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	7*10^142189+87	142190	Robert Price	07/2019
1752	2^472258+7	142164	Lelio R Paula	08/2015
1753	(23*10^142105+91)/3	142106	Robert Price	08/2019
1754	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
1755	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
1756	(16*10^142058+197)/3	142059	Robert Price	04/2019
1757	2^471792+1880881	142024	Enzo Doria	11/2016
1758	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
1759	(4*10^141926-79)/3	141927	Robert Price	02/2018
1760	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
1761	(14*10^141853+37)/3	141854	Robert Price	12/2018
1762	(41*10^141836-59)/9	141837	Robert Price	10/2018
1763	4*5^202913-9	141831	Lelio R Paula	04/2015
1764	2*7^167812-3	141818	Lelio R Paula	12/2014
1765	2^471043+35	141799	Robert Price	11/2015
1766	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
1767	(11*10^141718-131)/3	141719	Robert Price	09/2018
1768	2^470692+76771	141693	Enzo Doria	05/2016
1769	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
1770	2^470305-459373	141576	Enzo Doria	05/2015
1771	2^470183+72623	141540	Enzo Doria	04/2016
1772	2^470173-16465	141537	Enzo Doria	04/2013
1773	2^469974-1841	141477	Enzo Doria	05/2014
1774	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
1775	2*10^141448+63	141449	Robert Price	05/2018
1776	2^469824+43	141432	Lelio R Paula	09/2017
1777	2*10^141407-27	141408	Robert Price	05/2018
1778	2^469630-59711	141373	Enzo Doria	10/2015
1779	(25*10^141366-331)/9	141367	Robert Price	08/2018
1780	(2^469564-3)/611	141351	Lelio R Paula	08/2015
1781	197^61601+2	141342	Lelio R Paula	08/2017
1782	2^469372-112949	141296	Enzo Doria	07/2014
1784	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
1783	143^65536+106^65536	141253	Serge Batalov	03/2018
1785	2^469198+782569	141243	Enzo Doria	10/2016
1786	2^469076-2786939	141206	Enzo Doria	11/2015
1787	2^468804+1874941	141125	Enzo Doria	06/2016
1788	2^468787+81353	141119	Enzo Doria	08/2016
1789	2^468595-350407	141062	Enzo Doria	06/2015
1790	2^468564+87855	141052	Lelio R Paula	01/2016
1791	2^468551-21987	141048	Enzo Doria	07/2013
1792	2^468523-7	141040	Lelio R Paula	08/2015
1793	2^468405+87855	141004	Lelio R Paula	01/2016
1794	2^467978-113051	140876	Enzo Doria	07/2014
1795	2^467780-344429	140816	Enzo Doria	07/2015
1796	2^467605-1855603	140764	Enzo Doria	09/2015
1797	5*10^140744-7	140745	Robert Price	09/2015
1798	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
1799	2^467401-1850023	140702	Enzo Doria	08/2015
1800	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
1801	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
1802	2^467166-1854941	140631	Enzo Doria	09/2015
1803	2^466866-1840571	140541	Enzo Doria	06/2015
1804	2^466829-459523	140530	Enzo Doria	05/2015
1805	2^466692-113213	140489	Enzo Doria	07/2014
1806	(44*10^140410-503)/9	140411	Robert Price	12/2018
1807	153^64265-2	140400	Lelio R Paula	11/2017
1808	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
1809	2^466181-112735	140335	Enzo Doria	07/2014
1810	(5*10^140281-119)/3	140282	Robert Price	03/2018
1811	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
1812	2^465803-114817	140221	Enzo Doria	05/2015
1813	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
1814	2^465503-112735	140131	Enzo Doria	07/2014
1815	(16*10^140091+167)/3	140092	Robert Price	06/2019
1816	6^179964+179964^6-1	140040	Robert Price	04/2014
1817	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
1818	2^465072-344789	140001	Enzo Doria	07/2015
1819	5*10^139945+81	139946	Robert Price	03/2019
1820	2^464864-17	139939	Lelio R Paula	09/2017
1821	8*10^139920+51	139921	Robert Price	08/2019
1822	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
1823	(13*10^139782+191)/3	139783	Robert Price	11/2018
1824	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
1825	(74*10^139723+133)/9	139724	Robert Price	06/2019
1826	3*10^139722+13	139723	Robert Price	07/2018
1827	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
1828	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
1829	2^463633-2788423	139568	Enzo Doria	11/2015
1830	2^463271-109501	139459	Enzo Doria	04/2014
1831	(5*10^139457+79)/3	139458	Robert Price	03/2018
1832	2^463237-99	139449	Lelio R Paula	09/2017
