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	(37^87421-1)/36	137093	Robert Price	03/2012
1752	2^455323-57	137066	Lelio R Paula	09/2017
1753	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
1754	2^455025-112723	136977	Enzo Doria	06/2014
1755	2^454675-1777	136871	Yves Minet	10/2011
1756	3*10^136829+29	136830	Robert Price	05/2018
1757	4*10^136813-57	136814	Robert Price	10/2018
1758	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
1759	2^454348-53	136773	Lelio R Paula	09/2017
1760	31^91680-2	136729	Lelio R Paula	05/2017
1761	2^454199-113697	136728	Enzo Doria	09/2014
1762	(13*10^136687+47)/3	136688	Robert Price	10/2018
1763	2^453935-2791357	136649	Enzo Doria	01/2016
1764	2^453906-69131	136640	Enzo Doria	11/2015
1765	2^453791+1873913	136605	Enzo Doria	06/2016
1766	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
1767	2^453503-2788297	136519	Enzo Doria	11/2015
1768	2^453267-113827	136447	Enzo Doria	09/2014
1769	2^453102+1877629	136398	Enzo Doria	08/2016
1770	L(651821)	136223	Henri Lifchitz	09/2008
1771	2^452460+77701	136205	Enzo Doria	05/2016
1772	2^452440-114755	136199	Enzo Doria	04/2015
1773	2*10^136057-43	136058	Robert Price	04/2018
1774	(2^451956-5)/181	136051	Lelio R Paula	07/2015
1775	2^451947-22165	136050	Enzo Doria	07/2013
1776	2^451787-21805	136002	Enzo Doria	07/2013
1777	2^451734-112817	135986	Enzo Doria	06/2014
1778	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
1779	2^451705-21879	135977	Enzo Doria	07/2013
1780	2^451560-112349	135934	Enzo Doria	06/2014
1781	2^451530+45	135925	Lelio R Paula	08/2017
1782	2^451450-21743	135900	Enzo Doria	07/2013
1783	2^450805+65	135706	Lelio R Paula	08/2017
1784	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
1785	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
1786	2^449944-113247	135447	Enzo Doria	07/2014
1787	2^449770-113247	135395	Enzo Doria	07/2014
1788	2^449637-21471	135355	Enzo Doria	07/2013
1789	2^449571-75	135335	Lelio R Paula	08/2017
1790	(14*10^135301-53)/3	135302	Robert Price	12/2018
1791	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
1792	(13*10^135279+437)/9	135280	Robert Price	04/2018
1793	2^449330-35	135262	Lelio R Paula	08/2017
1794	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
1795	(13*10^135184-43)/3	135185	Robert Price	11/2018
1796	2^449049-115309	135178	Enzo Doria	07/2015
1797	(10^135174+191)/3	135174	Robert Price	02/2018
1798	2^449030-15	135172	Lelio R Paula	08/2017
1799	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
1800	2^448762-351401	135091	Enzo Doria	07/2015
1801	2*10^135083-43	135084	Robert Price	04/2018
1802	(10^135011+719)/9	135011	Serge Batalov	12/2014
1803	2^448386-2786261	134978	Enzo Doria	03/2016
1804	2^448113-113949	134896	Enzo Doria	11/2014
1805	2^447888-2786639	134828	Enzo Doria	03/2016
1806	2^447870-396765	134823	Enzo Doria	07/2013
1807	2^447766-21791	134791	Enzo Doria	07/2013
1808	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
1809	2^447552-1019	134727	Yves Minet	02/2014
1810	(2*10^134720-41)/3	134720	Robert Price	02/2018
1811	2^447437-113569	134692	Enzo Doria	08/2014
1812	2^447426-65	134689	Lelio R Paula	08/2017
1813	2^447357-2797573	134668	Enzo Doria	04/2016
1814	2^447278+93	134645	Lelio R Paula	08/2017
1815	2^447094-113193	134589	Enzo Doria	07/2014
1816	3^282041-9934	134568	Enzo Doria	05/2014
1817	2^447019-109039	134567	Enzo Doria	04/2014
1818	2^446990-22041	134558	Enzo Doria	07/2013
1819	123^64370+122	134528	Karsten Bonath	04/2018
1820	2^446782-39701	134495	Enzo Doria	09/2015
1821	2^446494-16485	134409	Enzo Doria	04/2013
1822	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
1823	2^446441+65	134393	Lelio R Paula	08/2017
1824	(10^134385+719)/9	134385	Serge Batalov	12/2014
1825	(2*10^134364+529)/9	134364	Robert Price	01/2018
1826	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
1827	(2^446022-7)/339	134264	Lelio R Paula	07/2015
1828	63^74568+2	134174	Lelio R Paula	06/2017
1829	2^445671-22071	134161	Enzo Doria	07/2013
1830	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
1831	2^445515-113859	134114	Enzo Doria	10/2014
1832	2^445328-216917	134058	Enzo Doria	05/2014
1833	2^445202+1874899	134020	Enzo Doria	06/2016
1834	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
