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	2^459063-345307	138192	Enzo Doria	06/2015
1752	2*10^138162-43	138163	Robert Price	04/2018
1753	2^458927-112747	138151	Enzo Doria	06/2014
1754	2^458927-69217	138151	Enzo Doria	11/2015
1755	555555*2^458524+1513	138036	Darren Bedwell	08/2009
1756	2^458465+2^32+1	138012	T. D. Noe	06/2007
1757	2^458321-113053	137969	Enzo Doria	07/2014
1758	2^458298+79459	137962	Enzo Doria	06/2016
1759	2^458248-21815	137947	Enzo Doria	07/2013
1760	2^458194+1876549	137931	Enzo Doria	07/2016
1761	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
1762	2^457937+57	137853	Lelio R Paula	09/2017
1763	(8*10^137845+13)/3	137846	Robert Price	06/2018
1764	2^457822+105	137819	Donovan Johnson	06/2006
1765	2^457754-113711	137798	Enzo Doria	09/2014
1766	11^132315-360	137792	Enzo Doria	09/2012
1767	2^457347-37	137676	Lelio R Paula	09/2017
1768	2^457322-2786393	137668	Enzo Doria	10/2015
1769	gcd(Phi(699340,10),(10^34967+1)^3(10^34967+1+10^17484)-(10^69934+10^34967)(10^17484-1)+10^104901)	137664	Serge Batalov	04/2015
1770	2^457240-59939	137643	Enzo Doria	10/2015
1771	2^457120-21575	137607	Enzo Doria	07/2013
1772	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
1773	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
1774	2^456796-113513	137510	Enzo Doria	08/2014
1775	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
1776	2^456503-114361	137422	Enzo Doria	01/2015
1777	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
1778	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
1779	2^455922+76249	137247	Enzo Doria	05/2016
1780	14^119741-119741^14	137239	Serge Batalov	04/2016
1781	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
1782	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
1783	124^65536+57^65536	137195	Serge Batalov	03/2018
1784	2^455689+72677	137177	Enzo Doria	04/2016
1785	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
1786	(37^87421-1)/36	137093	Robert Price	03/2012
1787	2^455323-57	137066	Lelio R Paula	09/2017
1788	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
1789	2^455025-112723	136977	Enzo Doria	06/2014
1790	2^454675-1777	136871	Yves Minet	10/2011
1791	3*10^136829+29	136830	Robert Price	05/2018
1792	4*10^136813-57	136814	Robert Price	10/2018
1793	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
1794	2^454348-53	136773	Lelio R Paula	09/2017
1795	31^91680-2	136729	Lelio R Paula	05/2017
1796	2^454199-113697	136728	Enzo Doria	09/2014
1797	(13*10^136687+47)/3	136688	Robert Price	10/2018
1798	2^453935-2791357	136649	Enzo Doria	01/2016
1799	2^453906-69131	136640	Enzo Doria	11/2015
1800	2^453791+1873913	136605	Enzo Doria	06/2016
1801	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
1802	2^453503-2788297	136519	Enzo Doria	11/2015
1803	2^453267-113827	136447	Enzo Doria	09/2014
1804	2^453102+1877629	136398	Enzo Doria	08/2016
1805	L(651821)	136223	Henri Lifchitz	09/2008
1806	2^452460+77701	136205	Enzo Doria	05/2016
1807	2^452440-114755	136199	Enzo Doria	04/2015
1808	2*10^136057-43	136058	Robert Price	04/2018
1809	(2^451956-5)/181	136051	Lelio R Paula	07/2015
1810	2^451947-22165	136050	Enzo Doria	07/2013
1811	2^451787-21805	136002	Enzo Doria	07/2013
1812	2^451734-112817	135986	Enzo Doria	06/2014
1813	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
1814	2^451705-21879	135977	Enzo Doria	07/2013
1815	2^451560-112349	135934	Enzo Doria	06/2014
1816	2^451530+45	135925	Lelio R Paula	08/2017
1817	2^451450-21743	135900	Enzo Doria	07/2013
1818	2^450805+65	135706	Lelio R Paula	08/2017
1819	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
1820	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
1821	2^449944-113247	135447	Enzo Doria	07/2014
1822	2^449770-113247	135395	Enzo Doria	07/2014
1823	2^449637-21471	135355	Enzo Doria	07/2013
1824	2^449571-75	135335	Lelio R Paula	08/2017
1825	(14*10^135301-53)/3	135302	Robert Price	12/2018
1826	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
1827	(13*10^135279+437)/9	135280	Robert Price	04/2018
1828	2^449330-35	135262	Lelio R Paula	08/2017
1829	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
1830	(13*10^135184-43)/3	135185	Robert Price	11/2018
1831	2^449049-115309	135178	Enzo Doria	07/2015
1832	(10^135174+191)/3	135174	Robert Price	02/2018
