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	2^479348-2792219	144299	Enzo Doria	02/2016
1752	3^302389-6242	144277	Enzo Doria	05/2014
1753	2*10^144220-3	144221	Robert Price	07/2015
1754	2^478904-109109	144165	Enzo Doria	04/2014
1755	2^478337-115333	143994	Enzo Doria	07/2015
1756	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
1757	88^74047-87^74047	143984	Robert Price	05/2015
1758	(19*10^143963+467)/9	143964	Robert Price	02/2018
1759	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
1760	2^478088+27	143919	Robert Price	11/2015
1761	2^477475-22071	143735	Enzo Doria	07/2013
1762	2^477417-22123	143717	Enzo Doria	07/2013
1763	2^477359-3577	143700	Yves Minet	03/2017
1764	(14*10^143662-71)/3	143663	Robert Price	12/2018
1765	2^476936-396765	143573	Enzo Doria	07/2013
1766	2^476888-2791229	143558	Enzo Doria	01/2016
1767	2^476868-1859939	143552	Enzo Doria	11/2015
1768	755^49878+49878^755	143547	Norbert Schneider	04/2019
1769	2^476558-113627	143459	Enzo Doria	08/2014
1770	2^476478-45	143435	Lelio R Paula	11/2017
1771	(2^475854+9)/73	143245	Lelio R Paula	08/2015
1772	2^475813-113239	143234	Enzo Doria	07/2014
1773	2^475624-114059	143178	Enzo Doria	11/2014
1774	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
1775	2^475480-2786129	143134	Enzo Doria	10/2015
1776	(19*10^143129-43)/3	143130	Robert Price	05/2019
1777	(14*10^143097+73)/3	143098	Robert Price	12/2018
1778	2^475299-111937	143080	Enzo Doria	05/2014
1779	2^475160-2797859	143038	Enzo Doria	04/2016
1780	(2^475069+3)/395	143008	Lelio R Paula	08/2015
1781	2^475027-461437	142998	Enzo Doria	07/2015
1782	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
1783	(8*10^142932+43)/3	142933	Robert Price	06/2018
1784	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
1785	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
1786	2^474417-59923	142814	Enzo Doria	10/2015
1787	4*10^142810-21	142811	Robert Price	09/2018
1788	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
1789	2^474053+2897	142705	Lelio R Paula	08/2012
1790	(10^142699+359)/9	142699	Serge Batalov	12/2014
1791	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
1792	2^473740-1856639	142610	Enzo Doria	09/2015
1793	2^473617-114223	142573	Enzo Doria	12/2014
1794	2^473257+1873217	142465	Enzo Doria	06/2016
1795	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
1796	(14*10^142440+61)/3	142441	Robert Price	12/2018
1797	(10^142425+359)/9	142425	Serge Batalov	12/2014
1798	2^473101+773027	142418	Enzo Doria	05/2016
1799	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
1800	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
1801	2^472634-109511	142278	Enzo Doria	04/2014
1802	(48^84589+1)/49	142213	Robert Price	01/2014
1803	7*10^142189+87	142190	Robert Price	07/2019
1804	2^472258+7	142164	Lelio R Paula	08/2015
1805	(23*10^142105+91)/3	142106	Robert Price	08/2019
1806	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
1807	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
1808	(16*10^142058+197)/3	142059	Robert Price	04/2019
1809	2^471792+1880881	142024	Enzo Doria	11/2016
1810	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
1811	(4*10^141926-79)/3	141927	Robert Price	02/2018
1812	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
1813	(14*10^141853+37)/3	141854	Robert Price	12/2018
1814	(41*10^141836-59)/9	141837	Robert Price	10/2018
1815	4*5^202913-9	141831	Lelio R Paula	04/2015
1816	2*7^167812-3	141818	Lelio R Paula	12/2014
1817	2^471043+35	141799	Robert Price	11/2015
1818	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
1819	(11*10^141718-131)/3	141719	Robert Price	09/2018
1820	2^470692+76771	141693	Enzo Doria	05/2016
1821	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
1822	2^470305-459373	141576	Enzo Doria	05/2015
1823	2^470183+72623	141540	Enzo Doria	04/2016
1824	2^470173-16465	141537	Enzo Doria	04/2013
1825	2^469974-1841	141477	Enzo Doria	05/2014
1826	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
1827	2*10^141448+63	141449	Robert Price	05/2018
1828	2^469824+43	141432	Lelio R Paula	09/2017
1829	2*10^141407-27	141408	Robert Price	05/2018
1830	2^469630-59711	141373	Enzo Doria	10/2015
1831	(25*10^141366-331)/9	141367	Robert Price	08/2018
1832	(2^469564-3)/611	141351	Lelio R Paula	08/2015
1833	197^61601+2	141342	Lelio R Paula	08/2017