1833	(49*10^139442+383)/9	139443	Robert Price	04/2019
1834	(7*10^139417-547)/9	139417	Robert Price	01/2018
1835	(10^139398+191)/3	139398	Robert Price	02/2018
1836	2^463019+79463	139383	Enzo Doria	06/2016
1837	3^292129-112756	139381	Enzo Doria	07/2014
1838	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
1839	2^462855-1865707	139334	Enzo Doria	02/2016
1840	2^462786-292043	139313	Enzo Doria	08/2015
1841	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
1842	(17*10^139239+67)/3	139240	Robert Price	01/2019
1843	2^462238-935	139148	Yves Minet	02/2014
1844	2^461228+1870441	138844	Enzo Doria	05/2016
1845	2^461204-113675	138837	Enzo Doria	08/2014
1846	(2^461139-7)/47	138815	Lelio R Paula	08/2015
1847	(17*10^138812-521)/9	138813	Robert Price	04/2018
1848	3*10^138811-11	138812	Robert Price	07/2018
1849	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
1850	(43*10^138648+101)/9	138649	Robert Price	11/2018
1851	2^460567-113541	138645	Enzo Doria	08/2014
1852	7*10^138604+3	138605	Robert Price	08/2015
1853	2^460330+69	138574	Lelio R Paula	09/2017
1854	(17*10^138569-77)/3	138570	Robert Price	08/2019
1855	2^460078-69581	138498	Enzo Doria	12/2015
1856	2^459768+1531	138404	Lelio R Paula	06/2012
1857	2^459343-113611	138277	Enzo Doria	08/2014
1858	2^459199+1874393	138233	Enzo Doria	06/2016
1859	2^459063-345307	138192	Enzo Doria	06/2015
1860	2*10^138162-43	138163	Robert Price	04/2018
1861	2^458927-112747	138151	Enzo Doria	06/2014
1862	2^458927-69217	138151	Enzo Doria	11/2015
1863	555555*2^458524+1513	138036	Darren Bedwell	08/2009
1864	2^458465+2^32+1	138012	T. D. Noe	06/2007
1865	2^458321-113053	137969	Enzo Doria	07/2014
1866	2^458298+79459	137962	Enzo Doria	06/2016
1867	2^458248-21815	137947	Enzo Doria	07/2013
1868	2^458194+1876549	137931	Enzo Doria	07/2016
1869	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
1870	(318259#+2625)/(3^257^5*22965193)	137899	Makoto Morimoto	06/2019
1871	2^457937+57	137853	Lelio R Paula	09/2017
1872	(8*10^137845+13)/3	137846	Robert Price	06/2018
1873	2^457822+105	137819	Donovan Johnson	06/2006
1874	2^457754-113711	137798	Enzo Doria	09/2014
1875	11^132315-360	137792	Enzo Doria	09/2012
1876	2^457347-37	137676	Lelio R Paula	09/2017
1877	2^457322-2786393	137668	Enzo Doria	10/2015
1878	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
1879	2^457240-59939	137643	Enzo Doria	10/2015
1880	2^457120-21575	137607	Enzo Doria	07/2013
1881	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
1882	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
1883	2^456796-113513	137510	Enzo Doria	08/2014
1884	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
1885	2^456503-114361	137422	Enzo Doria	01/2015
1886	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
1887	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
1888	2^455922+76249	137247	Enzo Doria	05/2016
1889	14^119741-119741^14	137239	Serge Batalov	04/2016
1890	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
1891	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
1892	124^65536+57^65536	137195	Serge Batalov	03/2018
1893	2^455689+72677	137177	Enzo Doria	04/2016
1894	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
1895	(37^87421-1)/36	137093	Robert Price	03/2012
1896	2^455323-57	137066	Lelio R Paula	09/2017
1897	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
1898	2^455025-112723	136977	Enzo Doria	06/2014
1899	2^454675-1777	136871	Yves Minet	10/2011
1900	3*10^136829+29	136830	Robert Price	05/2018
1901	4*10^136813-57	136814	Robert Price	10/2018
1902	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
1903	2^454348-53	136773	Lelio R Paula	09/2017
1904	31^91680-2	136729	Lelio R Paula	05/2017
1905	2^454199-113697	136728	Enzo Doria	09/2014
1906	7*10^136716+69	136717	Robert Price	07/2019
1907	(13*10^136687+47)/3	136688	Robert Price	10/2018
1908	2^453935-2791357	136649	Enzo Doria	01/2016
1909	2^453906-69131	136640	Enzo Doria	11/2015
1910	2^453791+1873913	136605	Enzo Doria	06/2016
1911	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
1912	580^49413+49413^580	136550	Norbert Schneider	02/2019
1913	2^453503-2788297	136519	Enzo Doria	11/2015
1914	2^453267-113827	136447	Enzo Doria	09/2014
1915	2^453102+1877629	136398	Enzo Doria	08/2016
1916	(62*10^136384-791)/9	136385	Robert Price	06/2019
