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	2^486840+1879141	146554	Enzo Doria	08/2016
1752	2^486774-87	146534	Lelio R Paula	12/2017
1753	96^73877-95^73877	146445	Robert Price	10/2015
1754	8*10^146421+81	146422	Robert Price	08/2019
1755	(52^85259+1)/53	146304	Paul Bourdelais	09/2017
1756	179^64935+2	146290	Lelio R Paula	10/2017
1757	(19*10^146181-49)/3	146182	Robert Price	05/2019
1758	2^485531-114621	146160	Enzo Doria	05/2015
1759	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
1760	2^485389+81887	146117	Enzo Doria	08/2016
1761	(10^146063+71)/9	146063	Serge Batalov	07/2015
1762	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
1763	(22*10^146029+257)/9	146030	Robert Price	06/2018
1764	2^484743+1872923	145923	Enzo Doria	05/2016
1765	2^484341+1879157	145802	Enzo Doria	08/2016
1766	2^484271-51	145781	Lelio R Paula	11/2017
1767	70^78989-69^78989	145743	Robert Price	01/2014
1768	51^85334+2	145714	Robert Price	07/2015
1769	2^483886-1857101	145665	Enzo Doria	10/2015
1770	2^483563-1863457	145567	Enzo Doria	12/2015
1771	2^483516-1861409	145553	Enzo Doria	11/2015
1772	2^483384-115019	145514	Enzo Doria	06/2015
1773	(19*10^145499-61)/3	145500	Robert Price	05/2019
1774	2^483302-3221	145489	Lelio R Paula	12/2012
1775	2^483046+1874029	145412	Enzo Doria	06/2016
1776	2^482991-2789317	145395	Enzo Doria	12/2015
1777	2^482978-2789711	145391	Enzo Doria	12/2015
1778	2^482966-2789711	145388	Enzo Doria	12/2015
1779	2^482817-1858843	145343	Enzo Doria	10/2015
1780	2^482751-113635	145323	Enzo Doria	08/2014
1781	2^482705-459763	145309	Enzo Doria	05/2015
1782	(4^241306+11)/3	145281	Robert Price	03/2017
1783	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
1784	53^84239-52^84239	145252	Robert Price	01/2013
1785	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
1786	2^482087+72623	145123	Enzo Doria	04/2016
1787	2^482016-286565	145102	Enzo Doria	07/2015
1788	(19*10^145093+101)/3	145094	Robert Price	09/2019
1789	2^481840+15	145049	Robert Price	09/2015
1790	2^481801-481801	145037	Henri Lifchitz	03/2005
1791	2^481775+1869083	145029	Enzo Doria	05/2016
1792	29^99167+2	145022	Ray Chandler	08/2011
1793	2^481663+1875653	144996	Enzo Doria	07/2016
1794	2^481149-459073	144841	Enzo Doria	05/2015
1795	2^481045-113215	144809	Enzo Doria	07/2014
1796	(64*10^144797+287)/9	144798	Robert Price	04/2019
1797	2^480859-113695	144753	Enzo Doria	09/2014
1798	2^480766-2787191	144725	Enzo Doria	11/2015
1799	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
1800	2^480678+1874239	144699	Enzo Doria	06/2016
1801	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
1802	L(692147)	144651	Henri Lifchitz	10/2008
1803	(76*10^144648+77)/9	144649	Robert Price	10/2019
1804	2^480417+35	144620	Robert Price	11/2015
1805	2^480296-59879	144584	Enzo Doria	10/2015
1806	2^479844+3	144448	Donovan Johnson	06/2006
1807	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
1808	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
1809	2^479348-2792219	144299	Enzo Doria	02/2016
1810	3^302389-6242	144277	Enzo Doria	05/2014
1811	2*10^144220-3	144221	Robert Price	07/2015
1812	2^478904-109109	144165	Enzo Doria	04/2014
1813	2^478337-115333	143994	Enzo Doria	07/2015
1814	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
1815	88^74047-87^74047	143984	Robert Price	05/2015
1816	(19*10^143963+467)/9	143964	Robert Price	02/2018
1817	(71^77761+1)/72	143954	Paul Bourdelais	09/2017
1818	2^478088+27	143919	Robert Price	11/2015
1819	2^477475-22071	143735	Enzo Doria	07/2013
1820	2^477417-22123	143717	Enzo Doria	07/2013
1821	2^477359-3577	143700	Yves Minet	03/2017
1822	(14*10^143662-71)/3	143663	Robert Price	12/2018
1823	2^476936-396765	143573	Enzo Doria	07/2013
1824	2^476888-2791229	143558	Enzo Doria	01/2016
1825	2^476868-1859939	143552	Enzo Doria	11/2015
1826	755^49878+49878^755	143547	Norbert Schneider	04/2019
1827	2^476558-113627	143459	Enzo Doria	08/2014
1828	2^476478-45	143435	Lelio R Paula	11/2017
1829	(2^475854+9)/73	143245	Lelio R Paula	08/2015
1830	2^475813-113239	143234	Enzo Doria	07/2014
1831	2^475624-114059	143178	Enzo Doria	11/2014
1832	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
1833	2^475480-2786129	143134	Enzo Doria	10/2015
1834	(19*10^143129-43)/3	143130	Robert Price	05/2019
1835	(14*10^143097+73)/3	143098	Robert Price	12/2018