1834	2^469372-112949	141296	Enzo Doria	07/2014
1836	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
1835	143^65536+106^65536	141253	Serge Batalov	03/2018
1837	2^469198+782569	141243	Enzo Doria	10/2016
1838	2^469076-2786939	141206	Enzo Doria	11/2015
1839	2^468804+1874941	141125	Enzo Doria	06/2016
1840	2^468787+81353	141119	Enzo Doria	08/2016
1841	2^468595-350407	141062	Enzo Doria	06/2015
1842	2^468564+87855	141052	Lelio R Paula	01/2016
1843	2^468551-21987	141048	Enzo Doria	07/2013
1844	2^468523-7	141040	Lelio R Paula	08/2015
1845	(25*10^141019-13)/3	141020	Robert Price	09/2019
1846	2^468405+87855	141004	Lelio R Paula	01/2016
1847	2^467978-113051	140876	Enzo Doria	07/2014
1848	2^467780-344429	140816	Enzo Doria	07/2015
1849	2^467605-1855603	140764	Enzo Doria	09/2015
1850	5*10^140744-7	140745	Robert Price	09/2015
1851	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
1852	2^467401-1850023	140702	Enzo Doria	08/2015
1853	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
1854	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
1855	2^467166-1854941	140631	Enzo Doria	09/2015
1856	2^466866-1840571	140541	Enzo Doria	06/2015
1857	2^466829-459523	140530	Enzo Doria	05/2015
1858	2^466692-113213	140489	Enzo Doria	07/2014
1859	(44*10^140410-503)/9	140411	Robert Price	12/2018
1860	153^64265-2	140400	Lelio R Paula	11/2017
1861	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
1862	(29*10^140337-17)/3	140338	Robert Price	09/2019
1863	2^466181-112735	140335	Enzo Doria	07/2014
1864	(5*10^140281-119)/3	140282	Robert Price	03/2018
1865	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
1866	2^465803-114817	140221	Enzo Doria	05/2015
1867	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
1868	2^465503-112735	140131	Enzo Doria	07/2014
1869	(16*10^140091+167)/3	140092	Robert Price	06/2019
1870	6^179964+179964^6-1	140040	Robert Price	04/2014
1871	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
1872	2^465072-344789	140001	Enzo Doria	07/2015
1873	5*10^139945+81	139946	Robert Price	03/2019
1874	2^464864-17	139939	Lelio R Paula	09/2017
1875	8*10^139920+51	139921	Robert Price	08/2019
1876	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
1877	(13*10^139782+191)/3	139783	Robert Price	11/2018
1878	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
1879	(74*10^139723+133)/9	139724	Robert Price	06/2019
1880	3*10^139722+13	139723	Robert Price	07/2018
1881	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
1882	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
1883	2^463633-2788423	139568	Enzo Doria	11/2015
1884	2^463271-109501	139459	Enzo Doria	04/2014
1885	(5*10^139457+79)/3	139458	Robert Price	03/2018
1886	2^463237-99	139449	Lelio R Paula	09/2017
1887	(49*10^139442+383)/9	139443	Robert Price	04/2019
1888	(7*10^139417-547)/9	139417	Robert Price	01/2018
1889	(10^139398+191)/3	139398	Robert Price	02/2018
1890	2^463019+79463	139383	Enzo Doria	06/2016
1891	3^292129-112756	139381	Enzo Doria	07/2014
1892	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
1893	2^462855-1865707	139334	Enzo Doria	02/2016
1894	(86*10^139315+121)/9	139316	Robert Price	08/2019
1895	2^462786-292043	139313	Enzo Doria	08/2015
1896	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
1897	(17*10^139239+67)/3	139240	Robert Price	01/2019
1898	2^462238-935	139148	Yves Minet	02/2014
1899	2^461228+1870441	138844	Enzo Doria	05/2016
1900	2^461204-113675	138837	Enzo Doria	08/2014
1901	(2^461139-7)/47	138815	Lelio R Paula	08/2015
1902	(17*10^138812-521)/9	138813	Robert Price	04/2018
1903	3*10^138811-11	138812	Robert Price	07/2018
1904	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
1905	(43*10^138648+101)/9	138649	Robert Price	11/2018
1906	2^460567-113541	138645	Enzo Doria	08/2014
1907	7*10^138604+3	138605	Robert Price	08/2015
1908	2^460330+69	138574	Lelio R Paula	09/2017
1909	(17*10^138569-77)/3	138570	Robert Price	08/2019
1910	2^460078-69581	138498	Enzo Doria	12/2015
1911	2^459768+1531	138404	Lelio R Paula	06/2012
1912	2^459343-113611	138277	Enzo Doria	08/2014
1913	2^459199+1874393	138233	Enzo Doria	06/2016
1914	2^459063-345307	138192	Enzo Doria	06/2015
1915	2*10^138162-43	138163	Robert Price	04/2018
1916	2^458927-112747	138151	Enzo Doria	06/2014
1917	2^458927-69217	138151	Enzo Doria	11/2015
