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	2^464864-17	139939	Lelio R Paula	09/2017
1752	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
1753	(13*10^139782+191)/3	139783	Robert Price	11/2018
1754	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
1755	3*10^139722+13	139723	Robert Price	07/2018
1756	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
1757	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
1758	2^463633-2788423	139568	Enzo Doria	11/2015
1759	2^463271-109501	139459	Enzo Doria	04/2014
1760	(5*10^139457+79)/3	139458	Robert Price	03/2018
1761	2^463237-99	139449	Lelio R Paula	09/2017
1762	(49*10^139442+383)/9	139443	Robert Price	04/2019
1763	(7*10^139417-547)/9	139417	Robert Price	01/2018
1764	(10^139398+191)/3	139398	Robert Price	02/2018
1765	2^463019+79463	139383	Enzo Doria	06/2016
1766	3^292129-112756	139381	Enzo Doria	07/2014
1767	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
1768	2^462855-1865707	139334	Enzo Doria	02/2016
1769	2^462786-292043	139313	Enzo Doria	08/2015
1770	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
1771	(17*10^139239+67)/3	139240	Robert Price	01/2019
1772	2^462238-935	139148	Yves Minet	02/2014
1773	2^461228+1870441	138844	Enzo Doria	05/2016
1774	2^461204-113675	138837	Enzo Doria	08/2014
1775	(2^461139-7)/47	138815	Lelio R Paula	08/2015
1776	(17*10^138812-521)/9	138813	Robert Price	04/2018
1777	3*10^138811-11	138812	Robert Price	07/2018
1778	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
1779	(43*10^138648+101)/9	138649	Robert Price	11/2018
1780	2^460567-113541	138645	Enzo Doria	08/2014
1781	7*10^138604+3	138605	Robert Price	08/2015
1782	2^460330+69	138574	Lelio R Paula	09/2017
1783	2^460078-69581	138498	Enzo Doria	12/2015
1784	2^459768+1531	138404	Lelio R Paula	06/2012
1785	2^459343-113611	138277	Enzo Doria	08/2014
1786	2^459199+1874393	138233	Enzo Doria	06/2016
1787	2^459063-345307	138192	Enzo Doria	06/2015
1788	2*10^138162-43	138163	Robert Price	04/2018
1789	2^458927-112747	138151	Enzo Doria	06/2014
1790	2^458927-69217	138151	Enzo Doria	11/2015
1791	555555*2^458524+1513	138036	Darren Bedwell	08/2009
1792	2^458465+2^32+1	138012	T. D. Noe	06/2007
1793	2^458321-113053	137969	Enzo Doria	07/2014
1794	2^458298+79459	137962	Enzo Doria	06/2016
1795	2^458248-21815	137947	Enzo Doria	07/2013
1796	2^458194+1876549	137931	Enzo Doria	07/2016
1797	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
1798	2^457937+57	137853	Lelio R Paula	09/2017
1799	(8*10^137845+13)/3	137846	Robert Price	06/2018
1800	2^457822+105	137819	Donovan Johnson	06/2006
1801	2^457754-113711	137798	Enzo Doria	09/2014
1802	11^132315-360	137792	Enzo Doria	09/2012
1803	2^457347-37	137676	Lelio R Paula	09/2017
1804	2^457322-2786393	137668	Enzo Doria	10/2015
1805	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
1806	2^457240-59939	137643	Enzo Doria	10/2015
1807	2^457120-21575	137607	Enzo Doria	07/2013
1808	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
1809	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
1810	2^456796-113513	137510	Enzo Doria	08/2014
1811	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
1812	2^456503-114361	137422	Enzo Doria	01/2015
1813	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
1814	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
1815	2^455922+76249	137247	Enzo Doria	05/2016
1816	14^119741-119741^14	137239	Serge Batalov	04/2016
1817	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
1818	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
1819	124^65536+57^65536	137195	Serge Batalov	03/2018
1820	2^455689+72677	137177	Enzo Doria	04/2016
1821	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
1822	(37^87421-1)/36	137093	Robert Price	03/2012
1823	2^455323-57	137066	Lelio R Paula	09/2017
1824	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
1825	2^455025-112723	136977	Enzo Doria	06/2014
1826	2^454675-1777	136871	Yves Minet	10/2011
1827	3*10^136829+29	136830	Robert Price	05/2018
1828	4*10^136813-57	136814	Robert Price	10/2018
1829	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
1830	2^454348-53	136773	Lelio R Paula	09/2017
1831	31^91680-2	136729	Lelio R Paula	05/2017
1832	2^454199-113697	136728	Enzo Doria	09/2014
1833	(13*10^136687+47)/3	136688	Robert Price	10/2018