1836	2^475299-111937	143080	Enzo Doria	05/2014
1837	2^475160-2797859	143038	Enzo Doria	04/2016
1838	(2^475069+3)/395	143008	Lelio R Paula	08/2015
1839	2^475027-461437	142998	Enzo Doria	07/2015
1840	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
1841	(8*10^142932+43)/3	142933	Robert Price	06/2018
1842	(54^82471-1)/53	142871	Paul Bourdelais	09/2017
1843	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
1844	2^474417-59923	142814	Enzo Doria	10/2015
1845	4*10^142810-21	142811	Robert Price	09/2018
1846	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
1847	2^474053+2897	142705	Lelio R Paula	08/2012
1848	(10^142699+359)/9	142699	Serge Batalov	12/2014
1849	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
1850	2^473740-1856639	142610	Enzo Doria	09/2015
1851	2^473617-114223	142573	Enzo Doria	12/2014
1852	2^473257+1873217	142465	Enzo Doria	06/2016
1853	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
1854	(61*10^142446-1)/3	142448	Robert Price	01/2020
1855	(14*10^142440+61)/3	142441	Robert Price	12/2018
1856	(10^142425+359)/9	142425	Serge Batalov	12/2014
1857	2^473101+773027	142418	Enzo Doria	05/2016
1858	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
1859	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
1860	2^472634-109511	142278	Enzo Doria	04/2014
1861	(48^84589+1)/49	142213	Robert Price	01/2014
1862	7*10^142189+87	142190	Robert Price	07/2019
1863	2^472258+7	142164	Lelio R Paula	08/2015
1864	(23*10^142105+91)/3	142106	Robert Price	08/2019
1865	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
1866	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
1867	(16*10^142058+197)/3	142059	Robert Price	04/2019
1868	2^471792+1880881	142024	Enzo Doria	11/2016
1869	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
1870	(4*10^141926-79)/3	141927	Robert Price	02/2018
1871	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
1872	(14*10^141853+37)/3	141854	Robert Price	12/2018
1873	(41*10^141836-59)/9	141837	Robert Price	10/2018
1874	4*5^202913-9	141831	Lelio R Paula	04/2015
1875	2*7^167812-3	141818	Lelio R Paula	12/2014
1876	2^471043+35	141799	Robert Price	11/2015
1877	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
1878	(11*10^141718-131)/3	141719	Robert Price	09/2018
1879	2^470692+76771	141693	Enzo Doria	05/2016
1880	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
1881	2^470305-459373	141576	Enzo Doria	05/2015
1882	2^470183+72623	141540	Enzo Doria	04/2016
1883	2^470173-16465	141537	Enzo Doria	04/2013
1884	2^469974-1841	141477	Enzo Doria	05/2014
1885	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
1886	2*10^141448+63	141449	Robert Price	05/2018
1887	2^469824+43	141432	Lelio R Paula	09/2017
1888	2*10^141407-27	141408	Robert Price	05/2018
1889	2^469630-59711	141373	Enzo Doria	10/2015
1890	(25*10^141366-331)/9	141367	Robert Price	08/2018
1891	(2^469564-3)/611	141351	Lelio R Paula	08/2015
1892	197^61601+2	141342	Lelio R Paula	08/2017
1893	2^469372-112949	141296	Enzo Doria	07/2014
1895	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
1894	143^65536+106^65536	141253	Serge Batalov	03/2018
1896	2^469198+782569	141243	Enzo Doria	10/2016
1897	2^469076-2786939	141206	Enzo Doria	11/2015
1898	2^468804+1874941	141125	Enzo Doria	06/2016
1899	2^468787+81353	141119	Enzo Doria	08/2016
1900	2^468595-350407	141062	Enzo Doria	06/2015
1901	2^468564+87855	141052	Lelio R Paula	01/2016
1902	2^468551-21987	141048	Enzo Doria	07/2013
1903	2^468523-7	141040	Lelio R Paula	08/2015
1904	(25*10^141019-13)/3	141020	Robert Price	09/2019
1905	2^468405+87855	141004	Lelio R Paula	01/2016
1906	2^467978-113051	140876	Enzo Doria	07/2014
1907	2^467780-344429	140816	Enzo Doria	07/2015
1908	2^467605-1855603	140764	Enzo Doria	09/2015
1909	5*10^140744-7	140745	Robert Price	09/2015
1910	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
1911	2^467401-1850023	140702	Enzo Doria	08/2015
1912	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
1913	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
1914	2^467166-1854941	140631	Enzo Doria	09/2015
1915	(85*10^140609+473)/9	140610	Robert Price	01/2020
1916	2^466866-1840571	140541	Enzo Doria	06/2015
1917	2^466829-459523	140530	Enzo Doria	05/2015
1918	2^466692-113213	140489	Enzo Doria	07/2014
1919	(44*10^140410-503)/9	140411	Robert Price	12/2018