1918	555555*2^458524+1513	138036	Darren Bedwell	08/2009
1919	2^458465+2^32+1	138012	T. D. Noe	06/2007
1920	2^458321-113053	137969	Enzo Doria	07/2014
1921	2^458298+79459	137962	Enzo Doria	06/2016
1922	2^458248-21815	137947	Enzo Doria	07/2013
1923	2^458194+1876549	137931	Enzo Doria	07/2016
1924	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
1925	(318259#+2625)/(3^257^5*22965193)	137899	Makoto Morimoto	06/2019
1926	2^457937+57	137853	Lelio R Paula	09/2017
1927	(8*10^137845+13)/3	137846	Robert Price	06/2018
1928	2^457822+105	137819	Donovan Johnson	06/2006
1929	2^457754-113711	137798	Enzo Doria	09/2014
1930	11^132315-360	137792	Enzo Doria	09/2012
1931	2^457347-37	137676	Lelio R Paula	09/2017
1932	2^457322-2786393	137668	Enzo Doria	10/2015
1933	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
1934	2^457240-59939	137643	Enzo Doria	10/2015
1935	2^457120-21575	137607	Enzo Doria	07/2013
1936	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
1937	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
1938	2^456796-113513	137510	Enzo Doria	08/2014
1939	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
1940	2^456503-114361	137422	Enzo Doria	01/2015
1941	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
1942	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
1943	2^455922+76249	137247	Enzo Doria	05/2016
1944	14^119741-119741^14	137239	Serge Batalov	04/2016
1945	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
1947	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
1946	124^65536+57^65536	137195	Serge Batalov	03/2018
1948	2^455689+72677	137177	Enzo Doria	04/2016
1949	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
1950	(37^87421-1)/36	137093	Robert Price	03/2012
1951	2^455323-57	137066	Lelio R Paula	09/2017
1952	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
1953	2^455025-112723	136977	Enzo Doria	06/2014
1954	2^454675-1777	136871	Yves Minet	10/2011
1955	3*10^136829+29	136830	Robert Price	05/2018
1956	4*10^136813-57	136814	Robert Price	10/2018
1957	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
1958	2^454348-53	136773	Lelio R Paula	09/2017
1959	31^91680-2	136729	Lelio R Paula	05/2017
1960	2^454199-113697	136728	Enzo Doria	09/2014
1961	7*10^136716+69	136717	Robert Price	07/2019
1962	(13*10^136687+47)/3	136688	Robert Price	10/2018
1963	2^453935-2791357	136649	Enzo Doria	01/2016
1964	2^453906-69131	136640	Enzo Doria	11/2015
1965	2^453791+1873913	136605	Enzo Doria	06/2016
1966	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
1967	580^49413+49413^580	136550	Norbert Schneider	02/2019
1968	2^453503-2788297	136519	Enzo Doria	11/2015
1969	2^453267-113827	136447	Enzo Doria	09/2014
1970	2^453102+1877629	136398	Enzo Doria	08/2016
1971	(62*10^136384-791)/9	136385	Robert Price	06/2019
1972	(25*10^136303+161)/3	136304	Robert Price	09/2019
1973	L(651821)	136223	Henri Lifchitz	09/2008
1974	2^452460+77701	136205	Enzo Doria	05/2016
1975	2^452440-114755	136199	Enzo Doria	04/2015
1976	(47*10^136141+493)/9	136142	Robert Price	03/2019
1977	2*10^136057-43	136058	Robert Price	04/2018
1978	(2^451956-5)/181	136051	Lelio R Paula	07/2015
1979	2^451947-22165	136050	Enzo Doria	07/2013
1980	2^451787-21805	136002	Enzo Doria	07/2013
1981	2^451734-112817	135986	Enzo Doria	06/2014
1982	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
1983	2^451705-21879	135977	Enzo Doria	07/2013
1984	2^451560-112349	135934	Enzo Doria	06/2014
1985	2^451530+45	135925	Lelio R Paula	08/2017
1986	(25*10^135906-73)/3	135907	Robert Price	09/2019
1987	2^451450-21743	135900	Enzo Doria	07/2013
1988	2^450805+65	135706	Lelio R Paula	08/2017
1989	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
1990	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
1991	2^449944-113247	135447	Enzo Doria	07/2014
1992	2^449770-113247	135395	Enzo Doria	07/2014
1993	2^449637-21471	135355	Enzo Doria	07/2013
1994	2^449571-75	135335	Lelio R Paula	08/2017
1995	(14*10^135301-53)/3	135302	Robert Price	12/2018
1996	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
1997	(13*10^135279+437)/9	135280	Robert Price	04/2018
1998	2^449330-35	135262	Lelio R Paula	08/2017
1999	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
2000	(13*10^135184-43)/3	135185	Robert Price	11/2018

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