1834	2^453935-2791357	136649	Enzo Doria	01/2016
1835	2^453906-69131	136640	Enzo Doria	11/2015
1836	2^453791+1873913	136605	Enzo Doria	06/2016
1837	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
1838	580^49413+49413^580	136550	Norbert Schneider	02/2019
1839	2^453503-2788297	136519	Enzo Doria	11/2015
1840	2^453267-113827	136447	Enzo Doria	09/2014
1841	2^453102+1877629	136398	Enzo Doria	08/2016
1842	L(651821)	136223	Henri Lifchitz	09/2008
1843	2^452460+77701	136205	Enzo Doria	05/2016
1844	2^452440-114755	136199	Enzo Doria	04/2015
1845	(47*10^136141+493)/9	136142	Robert Price	03/2019
1846	2*10^136057-43	136058	Robert Price	04/2018
1847	(2^451956-5)/181	136051	Lelio R Paula	07/2015
1848	2^451947-22165	136050	Enzo Doria	07/2013
1849	2^451787-21805	136002	Enzo Doria	07/2013
1850	2^451734-112817	135986	Enzo Doria	06/2014
1851	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
1852	2^451705-21879	135977	Enzo Doria	07/2013
1853	2^451560-112349	135934	Enzo Doria	06/2014
1854	2^451530+45	135925	Lelio R Paula	08/2017
1855	2^451450-21743	135900	Enzo Doria	07/2013
1856	2^450805+65	135706	Lelio R Paula	08/2017
1857	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
1858	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
1859	2^449944-113247	135447	Enzo Doria	07/2014
1860	2^449770-113247	135395	Enzo Doria	07/2014
1861	2^449637-21471	135355	Enzo Doria	07/2013
1862	2^449571-75	135335	Lelio R Paula	08/2017
1863	(14*10^135301-53)/3	135302	Robert Price	12/2018
1864	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
1865	(13*10^135279+437)/9	135280	Robert Price	04/2018
1866	2^449330-35	135262	Lelio R Paula	08/2017
1867	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
1868	(13*10^135184-43)/3	135185	Robert Price	11/2018
1869	2^449049-115309	135178	Enzo Doria	07/2015
1870	(10^135174+191)/3	135174	Robert Price	02/2018
1871	2^449030-15	135172	Lelio R Paula	08/2017
1872	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
1873	2^448762-351401	135091	Enzo Doria	07/2015
1874	2*10^135083-43	135084	Robert Price	04/2018
1875	5*10^135019+77	135020	Robert Price	12/2018
1876	(10^135011+719)/9	135011	Serge Batalov	12/2014
1877	2^448386-2786261	134978	Enzo Doria	03/2016
1878	2^448113-113949	134896	Enzo Doria	11/2014
1879	2^447888-2786639	134828	Enzo Doria	03/2016
1880	2^447870-396765	134823	Enzo Doria	07/2013
1881	2^447766-21791	134791	Enzo Doria	07/2013
1882	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
1883	2^447552-1019	134727	Yves Minet	02/2014
1884	(2*10^134720-41)/3	134720	Robert Price	02/2018
1885	2^447437-113569	134692	Enzo Doria	08/2014
1886	2^447426-65	134689	Lelio R Paula	08/2017
1887	2^447357-2797573	134668	Enzo Doria	04/2016
1888	2^447278+93	134645	Lelio R Paula	08/2017
1889	2^447094-113193	134589	Enzo Doria	07/2014
1890	3^282041-9934	134568	Enzo Doria	05/2014
1891	2^447019-109039	134567	Enzo Doria	04/2014
1892	2^446990-22041	134558	Enzo Doria	07/2013
1893	123^64370+122	134528	Karsten Bonath	04/2018
1894	2^446782-39701	134495	Enzo Doria	09/2015
1895	2^446494-16485	134409	Enzo Doria	04/2013
1896	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
1897	2^446441+65	134393	Lelio R Paula	08/2017
1898	(10^134385+719)/9	134385	Serge Batalov	12/2014
1899	(2*10^134364+529)/9	134364	Robert Price	01/2018
1900	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
1901	(2^446022-7)/339	134264	Lelio R Paula	07/2015
1902	63^74568+2	134174	Lelio R Paula	06/2017
1903	2^445671-22071	134161	Enzo Doria	07/2013
1904	532^49205+49205^532	134129	Norbert Schneider	02/2019
1905	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
1906	2^445515-113859	134114	Enzo Doria	10/2014
1907	(22*10^134111-37)/3	134112	Robert Price	04/2019
1908	2^445328-216917	134058	Enzo Doria	05/2014
1909	2^445202+1874899	134020	Enzo Doria	06/2016
1910	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
1911	(35*10^133979-593)/9	133980	Robert Price	07/2018
1912	2*10^133955+51	133956	Robert Price	05/2018
1913	2^444964-113639	133948	Enzo Doria	08/2014
1914	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
1915	2^444784-113859	133894	Enzo Doria	10/2014
1916	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
1917	62^74521-61^74521	133571	Robert Price	05/2013
1918	2^443198-1867301	133416	Enzo Doria	03/2016