1920	153^64265-2	140400	Lelio R Paula	11/2017
1921	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
1922	(29*10^140337-17)/3	140338	Robert Price	09/2019
1923	2^466181-112735	140335	Enzo Doria	07/2014
1924	(5*10^140281-119)/3	140282	Robert Price	03/2018
1925	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
1926	2^465803-114817	140221	Enzo Doria	05/2015
1927	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
1928	2^465503-112735	140131	Enzo Doria	07/2014
1929	(16*10^140091+167)/3	140092	Robert Price	06/2019
1930	6^179964+179964^6-1	140040	Robert Price	04/2014
1931	(89*10^140008-179)/9	140009	Robert Price	12/2019
1932	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
1933	2^465072-344789	140001	Enzo Doria	07/2015
1934	5*10^139945+81	139946	Robert Price	03/2019
1935	2^464864-17	139939	Lelio R Paula	09/2017
1936	8*10^139920+51	139921	Robert Price	08/2019
1937	(85*10^139913-1)/3	139915	Robert Price	02/2020
1938	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
1939	(13*10^139782+191)/3	139783	Robert Price	11/2018
1940	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
1941	(74*10^139723+133)/9	139724	Robert Price	06/2019
1942	3*10^139722+13	139723	Robert Price	07/2018
1943	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
1944	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
1945	2^463633-2788423	139568	Enzo Doria	11/2015
1946	2^463271-109501	139459	Enzo Doria	04/2014
1947	(5*10^139457+79)/3	139458	Robert Price	03/2018
1948	2^463237-99	139449	Lelio R Paula	09/2017
1949	(49*10^139442+383)/9	139443	Robert Price	04/2019
1950	(7*10^139417-547)/9	139417	Robert Price	01/2018
1951	(10^139398+191)/3	139398	Robert Price	02/2018
1952	2^463019+79463	139383	Enzo Doria	06/2016
1953	3^292129-112756	139381	Enzo Doria	07/2014
1954	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
1955	2^462855-1865707	139334	Enzo Doria	02/2016
1956	(86*10^139315+121)/9	139316	Robert Price	08/2019
1957	2^462786-292043	139313	Enzo Doria	08/2015
1958	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
1959	(17*10^139239+67)/3	139240	Robert Price	01/2019
1960	2^462238-935	139148	Yves Minet	02/2014
1961	2^461228+1870441	138844	Enzo Doria	05/2016
1962	2^461204-113675	138837	Enzo Doria	08/2014
1963	(2^461139-7)/47	138815	Lelio R Paula	08/2015
1964	(17*10^138812-521)/9	138813	Robert Price	04/2018
1965	3*10^138811-11	138812	Robert Price	07/2018
1966	(28*10^138768+173)/3	138769	Robert Price	12/2019
1967	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
1968	(379*10^138737-1)/9	138739	Robert Price	02/2020
1969	(43*10^138648+101)/9	138649	Robert Price	11/2018
1970	2^460567-113541	138645	Enzo Doria	08/2014
1971	7*10^138604+3	138605	Robert Price	08/2015
1972	2^460330+69	138574	Lelio R Paula	09/2017
1973	(17*10^138569-77)/3	138570	Robert Price	08/2019
1974	2^460078-69581	138498	Enzo Doria	12/2015
1975	2^459768+1531	138404	Lelio R Paula	06/2012
1976	2^459343-113611	138277	Enzo Doria	08/2014
1977	(28*10^138240+113)/3	138241	Robert Price	03/2020
1978	2^459199+1874393	138233	Enzo Doria	06/2016
1979	2^459063-345307	138192	Enzo Doria	06/2015
1980	2*10^138162-43	138163	Robert Price	04/2018
1981	2^458927-112747	138151	Enzo Doria	06/2014
1982	2^458927-69217	138151	Enzo Doria	11/2015
1983	555555*2^458524+1513	138036	Darren Bedwell	08/2009
1984	2^458465+2^32+1	138012	T. D. Noe	06/2007
1985	2^458321-113053	137969	Enzo Doria	07/2014
1986	2^458298+79459	137962	Enzo Doria	06/2016
1987	2^458248-21815	137947	Enzo Doria	07/2013
1988	2^458194+1876549	137931	Enzo Doria	07/2016
1989	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
1990	(318259#+2625)/(3^257^5*22965193)	137899	Makoto Morimoto	06/2019
1991	2^457937+57	137853	Lelio R Paula	09/2017
1992	(8*10^137845+13)/3	137846	Robert Price	06/2018
1993	2^457822+105	137819	Donovan Johnson	06/2006
1994	2^457754-113711	137798	Enzo Doria	09/2014
1995	11^132315-360	137792	Enzo Doria	09/2012
1996	2^457347-37	137676	Lelio R Paula	09/2017
1997	2^457322-2786393	137668	Enzo Doria	10/2015
1998	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
1999	2^457240-59939	137643	Enzo Doria	10/2015
2000	2^457120-21575	137607	Enzo Doria	07/2013

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Probable Primes Top 10000

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