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	2^572592-114893	172368	Enzo Doria	05/2015
1752	4*10^172354-39	172355	Robert Price	09/2020
1753	37535^37674+37674^37535	172338	Norbert Schneider	05/2022
1754	(11*10^172322-119)/9	172323	Robert Price	11/2021
1755	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
1756	(38^109037-1)/37	172254	Paul Bourdelais	10/2017
1757	(4*10^172241+89)/3	172242	Robert Price	08/2021
1758	3*10^172219+73	172220	Robert Price	08/2018
1759	A352736(15)	172032	Kellen Shenton	05/2022
1760	(36^110503+1)/37	171975	Lelio R Paula	04/2017
1761	8*10^171934+71	171935	Robert Price	05/2022
1762	(11*10^171933+601)/9	171934	Robert Price	02/2022
1763	(22*10^171929-73)/3	171930	Robert Price	04/2019
1764	(49*10^171892-319)/9	171893	Robert Price	10/2021
1765	4*10^171891-63	171892	Robert Price	10/2018
1766	67*10^171882-9	171884	Robert Price	03/2021
1767	2^570980-2782289	171883	Enzo Doria	09/2015
1768	(25*10^171849-37)/3	171850	Robert Price	10/2019
1769	10^171832+387909	171833	Patrick De Geest	08/2021
1770	10^171832-10001	171832	Robert Price	02/2021
1771	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
1772	(74*10^171651-29)/9	171652	Robert Price	06/2022
1773	(536*10^171601-23)/9	171603	Robert Price	02/2020
1774	7*10^171535-99	171536	Robert Price	06/2019
1775	(28*10^171534+101)/3	171535	Robert Price	09/2020
1776	2^569563-1854607	171456	Enzo Doria	09/2015
1777	3*10^171391+59	171392	Robert Price	08/2018
1778	(13*10^171306-37)/3	171307	Robert Price	01/2019
1779	8*10^171296+87	171297	Robert Price	10/2019
1780	(55^98419-1)/54	171284	Paul Bourdelais	12/2017
1781	(29*10^171275+67)/3	171276	Robert Price	12/2019
1782	(194*10^171193+1)/3	171195	Robert Price	01/2022
1783	2^568642+1876129	171179	Enzo Doria	07/2016
1784	4*10^171146-47	171147	Robert Price	10/2021
1785	(19*10^170970+131)/3	170971	Robert Price	06/2020
1786	(46*10^170932+143)/9	170933	Robert Price	01/2019
1787	(79*10^170901-1)/3	170903	Robert Price	02/2020
1788	(58*10^170842+221)/9	170843	Robert Price	02/2017
1789	(29*10^170830+583)/9	170831	Robert Price	06/2021
1790	3*10^170800+73	170801	Robert Price	08/2018
1791	(29*10^170799-119)/9	170800	Robert Price	12/2021
1792	11^164009-270	170798	Enzo Doria	10/2012
1793	2*10^170767+41	170768	Robert Price	05/2018
1794	3^357706-112358	170670	Enzo Doria	07/2014
1795	TheodorusPrime(170657)	170657	Eric W. Weisstein	08/2013
1796	2^566871+1876163	170646	Enzo Doria	07/2016
1797	(10657#+(404267#)/(10657#))/(1675379)	170624	Makoto Morimoto	10/2017
1798	2^566496+7	170533	Donovan Johnson	07/2006
1799	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
1800	7*10^170348+33	170349	Robert Price	06/2020
1801	2^565183-352021	170138	Enzo Doria	07/2015
1802	2^565143-114457	170125	Enzo Doria	02/2015
1803	2^564976-49869	170075	Enzo Doria	10/2015
1804	(7*10^169944+23)/3	169945	Robert Price	06/2020
1805	(37*10^169943+251)/9	169944	Robert Price	09/2021
1806	2^564526-351401	169940	Enzo Doria	07/2015
1807	4*10^169759+19	169760	Robert Price	10/2018
1808	21^128327-20^128327	169677	Jean-Louis Charton	11/2014
1809	2^563583+89	169656	Stefano Morozzi	04/2021
1810	(4*10^169559+83)/3	169560	Robert Price	02/2018
1811	(194*10^169461-17)/3	169463	Robert Price	09/2020