1917	L(651821)	136223	Henri Lifchitz	09/2008
1918	2^452460+77701	136205	Enzo Doria	05/2016
1919	2^452440-114755	136199	Enzo Doria	04/2015
1920	(47*10^136141+493)/9	136142	Robert Price	03/2019
1921	2*10^136057-43	136058	Robert Price	04/2018
1922	(2^451956-5)/181	136051	Lelio R Paula	07/2015
1923	2^451947-22165	136050	Enzo Doria	07/2013
1924	2^451787-21805	136002	Enzo Doria	07/2013
1925	2^451734-112817	135986	Enzo Doria	06/2014
1926	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
1927	2^451705-21879	135977	Enzo Doria	07/2013
1928	2^451560-112349	135934	Enzo Doria	06/2014
1929	2^451530+45	135925	Lelio R Paula	08/2017
1930	2^451450-21743	135900	Enzo Doria	07/2013
1931	2^450805+65	135706	Lelio R Paula	08/2017
1932	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
1933	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
1934	2^449944-113247	135447	Enzo Doria	07/2014
1935	2^449770-113247	135395	Enzo Doria	07/2014
1936	2^449637-21471	135355	Enzo Doria	07/2013
1937	2^449571-75	135335	Lelio R Paula	08/2017
1938	(14*10^135301-53)/3	135302	Robert Price	12/2018
1939	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
1940	(13*10^135279+437)/9	135280	Robert Price	04/2018
1941	2^449330-35	135262	Lelio R Paula	08/2017
1942	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
1943	(13*10^135184-43)/3	135185	Robert Price	11/2018
1944	2^449049-115309	135178	Enzo Doria	07/2015
1945	(10^135174+191)/3	135174	Robert Price	02/2018
1946	2^449030-15	135172	Lelio R Paula	08/2017
1947	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
1948	2^448762-351401	135091	Enzo Doria	07/2015
1949	2*10^135083-43	135084	Robert Price	04/2018
1950	5*10^135019+77	135020	Robert Price	12/2018
1951	(10^135011+719)/9	135011	Serge Batalov	12/2014
1952	2^448386-2786261	134978	Enzo Doria	03/2016
1953	(73*10^134939+143)/9	134940	Robert Price	07/2019
1954	2^448113-113949	134896	Enzo Doria	11/2014
1955	2^447888-2786639	134828	Enzo Doria	03/2016
1956	2^447870-396765	134823	Enzo Doria	07/2013
1957	2^447766-21791	134791	Enzo Doria	07/2013
1958	(19*10^134786-49)/3	134787	Robert Price	05/2019
1959	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
1960	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
1961	2^447552-1019	134727	Yves Minet	02/2014
1962	(2*10^134720-41)/3	134720	Robert Price	02/2018
1963	2^447437-113569	134692	Enzo Doria	08/2014
1964	2^447426-65	134689	Lelio R Paula	08/2017
1965	2^447357-2797573	134668	Enzo Doria	04/2016
1966	2^447278+93	134645	Lelio R Paula	08/2017
1967	2^447094-113193	134589	Enzo Doria	07/2014
1968	3^282041-9934	134568	Enzo Doria	05/2014
1969	2^447019-109039	134567	Enzo Doria	04/2014
1970	2^446990-22041	134558	Enzo Doria	07/2013
1971	123^64370+122	134528	Karsten Bonath	04/2018
1972	2^446782-39701	134495	Enzo Doria	09/2015
1973	2^446494-16485	134409	Enzo Doria	04/2013
1974	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
1975	2^446441+65	134393	Lelio R Paula	08/2017
1976	(10^134385+719)/9	134385	Serge Batalov	12/2014
1977	(2*10^134364+529)/9	134364	Robert Price	01/2018
1978	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
1979	(2^446022-7)/339	134264	Lelio R Paula	07/2015
1980	63^74568+2	134174	Lelio R Paula	06/2017
1981	2^445671-22071	134161	Enzo Doria	07/2013
1982	532^49205+49205^532	134129	Norbert Schneider	02/2019
1983	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
1984	2^445515-113859	134114	Enzo Doria	10/2014
1985	(22*10^134111-37)/3	134112	Robert Price	04/2019
1986	2^445328-216917	134058	Enzo Doria	05/2014
1987	2^445202+1874899	134020	Enzo Doria	06/2016
1988	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
1989	(35*10^133979-593)/9	133980	Robert Price	07/2018
1990	2*10^133955+51	133956	Robert Price	05/2018
1991	2^444964-113639	133948	Enzo Doria	08/2014
1992	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
1993	2^444784-113859	133894	Enzo Doria	10/2014
1994	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
1995	62^74521-61^74521	133571	Robert Price	05/2013
1996	2^443198-1867301	133416	Enzo Doria	03/2016
1997	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
1998	2^442799+1874633	133296	Enzo Doria	06/2016
1999	L(637751)	133283	Henri Lifchitz	09/2008
2000	109^65410-2	133269	Lelio R Paula	10/2017

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