	(21*2^407433-1)/13	122650	Lelio R Paula	04/2014
1808	(73*10^122592-1)/9	122593	Robert Price	01/2015
1809	2^407179-112075	122574	Enzo Doria	06/2014
1810	(21*2^407131+1)/207517523	122552	Lelio R Paula	04/2014
1811	(66^67349+1)/67	122543	Paul Bourdelais	09/2017
1812	2^407008-1867919	122522	Enzo Doria	04/2016
1813	11^117642-300	122512	Enzo Doria	10/2012
1814	2^406949+72197	122504	Enzo Doria	04/2016
1815	2^406826-65	122467	Lelio R Paula	11/2013
1816	2^406821-2797363	122466	Enzo Doria	04/2016
1817	2^406758-17	122447	Lelio R Paula	11/2013
1818	(30^82883-1)/29	122427	Robert Price	12/2011
1819	(2^406583-1)/813167	122388	Jens K. Andersen	02/2009
1820	97^61575-2	122336	Lelio R Paula	12/2014
1821	2^406298+2799109	122308	Enzo Doria	04/2016
1822	(27*2^406241-1)/10277	122289	Lelio R Paula	04/2014
1823	2^406229-1849993	122288	Enzo Doria	08/2015
1824	3*10^122274+7	122275	Robert Price	07/2015
1825	2^406117+1876577	122254	Enzo Doria	07/2016
1826	3^256199-2^256199	122238	Mike Oakes	06/2005
1827	2^405774+179149	122151	Enzo Doria	06/2016
1828	2^405514-3311	122072	Yves Minet	12/2014
1829	2^405514-115511	122072	Enzo Doria	07/2015
1830	2^405422-113261	122045	Enzo Doria	07/2014
1831	2^405173+71237	121970	Enzo Doria	04/2016
1832	(2^405016+1)/257	121920	Lelio R Paula	04/2014
1833	2^404858+71329	121875	Enzo Doria	04/2016
1834	2^404813-114703	121861	Enzo Doria	04/2015
1835	2^404764+77791	121847	Enzo Doria	05/2016
1836	317^48694+48694^317	121787	Norbert Schneider	08/2015
1837	2^404536-115259	121778	Enzo Doria	06/2015
1838	2^404501-631	121767	Yves Minet	07/2012
1839	63^67620+2	121672	Lelio R Paula	08/2015
1840	(17*10^121621+1)/9	121622	Serge Batalov	05/2010
1841	(15*2^403912+1)/271	121589	Lelio R Paula	05/2014
1842	2^403676+76831	121519	Enzo Doria	05/2016
1843	2^403363-113635	121425	Enzo Doria	08/2014
1844	2^403336-1861469	121417	Enzo Doria	03/2016
1845	p(24442)#/2-64	121381	Robert Price	04/2017
1846	11^116555-720	121380	Enzo Doria	11/2012
1847	2^403100-461267	121346	Enzo Doria	07/2015
1848	2^403093-112213	121344	Enzo Doria	06/2014
1849	2^403004+1866361	121317	Enzo Doria	03/2016
1850	2^402953+89	121301	Lelio R Paula	10/2013
1851	2^402944-2788319	121299	Enzo Doria	03/2016
1852	(27*2^402865+1)/5	121276	Lelio R Paula	04/2014
1853	2^402828-113183	121264	Enzo Doria	07/2014
1854	(17*10^121242+1)/9	121243	Serge Batalov	05/2010
1855	(15*2^402757+1)/101	121242	Lelio R Paula	05/2014
1856	2^402715+1874223	121230	Enzo Doria	06/2016
1857	(91^61879+1)/92	121222	Paul Bourdelais	09/2017
1858	7*10^121144+9	121145	Robert Price	09/2015
1859	2^401725-113251	120932	Enzo Doria	07/2014
1860	(15*2^401677-1)/19	120917	Lelio R Paula	05/2014
1861	2^401652+73711	120910	Enzo Doria	04/2016
1862	(2^401632+3)/79	120902	Lelio R Paula	04/2014
1863	2^401406-2791331	120836	Enzo Doria	03/2016
1864	(28^83497+1)/29	120832	Robert Price	07/2013
1865	2^401369+1867367	120825	Enzo Doria	03/2016
1866	(10^120782+29)/3	120782	Serge Batalov	12/2014
1867	2^401215-1657	120778	Yves Minet	07/2014
1868	2^401159+53	120761	Lelio R Paula	10/2013
1869	2^401031-113047	120723	Enzo Doria	07/2014
1870	(29*2^400909-1)/303	120685	Lelio R Paula	04/2014
1871	2^400571-15	120584	Lelio R Paula	10/2013
1872	(10^120574+359)/9	120574	Serge Batalov	12/2014