1812	2^562749+2793047	169405	Enzo Doria	02/2016
1813	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
1814	(109*10^169337+11)/3	169339	Robert Price	06/2022
1815	(56*10^169311+691)/9	169312	Robert Price	05/2019
1816	2^562369-29503	169290	Enzo Doria	08/2015
1817	(17*10^169283+19)/9	169284	Robert Price	03/2021
1818	8*10^169071+59	169072	Robert Price	11/2021
1819	(10^169044+173)/3	169044	Robert Price	05/2021
1820	(22*10^169019+383)/9	169020	Robert Price	05/2018
1821	(64*10^168935+143)/9	168936	Robert Price	05/2021
1822	(22*10^168906+47)/3	168907	Robert Price	06/2021
1823	5*10^168807+87	168808	Robert Price	02/2019
1824	(77*10^168803-149)/9	168804	Robert Price	03/2022
1825	4*10^168788-47	168789	Robert Price	10/2021
1826	(154*10^168781+17)/9	168783	Robert Price	06/2022
1827	(418*10^168751-31)/9	168753	Robert Price	05/2022
1828	(29*10^168711+691)/9	168712	Robert Price	08/2021
1829	2^560405-39943	168699	Enzo Doria	09/2015
1830	(397*10^168634+17)/9	168636	Robert Price	03/2022
1831	89*10^168614-7	168616	Robert Price	04/2020
1832	(23*10^168608-83)/3	168609	Robert Price	08/2019
1833	(94*10^168541+11)/3	168543	Robert Price	04/2020
1834	2^559686-350471	168483	Enzo Doria	06/2015
1835	2^559672-1855889	168479	Enzo Doria	09/2015
1836	(5*10^168379-473)/9	168379	Robert Price	01/2018
1837	2^559000-59939	168276	Enzo Doria	11/2015
1838	(16*10^168181+41)/3	168182	Robert Price	03/2019
1839	(19*10^168173+77)/3	168174	Robert Price	05/2019
1840	(74*10^168170+529)/9	168171	Robert Price	02/2022
1841	2^558640-114149	168168	Enzo Doria	12/2014
1842	2^558498-1849277	168125	Enzo Doria	08/2015
1843	2^558476-1850249	168119	Enzo Doria	08/2015
1844	(7*10^168067+71)/3	168068	Robert Price	05/2018
1845	2^558150-1852211	168020	Enzo Doria	08/2015
1846	2^558125-113661	168013	Enzo Doria	09/2014
1847	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
1848	(13*10^167911+179)/3	167912	Robert Price	11/2018
1849	(26*10^167861-167)/3	167862	Robert Price	10/2019
1850	39^105456+2	167788	Robert Price	04/2015
1851	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
1852	10^167639+121911	167640	Patrick De Geest	07/2018
1853	10^167639-8001	167639	Robert Price	03/2018
1854	2^556504-462059	167525	Enzo Doria	07/2015
1855	(88*10^167522-637)/9	167523	Robert Price	11/2020
1856	5*10^167510+9	167511	Robert Price	08/2015
1857	7*10^167437-93	167438	Robert Price	08/2020
1858	11^160663+6	167314	Paul Bourdelais	02/2021
1859	(7*10^167308-493)/9	167308	Robert Price	04/2021
1860	2^555343+1874333	167175	Enzo Doria	06/2016
1861	2^555210-461261	167135	Enzo Doria	07/2015
1862	9*10^166996+59	166997	Robert Price	01/2020
1863	(68*10^166976-329)/9	166977	Robert Price	03/2021
1864	(64*10^166901+683)/9	166902	Robert Price	06/2022
1865	2^554372+1880527	166883	Enzo Doria	11/2016
1866	2^554299+72173	166861	Enzo Doria	04/2016
1867	(185*10^166837+7)/3	166839	Robert Price	03/2020
1868	(14*10^166813+139)/9	166814	Robert Price	11/2021
1869	2^554037-2797063	166782	Enzo Doria	03/2016
1870	(49*10^166721-139)/9	166722	Robert Price	03/2019
1871	2*10^166646+69	166647	Robert Price	06/2020
1872	2^553484-29819	166616	Enzo Doria	08/2015
1873	(188*10^166611+7)/3	166613	Robert Price	03/2020
1874	2^553383-2784217	166585	Enzo Doria	10/2015
1875	2^553069+76427	166491	Enzo Doria	05/2016