1833	2^449030-15	135172	Lelio R Paula	08/2017
1834	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
1835	2^448762-351401	135091	Enzo Doria	07/2015
1836	2*10^135083-43	135084	Robert Price	04/2018
1837	5*10^135019+77	135020	Robert Price	12/2018
1838	(10^135011+719)/9	135011	Serge Batalov	12/2014
1839	2^448386-2786261	134978	Enzo Doria	03/2016
1840	2^448113-113949	134896	Enzo Doria	11/2014
1841	2^447888-2786639	134828	Enzo Doria	03/2016
1842	2^447870-396765	134823	Enzo Doria	07/2013
1843	2^447766-21791	134791	Enzo Doria	07/2013
1844	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
1845	2^447552-1019	134727	Yves Minet	02/2014
1846	(2*10^134720-41)/3	134720	Robert Price	02/2018
1847	2^447437-113569	134692	Enzo Doria	08/2014
1848	2^447426-65	134689	Lelio R Paula	08/2017
1849	2^447357-2797573	134668	Enzo Doria	04/2016
1850	2^447278+93	134645	Lelio R Paula	08/2017
1851	2^447094-113193	134589	Enzo Doria	07/2014
1852	3^282041-9934	134568	Enzo Doria	05/2014
1853	2^447019-109039	134567	Enzo Doria	04/2014
1854	2^446990-22041	134558	Enzo Doria	07/2013
1855	123^64370+122	134528	Karsten Bonath	04/2018
1856	2^446782-39701	134495	Enzo Doria	09/2015
1857	2^446494-16485	134409	Enzo Doria	04/2013
1858	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
1859	2^446441+65	134393	Lelio R Paula	08/2017
1860	(10^134385+719)/9	134385	Serge Batalov	12/2014
1861	(2*10^134364+529)/9	134364	Robert Price	01/2018
1862	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
1863	(2^446022-7)/339	134264	Lelio R Paula	07/2015
1864	63^74568+2	134174	Lelio R Paula	06/2017
1865	2^445671-22071	134161	Enzo Doria	07/2013
1866	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
1867	2^445515-113859	134114	Enzo Doria	10/2014
1868	2^445328-216917	134058	Enzo Doria	05/2014
1869	2^445202+1874899	134020	Enzo Doria	06/2016
1870	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
1871	(35*10^133979-593)/9	133980	Robert Price	07/2018
1872	2*10^133955+51	133956	Robert Price	05/2018
1873	2^444964-113639	133948	Enzo Doria	08/2014
1874	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
1875	2^444784-113859	133894	Enzo Doria	10/2014
1876	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
1877	62^74521-61^74521	133571	Robert Price	05/2013
1878	2^443198-1867301	133416	Enzo Doria	03/2016
1879	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
1880	2^442799+1874633	133296	Enzo Doria	06/2016
1881	L(637751)	133283	Henri Lifchitz	09/2008
1882	109^65410-2	133269	Lelio R Paula	10/2017
1883	2^442688-113489	133263	Enzo Doria	08/2014
1884	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
1885	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
1886	2^442437-1849993	133187	Enzo Doria	08/2015
1887	2^442430-2791721	133185	Enzo Doria	03/2016
1888	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
1889	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
1890	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
1891	2^441781-2787883	132990	Enzo Doria	03/2016
1892	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
1893	2^441618+37	132941	Lelio R Paula	08/2017
1894	2^441521-113575	132912	Enzo Doria	08/2014
1895	2^441396-65	132874	Lelio R Paula	08/2017
1896	2^441330+1871959	132854	Enzo Doria	05/2016
1897	2^441063+383	132774	Lelio R Paula	06/2012
1898	2^440846+1870909	132708	Enzo Doria	05/2016
1899	2^440656-113489	132651	Enzo Doria	08/2014
1900	numbpart(14180123587)	132646	Serge Batalov	04/2017
1901	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
1902	(38^83891+1)/39	132529	Robert Price	09/2013
1903	2*10^132493-43	132494	Robert Price	04/2018
1904	2^439931-21	132433	Lelio R Paula	08/2017
1905	47^79201-46^79201	132432	Robert Price	10/2012
1906	2^439897-113653	132423	Enzo Doria	08/2014
1907	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
1908	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
1909	2^439576-113247	132326	Enzo Doria	07/2014
1910	2^439497-29143	132302	Enzo Doria	07/2015
1911	2^439409-114193	132276	Enzo Doria	12/2014
1912	(44*10^132233-233)/9	132234	Robert Price	01/2019
1913	9*10^132148-7	132149	Robert Price	09/2015
1914	2^438845+1870217	132106	Enzo Doria	05/2016
1915	2^438789+87855	132089	Lelio R Paula	01/2016
1916	2^438774-2786411	132085	Enzo Doria	03/2016
1917	2^438755-1848205	132079	Enzo Doria	07/2015