1873	2^400424-216413	120540	Enzo Doria	04/2013
1874	(17*2^400200-1)/587	120471	Lelio R Paula	05/2014
1875	2^400166+1874899	120462	Enzo Doria	06/2016
1876	(3*2^400045-1)/865	120424	Lelio R Paula	04/2014
1877	2^399966+73759	120402	Enzo Doria	04/2016
1878	(112*10^120395-1)/3	120397	Serge Batalov	12/2014
1879	2^399918-95	120388	Lelio R Paula	04/2013
1880	2^399792-1849259	120350	Enzo Doria	08/2015
1881	9*10^120342-7	120343	Robert Price	09/2015
1882	2^399526-1861721	120270	Enzo Doria	11/2015
1883	(10^(260126+1)+3610^60126-1)/9	120253	Robert Price	10/2015
1884	2^399322-2798111	120208	Enzo Doria	04/2016
1885	72^64693-71^64693	120157	Robert Price	03/2014
1886	2^399111-28489	120145	Enzo Doria	08/2015
1888	2^398877+105	120074	Donovan Johnson	01/2006
1887	(101*10^120072-87)/7	120074	Hans Havermann	02/2015
1889	(88^61751+1)/89	120072	Paul Bourdelais	09/2017
1890	2^398710+57	120024	Lelio R Paula	04/2013
1891	2^398691-115057	120018	Enzo Doria	06/2015
1892	L(574219)	120005	Renaud Lifchitz	03/2004
1893	2^398571+60413	119982	Yves Minet	03/2011
1894	p(24179)#/2-64	119949	Robert Price	04/2017
1895	2^398448+1872001	119945	Enzo Doria	05/2016
1896	8*10^119930-3	119931	Ray Chandler	04/2011
1897	(10^119880+179)/9	119880	Serge Batalov	12/2014
1898	(9*2^398145+1)/73	119853	Lelio R Paula	04/2014
1899	2^398029+1872527	119819	Enzo Doria	05/2016
1900	2^397897-113541	119779	Enzo Doria	08/2014
1901	(21*2^397661-1)/27593	119705	Lelio R Paula	04/2014
1902	(58^67853-1)/57	119653	Paul Bourdelais	09/2017
1903	2^397426+73849	119638	Enzo Doria	04/2016
1904	2^396933-112723	119489	Enzo Doria	06/2014
1905	11^114738-150	119488	Enzo Doria	10/2012
1906	2^396790-21	119446	Lelio R Paula	04/2013
1907	(2^396633-7)/5	119398	Lelio R Paula	04/2014
1908	105^59050+104	119352	Norbert Schneider	11/2016
1909	2^396374+73729	119321	Enzo Doria	04/2016
1910	2^396258-459491	119286	Enzo Doria	05/2015
1911	(2^395986+5)/76881	119199	Lelio R Paula	04/2014
1912	(23*2^395942-1)/91	119190	Lelio R Paula	04/2014
1913	(11*2^395548+1)/3	119073	Lelio R Paula	04/2014
1914	(30^80599+1)/31	119054	Robert Price	07/2013
1915	2^395062-109121	118926	Enzo Doria	04/2014
1916	(2^394918+78557)/3	118882	Lelio R Paula	01/2015
1917	(2^394739+3)/1883	118826	Lelio R Paula	04/2014
1918	2^394266+71389	118686	Enzo Doria	04/2016
1919	5^169727+2	118635	Lelio R Paula	08/2013
1920	2^394034-3	118617	M. Frind & P. Underwood	09/2002
1921	3^248572-6242	118599	Enzo Doria	05/2014
1922	(3*2^393964-1)/181	118594	Lelio R Paula	04/2014
1923	7^140303-6	118570	Robert Price	11/2014
1924	2^393427+75683	118434	Enzo Doria	04/2016
1925	2^393376-114749	118418	Enzo Doria	04/2015
1926	2^393180+73	118359	Lelio R Paula	04/2013
1927	p(23881)#/2+256	118328	Robert Price	05/2017
1928	(10^118324+359)/9	118324	Serge Batalov	12/2014
1929	p(23879)#/2+64	118317	Robert Price	03/2017
1930	(53*10^118216+1)/9	118217	Serge Batalov	11/2010
1931	(7*2^392697+1)/15	118214	Renaud Lifchitz	03/2011
1932	(157^53819-1)/156	118179	Alexander Zhirkov	06/2016
1933	(19*2^392551+1)/3	118171	Lelio R Paula	04/2014
1934	2^392516-29219	118160	Enzo Doria	07/2015
1935	Phi(177231,10)	118152	Maksym Voznyy	09/2015
1936	2^392413-112123	118129	Enzo Doria	06/2014
1937	(2^392342+5)/27	118106	Lelio R Paula	04/2014