1876	2*10^166458+51	166459	Robert Price	05/2018
1877	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
1878	11^159756-2424	166369	Mike Oakes	06/2010
1879	2^552649-361275	166364	Enzo Doria	05/2014
1880	2^552628-113669	166358	Enzo Doria	09/2014
1881	(19*10^166325+137)/3	166326	Robert Price	03/2022
1882	10^166324+550603	166325	Patrick De Geest	07/2018
1883	10^166324-801	166324	Robert Price	02/2018
1884	(85*10^166297-1)/3	166299	Robert Price	02/2020
1885	8*10^166227+87	166228	Robert Price	10/2019
1886	2^552137+1879397	166210	Enzo Doria	09/2016
1887	(103*10^166126+11)/3	166128	Robert Price	01/2021
1888	(22*10^166077+179)/3	166078	Robert Price	02/2022
1889	(23^121949-1)/22	166061	Paul Bourdelais	10/2017
1890	2^551542+19249	166031	Payam Samidoost	08/2002
1891	2^551535-23821	166029	Enzo Doria	08/2013
1892	2^551507-23557	166021	Enzo Doria	08/2013
1893	10^165947-7000000001	165947	Robert Price	12/2021
1894	4*10^165938-47	165939	Robert Price	10/2021
1895	7*10^165916-3	165917	Robert Price	08/2015
1896	(29*10^165796+67)/3	165797	Robert Price	12/2019
1897	81^86837-80^86837	165728	Robert Price	01/2015
1898	(71*10^165663-539)/9	165664	Robert Price	07/2019
1899	2^550270-69551	165648	Enzo Doria	12/2015
1900	(202*10^165569-13)/9	165571	Robert Price	01/2020
1901	2^550000-23625	165567	Enzo Doria	08/2013
1902	2^549675-1852057	165469	Enzo Doria	08/2015
1903	(529*10^165394-7)/9	165396	Robert Price	08/2021
1904	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
1905	(28*10^165358-1)/9	165359	Serge Batalov	10/2014
1906	2^549278+1879669	165350	Enzo Doria	09/2016
1907	(7*10^165350-439)/9	165350	Robert Price	02/2018
1908	2^549252-351269	165342	Enzo Doria	06/2015
1909	67*10^165327-9	165329	Robert Price	03/2021
1911	(14*10^165282+73)/3	165283	Robert Price	12/2018
1910	(8*10^165283-629)/9	165283	Robert Price	01/2022
1912	2^549049+2797607	165281	Enzo Doria	04/2016
1913	(218*10^165258+7)/9	165260	Robert Price	06/2022
1914	(7*10^165239+107)/3	165240	Robert Price	02/2018
1915	(44^100511-1)/43	165184	Paul Bourdelais	11/2017
1916	(7*10^165134+107)/3	165135	Robert Price	02/2018
1917	(301*10^165082+23)/9	165084	Robert Price	06/2021
1918	(23*10^165060-83)/3	165061	Robert Price	08/2019
1919	(76*10^164984+77)/9	164985	Robert Price	10/2019
1920	(4*10^164929-211)/9	164929	Robert Price	03/2022
1921	10^164878-500001	164878	Robert Price	03/2022
1922	9*10^164791-89	164792	Robert Price	04/2020
1923	2^547178-1856501	164717	Enzo Doria	10/2015
1924	11^158160-60	164707	Enzo Doria	07/2012
1925	(26*10^164643-167)/3	164644	Robert Price	10/2019
1926	(10^164643+83)/3	164643	Robert Price	08/2021
1927	2^546398-59201	164483	Enzo Doria	10/2015
1928	2^546332-114893	164463	Enzo Doria	05/2015
1929	(65*10^164427+277)/9	164428	Robert Price	08/2021
1930	2^545958+1876189	164350	Enzo Doria	07/2016
1931	2^545878-49841	164326	Enzo Doria	10/2015
1932	(10^164284+77)/3	164284	Robert Price	01/2018
1933	2^545668-4019	164263	Yves Minet	04/2017
1934	10^164216+780639	164217	Patrick De Geest	08/2021
1936	10^164216-50000000001	164216	Robert Price	12/2020
1935	10^164216-891051	164216	Patrick De Geest	08/2021
1937	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
1938	(16*10^164122+197)/3	164123	Robert Price	04/2019