1918	2^438739-112087	132074	Enzo Doria	06/2014
1919	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
1920	L(631181)	131910	Henri Lifchitz	09/2008
1921	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
1922	2^438079-1863877	131875	Enzo Doria	03/2016
1923	(2^438067+5)/329	131869	Lelio R Paula	06/2015
1924	2^437908-113855	131824	Enzo Doria	09/2014
1925	2^437884-286349	131817	Enzo Doria	07/2015
1926	(11*10^131784-17)/3	131785	Robert Price	06/2018
1927	3^276062-112292	131716	Enzo Doria	07/2014
1928	2^437343+75953	131654	Enzo Doria	04/2016
1929	35^85243-34^85243	131621	Robert Price	05/2012
1930	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
1931	2^436451+1884713	131385	Enzo Doria	03/2017
1932	2^436365+35	131359	Robert Price	11/2015
1934	2^436300+1866871	131340	Enzo Doria	03/2016
1933	(7*10^131339+179)/3	131340	Robert Price	09/2018
1935	(37*10^131270+341)/9	131271	Robert Price	08/2018
1936	(5*10^131223-29)/3	131224	Robert Price	03/2018
1937	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
1938	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
1940	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
1939	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
1941	2^435773+1875557	131181	Enzo Doria	06/2016
1942	(25*10^131144-7)/9	131145	Robert Price	05/2018
1943	2^435612-2789939	131133	Enzo Doria	12/2015
1944	66^72047-65^72047	131093	Robert Price	09/2013
1945	(5*10^131090+37)/3	131091	Robert Price	03/2018
1946	2^435468+75631	131089	Enzo Doria	04/2016
1947	37^83588-2	131083	Lelio R Paula	08/2015
1948	(4^217720+11)/3	131081	Robert Price	02/2017
1949	2^435202-113193	131009	Enzo Doria	07/2014
1950	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
1951	2^434835-111937	130899	Enzo Doria	05/2014
1952	2^434685+72257	130854	Enzo Doria	04/2016
1953	(7*10^130825+113)/3	130826	Robert Price	02/2018
1954	2^434539-29317	130810	Enzo Doria	07/2015
1955	2^434469-114259	130789	Enzo Doria	01/2015
1956	2^434246+33	130722	Robert Price	11/2015
1957	2^433911-91	130621	Lelio R Paula	06/2017
1958	2^433744-114419	130570	Enzo Doria	02/2015
1960	2^433708+1869451	130560	Enzo Doria	05/2016
1959	2^433710+93	130560	Lelio R Paula	06/2017
1961	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
1962	4*10^130480+9	130481	Robert Price	05/2015
1963	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
1964	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
1965	2^433023-113497	130353	Enzo Doria	08/2014
1966	2^433002+1179379	130347	Enzo Doria	06/2016
1967	2^432974+19	130339	Robert Price	08/2015
1968	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
1969	2^432217+41	130111	Lelio R Paula	06/2017
1970	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
1971	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
1972	97^65480-2	130094	Lelio R Paula	05/2017
1973	4*10^130088-89	130089	Robert Price	11/2018
1974	2^432117-113215	130081	Enzo Doria	07/2014
1975	2^431804+72511	129986	Enzo Doria	04/2016
1976	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
1977	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
1978	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
1979	2^430807+1869563	129686	Enzo Doria	05/2016
1980	2^430721-21429	129660	Enzo Doria	07/2013
1981	2^430415-276271	129568	Enzo Doria	07/2015
1982	2^430142-2791721	129486	Enzo Doria	03/2016
1983	(7*10^129472-13)/3	129473	Robert Price	07/2018
1984	2^429568-21017	129313	Enzo Doria	07/2013
1985	(11*10^129239-179)/3	129240	Robert Price	09/2018
1986	2^429194-112685	129201	Enzo Doria	06/2014
1987	2^429145-2780449	129186	Enzo Doria	04/2016
1988	2^428892-113453	129110	Enzo Doria	07/2014
1989	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
1990	2^428727-113959	129060	Enzo Doria	10/2014
1991	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
1992	(10^129051-31)/3	129051	Serge Batalov	12/2014
1993	2^428564+71161	129011	Enzo Doria	04/2016
1994	2^428502-113285	128992	Enzo Doria	07/2014
1995	2^428421-21373	128968	Enzo Doria	06/2013
1996	L(616787)	128901	Henri Lifchitz	09/2008
1997	91^65772-2	128851	Lelio R Paula	05/2017
1998	2^428022+43	128848	Lelio R Paula	05/2017
1999	2^427999-459397	128841	Enzo Doria	05/2015
2000	2^427993+76847	128839	Enzo Doria	05/2016

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