1835	(35*10^133979-593)/9	133980	Robert Price	07/2018
1836	2*10^133955+51	133956	Robert Price	05/2018
1837	2^444964-113639	133948	Enzo Doria	08/2014
1838	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
1839	2^444784-113859	133894	Enzo Doria	10/2014
1840	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
1841	62^74521-61^74521	133571	Robert Price	05/2013
1842	2^443198-1867301	133416	Enzo Doria	03/2016
1843	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
1844	2^442799+1874633	133296	Enzo Doria	06/2016
1845	L(637751)	133283	Henri Lifchitz	09/2008
1846	109^65410-2	133269	Lelio R Paula	10/2017
1847	2^442688-113489	133263	Enzo Doria	08/2014
1848	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
1849	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
1850	2^442437-1849993	133187	Enzo Doria	08/2015
1851	2^442430-2791721	133185	Enzo Doria	03/2016
1852	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
1853	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
1854	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
1855	2^441781-2787883	132990	Enzo Doria	03/2016
1856	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
1857	2^441618+37	132941	Lelio R Paula	08/2017
1858	2^441521-113575	132912	Enzo Doria	08/2014
1859	2^441396-65	132874	Lelio R Paula	08/2017
1860	2^441330+1871959	132854	Enzo Doria	05/2016
1861	2^441063+383	132774	Lelio R Paula	06/2012
1862	2^440846+1870909	132708	Enzo Doria	05/2016
1863	2^440656-113489	132651	Enzo Doria	08/2014
1864	numbpart(14180123587)	132646	Serge Batalov	04/2017
1865	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
1866	(38^83891+1)/39	132529	Robert Price	09/2013
1867	2*10^132493-43	132494	Robert Price	04/2018
1868	2^439931-21	132433	Lelio R Paula	08/2017
1869	47^79201-46^79201	132432	Robert Price	10/2012
1870	2^439897-113653	132423	Enzo Doria	08/2014
1871	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
1872	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
1873	2^439576-113247	132326	Enzo Doria	07/2014
1874	2^439497-29143	132302	Enzo Doria	07/2015
1875	2^439409-114193	132276	Enzo Doria	12/2014
1876	9*10^132148-7	132149	Robert Price	09/2015
1877	2^438845+1870217	132106	Enzo Doria	05/2016
1878	2^438789+87855	132089	Lelio R Paula	01/2016
1879	2^438774-2786411	132085	Enzo Doria	03/2016
1880	2^438755-1848205	132079	Enzo Doria	07/2015
1881	2^438739-112087	132074	Enzo Doria	06/2014
1882	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
1883	L(631181)	131910	Henri Lifchitz	09/2008
1884	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
1885	2^438079-1863877	131875	Enzo Doria	03/2016
1886	(2^438067+5)/329	131869	Lelio R Paula	06/2015
1887	2^437908-113855	131824	Enzo Doria	09/2014
1888	2^437884-286349	131817	Enzo Doria	07/2015
1889	(11*10^131784-17)/3	131785	Robert Price	06/2018
1890	3^276062-112292	131716	Enzo Doria	07/2014
1891	2^437343+75953	131654	Enzo Doria	04/2016
1892	35^85243-34^85243	131621	Robert Price	05/2012
1893	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
1894	2^436451+1884713	131385	Enzo Doria	03/2017
1895	2^436365+35	131359	Robert Price	11/2015
1897	2^436300+1866871	131340	Enzo Doria	03/2016
1896	(7*10^131339+179)/3	131340	Robert Price	09/2018
1898	(37*10^131270+341)/9	131271	Robert Price	08/2018
1899	(5*10^131223-29)/3	131224	Robert Price	03/2018
1900	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
1901	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
1903	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
1902	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
1904	2^435773+1875557	131181	Enzo Doria	06/2016
1905	(25*10^131144-7)/9	131145	Robert Price	05/2018
1906	2^435612-2789939	131133	Enzo Doria	12/2015
1907	66^72047-65^72047	131093	Robert Price	09/2013
1908	(5*10^131090+37)/3	131091	Robert Price	03/2018
1909	2^435468+75631	131089	Enzo Doria	04/2016
1910	37^83588-2	131083	Lelio R Paula	08/2015
1911	(4^217720+11)/3	131081	Robert Price	02/2017
1912	2^435202-113193	131009	Enzo Doria	07/2014
1913	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
1914	2^434835-111937	130899	Enzo Doria	05/2014
1915	2^434685+72257	130854	Enzo Doria	04/2016
1916	(7*10^130825+113)/3	130826	Robert Price	02/2018
1917	2^434539-29317	130810	Enzo Doria	07/2015