1939	2^545185+76757	164118	Enzo Doria	05/2016
1940	2^545076-114329	164085	Enzo Doria	01/2015
1941	(2*10^164043-143)/3	164043	Robert Price	03/2018
1942	(29^112153+1)/30	164011	Lelio R Paula	03/2017
1943	2^544757+1874777	163989	Enzo Doria	06/2016
1944	2^544444-457199	163894	Enzo Doria	01/2015
1945	2^544264-343529	163840	Enzo Doria	07/2015
1946	7*10^163780+9	163781	Robert Price	09/2015
1947	2^543989+2793047	163758	Enzo Doria	02/2016
1948	(28*10^163709+113)/3	163710	Robert Price	03/2020
1949	(23*10^163523+301)/9	163524	Robert Price	06/2021
1950	(68*10^163521-329)/9	163522	Robert Price	03/2021
1951	35820^35899+35899^35820	163489	Norbert Schneider	11/2021
1952	2^542870-69551	163421	Enzo Doria	12/2015
1953	2^542395+72533	163278	Enzo Doria	04/2016
1954	2^542072-3683	163180	Yves Minet	03/2017
1955	(682*10^163106-7)/9	163108	Robert Price	08/2021
1956	2^541779-1867357	163092	Enzo Doria	04/2016
1957	(29*10^163056+313)/9	163057	Robert Price	04/2021
1958	8*10^162924+9	162925	Robert Price	12/2015
1959	2^540905+81557	162829	Enzo Doria	08/2016
1960	2^540628-2939	162746	Yves Minet	09/2014
1961	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
1962	(203*10^162689+1)/3	162691	Robert Price	03/2020
1963	3*10^162620-59	162621	Robert Price	09/2018
1964	3^340694-112960	162553	Enzo Doria	07/2014
1965	2^539807-114081	162499	Enzo Doria	12/2014
1966	414^62093+62093^414	162498	Norbert Schneider	03/2022
1967	2^539654-114893	162453	Enzo Doria	05/2015
1968	9*10^162449-71	162450	Robert Price	11/2020
1969	2^539617-1851583	162441	Enzo Doria	08/2015
1970	(91*10^162410+11)/3	162412	Robert Price	02/2020
1971	2^539346+81049	162360	Enzo Doria	07/2016
1972	2^539220-115499	162322	Enzo Doria	07/2015
1973	2^539217-113713	162321	Enzo Doria	09/2014
1974	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
1975	4*10^162263-39	162264	Robert Price	09/2020
1976	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
1977	(10^162138+11)/3	162138	Serge Batalov	07/2015
1978	(61*10^162100-403)/9	162101	Robert Price	10/2021
1979	2^538473-112723	162097	Enzo Doria	06/2014
1980	2^538157+79337	162002	Enzo Doria	06/2016
1981	2^538136-114749	161996	Enzo Doria	05/2015
1982	2^538104+1531	161986	Lelio R Paula	01/2013
1983	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
1984	2^537815-22737	161899	Enzo Doria	07/2013
1985	2^537804-39839	161896	Enzo Doria	09/2015
1986	(754*10^161816-7)/9	161818	Robert Price	05/2020
1987	2^537458-59201	161791	Enzo Doria	10/2015
1988	2*10^161766+51	161767	Robert Price	05/2018
1989	(7*10^161760+131)/3	161761	Robert Price	06/2020
1990	2^537209-49849	161717	Enzo Doria	10/2015
1991	(58*10^161691+329)/9	161692	Robert Price	05/2019
1992	23*10^161668-3	161670	Robert Price	10/2021
1993	2^536937+1879397	161635	Enzo Doria	09/2016
1994	34*10^161593-9	161595	Robert Price	06/2020
1995	(31*10^161582-1)/3	161584	Robert Price	02/2020
1996	2^536569-22881	161524	Enzo Doria	07/2013
1997	(46*10^161505+593)/9	161506	Robert Price	04/2022
1998	10^161253+573493	161254	Patrick De Geest	07/2018
1999	10^161253-8001	161253	Robert Price	03/2018
2000	97*10^161247-3	161249	Robert Price	05/2020

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PRP Records

Probable Primes Top 10000

(290751 PRPs in the top)