1938	2^392300-1841429	118095	Enzo Doria	06/2015
1939	2^392220+75241	118070	Enzo Doria	04/2016
1940	2^391933+5897	117984	Yves Minet	02/2011
1941	2^391912-1849259	117978	Enzo Doria	08/2015
1942	(2^391812+5)/14181	117944	Lelio R Paula	04/2014
1943	(7*2^391521+1)/285	117858	Lelio R Paula	04/2014
1944	2^391324+90901	117801	Yves Minet	02/2011
1945	2^391301-1859923	117794	Enzo Doria	03/2016
1946	(2^391115-7)/11791	117734	Lelio R Paula	04/2014
1947	2^390960+1880881	117691	Enzo Doria	11/2016
1948	2^390897-1860553	117672	Enzo Doria	11/2015
1949	2^390889-115003	117670	Enzo Doria	06/2015
1950	2^390779-30337	117637	Paul Bourdelais	02/2012
1951	11^112916-780	117590	Enzo Doria	12/2012
1952	(16^97613-5^97613)/11	117537	Robert Price	07/2013
1953	(17*2^390272+1)/1983	117482	Lelio R Paula	04/2014
1954	31^78759-30	117459	Theodore Burton	02/2007
1955	2^389998+37	117402	Lelio R Paula	03/2013
1956	2^389478+43	117245	Lelio R Paula	03/2013
1957	(29*2^389351-1)/9	117207	Lelio R Paula	04/2014
1958	(2^389341-7)/3865	117200	Lelio R Paula	03/2014
1959	2^389033-12797413	117111	Enzo Doria	04/2016
1960	2^388960-109505	117089	Enzo Doria	04/2014
1961	(2^388928-5)/569	117077	Lelio R Paula	03/2014
1962	2^388888-1529	117067	Yves Minet	01/2013
1963	10^117059+28879	117060	Patrick De Geest	05/2016
1964	(10^117059-71)/1	117059	Serge Batalov	12/2014
1965	3^245154-6256	116969	Enzo Doria	05/2014
1966	2^388536-113495	116961	Enzo Doria	08/2014
1967	2^388469-43	116941	Lelio R Paula	03/2013
1968	(7*2^388372-1)/111	116911	Lelio R Paula	04/2014
1969	(7*2^388335-1)/25	116900	Lelio R Paula	04/2014
1970	2^388180+93	116854	Donovan Johnson	07/2008
1971	(2^388081+7)/1179	116821	Lelio R Paula	03/2014
1972	2^387946-113261	116784	Enzo Doria	07/2014
1973	2^387745+75557	116723	Enzo Doria	04/2016
1974	2^387554+71455	116666	Enzo Doria	04/2016
1975	(2^387447+78557)/365	116631	Lelio R Paula	12/2014
1976	(145*10^116610-1)/9	116612	Serge Batalov	12/2014
1977	(17*2^387284-1)/59	116584	Lelio R Paula	04/2014
1978	(31*2^386968+1)/7	116490	Lelio R Paula	03/2014
1979	2^386947+1869143	116483	Enzo Doria	05/2016
1980	(30^78857-1)/29	116480	Robert Price	12/2011
1981	(2^386903-3)/5	116469	Lelio R Paula	03/2014
1982	2^386389-1864783	116315	Enzo Doria	03/2016
1983	(31*2^386231-1)/1711	116266	Lelio R Paula	03/2014
1984	(2^386087-5)/40959	116220	Lelio R Paula	03/2014
1985	2^385969-823	116189	Yves Minet	05/2012
1986	57^66162+2	116173	Lelio R Paula	08/2013
1987	2^385854+75049	116154	Enzo Doria	04/2016
1988	2^385775-109587	116130	Enzo Doria	04/2014
1989	2^385622+71839	116084	Enzo Doria	04/2016
1990	2^385564+781	116067	Lelio R Paula	01/2012
1991	2^385410+71893	116020	Enzo Doria	04/2016
1992	(25*2^385091+1)/27	115924	Lelio R Paula	04/2014
1993	2^384953-111943	115883	Paul Bourdelais	02/2012
1994	43^70942-2	115882	Lelio R Paula	04/2014
1995	7*10^115863+3	115864	Robert Price	08/2015
1996	2^384834+93	115847	Donovan Johnson	07/2008
1997	2^384809+71297	115840	Enzo Doria	04/2016
1998	(7*2^384759-1)/5	115825	Lelio R Paula	04/2014
1999	(71*10^115810-17)/9	115811	Ray Chandler	08/2011
2000	(97*10^115794-1)/3	115796	Serge Batalov	12/2014

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PRP Records

Probable Primes Top 10000

(181746 PRPs in the top)