1918	2^434469-114259	130789	Enzo Doria	01/2015
1919	2^434246+33	130722	Robert Price	11/2015
1920	2^433911-91	130621	Lelio R Paula	06/2017
1921	2^433744-114419	130570	Enzo Doria	02/2015
1923	2^433708+1869451	130560	Enzo Doria	05/2016
1922	2^433710+93	130560	Lelio R Paula	06/2017
1924	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
1925	4*10^130480+9	130481	Robert Price	05/2015
1926	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
1927	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
1928	2^433023-113497	130353	Enzo Doria	08/2014
1929	2^433002+1179379	130347	Enzo Doria	06/2016
1930	2^432974+19	130339	Robert Price	08/2015
1931	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
1932	2^432217+41	130111	Lelio R Paula	06/2017
1933	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
1934	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
1935	97^65480-2	130094	Lelio R Paula	05/2017
1936	4*10^130088-89	130089	Robert Price	11/2018
1937	2^432117-113215	130081	Enzo Doria	07/2014
1938	2^431804+72511	129986	Enzo Doria	04/2016
1939	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
1940	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
1941	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
1942	2^430807+1869563	129686	Enzo Doria	05/2016
1943	2^430721-21429	129660	Enzo Doria	07/2013
1944	2^430415-276271	129568	Enzo Doria	07/2015
1945	2^430142-2791721	129486	Enzo Doria	03/2016
1946	(7*10^129472-13)/3	129473	Robert Price	07/2018
1947	2^429568-21017	129313	Enzo Doria	07/2013
1948	(11*10^129239-179)/3	129240	Robert Price	09/2018
1949	2^429194-112685	129201	Enzo Doria	06/2014
1950	2^429145-2780449	129186	Enzo Doria	04/2016
1951	2^428892-113453	129110	Enzo Doria	07/2014
1952	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
1953	2^428727-113959	129060	Enzo Doria	10/2014
1954	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
1955	(10^129051-31)/3	129051	Serge Batalov	12/2014
1956	2^428564+71161	129011	Enzo Doria	04/2016
1957	2^428502-113285	128992	Enzo Doria	07/2014
1958	2^428421-21373	128968	Enzo Doria	06/2013
1959	L(616787)	128901	Henri Lifchitz	09/2008
1960	91^65772-2	128851	Lelio R Paula	05/2017
1961	2^428022+43	128848	Lelio R Paula	05/2017
1962	2^427999-459397	128841	Enzo Doria	05/2015
1963	2^427993+76847	128839	Enzo Doria	05/2016
1964	2^427824-1851507	128788	Enzo Doria	08/2015
1965	2^427807-21469	128783	Enzo Doria	07/2013
1966	11^123594-240	128710	Enzo Doria	09/2012
1967	2^427504-21503	128692	Enzo Doria	07/2013
1968	2^427420+91	128667	Lelio R Paula	05/2017
1969	2^427269-113635	128621	Enzo Doria	08/2014
1970	2^427130+1877569	128579	Enzo Doria	08/2016
1971	2^427016-115349	128545	Enzo Doria	07/2015
1972	(4*10^128510+137)/3	128511	Robert Price	03/2018
1973	2^426889-112879	128507	Enzo Doria	06/2014
1974	2^426804+1869931	128481	Enzo Doria	05/2016
1975	2^426750+77635	128465	Enzo Doria	05/2016
1976	2^426425-91	128367	Lelio R Paula	05/2017
1977	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
1978	2^426352+74971	128345	Enzo Doria	04/2016
1979	4*10^128343-21	128344	Robert Price	09/2018
1980	2^426300-1863689	128330	Enzo Doria	03/2016
1981	2^426293+1881017	128327	Enzo Doria	11/2016
1982	2^426043+35	128252	Robert Price	11/2015
1983	(4*10^128244-19)/3	128245	Robert Price	03/2018
1984	2^425808-459959	128181	Enzo Doria	06/2015
1985	2^425627-113605	128127	Enzo Doria	08/2014
1986	18565^30002-30002^18565	128070	Norbert Schneider	01/2015
1987	(2^425287-9)/2737	128021	Lelio R Paula	05/2015
1988	(3*2^425233-1)/25	128007	Lelio R Paula	05/2014
1989	2^425205+4911	128000	Marek Hubal	02/2017
1990	2^425118-113663	127974	Enzo Doria	08/2014
1991	2^425061+1869761	127957	Enzo Doria	05/2016
1992	2^424918-21141	127914	Enzo Doria	07/2013
1993	2^424864-29489	127897	Enzo Doria	08/2015
1994	(97*10^127858-1)/3	127860	Serge Batalov	12/2014
1995	2^424632-2786639	127827	Enzo Doria	03/2016
1996	2^424577-113755	127811	Enzo Doria	09/2014
1997	(7*2^424512-1)/3	127792	Lelio R Paula	05/2014
1998	11^122629-720	127705	Enzo Doria	11/2012
1999	2^423696-21429	127546	Enzo Doria	07/2013
2000	2^423664-1864559	127536	Enzo Doria	03/2016

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Probable Primes Top 10000

(252402 PRPs in the top)