1919	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
1920	2^442799+1874633	133296	Enzo Doria	06/2016
1921	L(637751)	133283	Henri Lifchitz	09/2008
1922	109^65410-2	133269	Lelio R Paula	10/2017
1923	2^442688-113489	133263	Enzo Doria	08/2014
1924	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
1925	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
1926	2^442437-1849993	133187	Enzo Doria	08/2015
1927	2^442430-2791721	133185	Enzo Doria	03/2016
1928	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
1929	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
1930	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
1931	2^441781-2787883	132990	Enzo Doria	03/2016
1932	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
1933	2^441618+37	132941	Lelio R Paula	08/2017
1934	2^441521-113575	132912	Enzo Doria	08/2014
1935	2^441396-65	132874	Lelio R Paula	08/2017
1936	2^441330+1871959	132854	Enzo Doria	05/2016
1937	2^441063+383	132774	Lelio R Paula	06/2012
1938	2^440846+1870909	132708	Enzo Doria	05/2016
1939	2^440656-113489	132651	Enzo Doria	08/2014
1940	numbpart(14180123587)	132646	Serge Batalov	04/2017
1941	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
1942	(38^83891+1)/39	132529	Robert Price	09/2013
1943	2*10^132493-43	132494	Robert Price	04/2018
1944	2^439931-21	132433	Lelio R Paula	08/2017
1945	47^79201-46^79201	132432	Robert Price	10/2012
1946	2^439897-113653	132423	Enzo Doria	08/2014
1947	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
1948	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
1949	2^439576-113247	132326	Enzo Doria	07/2014
1950	2^439497-29143	132302	Enzo Doria	07/2015
1951	2^439409-114193	132276	Enzo Doria	12/2014
1952	(44*10^132233-233)/9	132234	Robert Price	01/2019
1953	9*10^132148-7	132149	Robert Price	09/2015
1954	2^438845+1870217	132106	Enzo Doria	05/2016
1955	2^438789+87855	132089	Lelio R Paula	01/2016
1956	2^438774-2786411	132085	Enzo Doria	03/2016
1957	2^438755-1848205	132079	Enzo Doria	07/2015
1958	2^438739-112087	132074	Enzo Doria	06/2014
1959	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
1960	L(631181)	131910	Henri Lifchitz	09/2008
1961	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
1962	2^438079-1863877	131875	Enzo Doria	03/2016
1963	(2^438067+5)/329	131869	Lelio R Paula	06/2015
1964	2^437908-113855	131824	Enzo Doria	09/2014
1965	2^437884-286349	131817	Enzo Doria	07/2015
1966	(11*10^131784-17)/3	131785	Robert Price	06/2018
1967	3^276062-112292	131716	Enzo Doria	07/2014
1968	2^437343+75953	131654	Enzo Doria	04/2016
1969	35^85243-34^85243	131621	Robert Price	05/2012
1970	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
1971	2^436451+1884713	131385	Enzo Doria	03/2017
1972	2^436365+35	131359	Robert Price	11/2015
1973	2^436300+1866871	131340	Enzo Doria	03/2016
1974	(7*10^131339+179)/3	131340	Robert Price	09/2018
1975	(37*10^131270+341)/9	131271	Robert Price	08/2018
1976	(5*10^131223-29)/3	131224	Robert Price	03/2018
1977	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
1978	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
1979	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
1980	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
1981	2^435773+1875557	131181	Enzo Doria	06/2016
1982	(25*10^131144-7)/9	131145	Robert Price	05/2018
1983	2^435612-2789939	131133	Enzo Doria	12/2015
1984	66^72047-65^72047	131093	Robert Price	09/2013
1985	(5*10^131090+37)/3	131091	Robert Price	03/2018
1986	2^435468+75631	131089	Enzo Doria	04/2016
1987	37^83588-2	131083	Lelio R Paula	08/2015
1988	(4^217720+11)/3	131081	Robert Price	02/2017
1989	2^435202-113193	131009	Enzo Doria	07/2014
1990	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
1991	2^434835-111937	130899	Enzo Doria	05/2014
1992	2^434685+72257	130854	Enzo Doria	04/2016
1993	(7*10^130825+113)/3	130826	Robert Price	02/2018
1994	2^434539-29317	130810	Enzo Doria	07/2015
1995	2^434469-114259	130789	Enzo Doria	01/2015
1996	2^434246+33	130722	Robert Price	11/2015
1997	2^433911-91	130621	Lelio R Paula	06/2017
1998	2^433744-114419	130570	Enzo Doria	02/2015
1999	2^433708+1869451	130560	Enzo Doria	05/2016
2000	2^433710+93	130560	Lelio R Paula	06/2017

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Probable Primes Top 10000

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