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 ?
2001	(194*10^169461-17)/3	169463	Robert Price	09/2020
2002	2^562749+2793047	169405	Enzo Doria	02/2016
2003	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
2004	(109*10^169337+11)/3	169339	Robert Price	06/2022
2005	(56*10^169311+691)/9	169312	Robert Price	05/2019
2006	2^562369-29503	169290	Enzo Doria	08/2015
2007	(17*10^169283+19)/9	169284	Robert Price	03/2021
2008	10^169074-5000000001	169074	Robert Price	09/2022
2009	8*10^169071+59	169072	Robert Price	11/2021
2010	(10^169044+173)/3	169044	Robert Price	05/2021
2011	(22*10^169019+383)/9	169020	Robert Price	05/2018
2012	(64*10^168935+143)/9	168936	Robert Price	05/2021
2013	(22*10^168906+47)/3	168907	Robert Price	06/2021
2014	5*10^168807+87	168808	Robert Price	02/2019
2015	(77*10^168803-149)/9	168804	Robert Price	03/2022
2016	4*10^168788-47	168789	Robert Price	10/2021
2017	(154*10^168781+17)/9	168783	Robert Price	06/2022
2018	(418*10^168751-31)/9	168753	Robert Price	05/2022
2019	(29*10^168711+691)/9	168712	Robert Price	08/2021
2020	2^560405-39943	168699	Enzo Doria	09/2015
2021	(397*10^168634+17)/9	168636	Robert Price	03/2022
2022	89*10^168614-7	168616	Robert Price	04/2020
2023	(23*10^168608-83)/3	168609	Robert Price	08/2019
2024	(94*10^168541+11)/3	168543	Robert Price	04/2020
2025	2^559686-350471	168483	Enzo Doria	06/2015
2026	2^559672-1855889	168479	Enzo Doria	09/2015
2027	(5*10^168379-473)/9	168379	Robert Price	01/2018
2028	2^559000-59939	168276	Enzo Doria	11/2015
2029	(16*10^168181+41)/3	168182	Robert Price	03/2019
2030	(19*10^168173+77)/3	168174	Robert Price	05/2019
2031	(74*10^168170+529)/9	168171	Robert Price	02/2022
2032	2^558640-114149	168168	Enzo Doria	12/2014
2033	2^558498-1849277	168125	Enzo Doria	08/2015
2034	2^558476-1850249	168119	Enzo Doria	08/2015
2035	(7*10^168067+71)/3	168068	Robert Price	05/2018
2036	2^558150-1852211	168020	Enzo Doria	08/2015
2037	2^558125-113661	168013	Enzo Doria	09/2014
2038	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
2039	(13*10^167911+179)/3	167912	Robert Price	11/2018
2040	(26*10^167861-167)/3	167862	Robert Price	10/2019
2041	39^105456+2	167788	Robert Price	04/2015
2042	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
2043	6*10^167662-13	167663	Robert Price	07/2022
2044	10^167639+121911	167640	Patrick De Geest	07/2018
2045	10^167639-8001	167639	Robert Price	03/2018
2046	2^556504-462059	167525	Enzo Doria	07/2015
2047	(88*10^167522-637)/9	167523	Robert Price	11/2020
2048	5*10^167510+9	167511	Robert Price	08/2015
2049	7*10^167437-93	167438	Robert Price	08/2020
2050	11^160663+6	167314	Paul Bourdelais	02/2021
2051	(7*10^167308-493)/9	167308	Robert Price	04/2021
2052	2^555343+1874333	167175	Enzo Doria	06/2016
2053	2^555210-461261	167135	Enzo Doria	07/2015
2054	9*10^166996+59	166997	Robert Price	01/2020
2055	(68*10^166976-329)/9	166977	Robert Price	03/2021
2056	(64*10^166901+683)/9	166902	Robert Price	06/2022
2057	2^554372+1880527	166883	Enzo Doria	11/2016
2058	2^554299+72173	166861	Enzo Doria	04/2016
2059	(185*10^166837+7)/3	166839	Robert Price	03/2020
2060	(14*10^166813+139)/9	166814	Robert Price	11/2021
2061	2^554037-2797063	166782	Enzo Doria	03/2016
2062	(49*10^166721-139)/9	166722	Robert Price	03/2019
2063	2*10^166646+69	166647	Robert Price	06/2020
2064	2^553484-29819	166616	Enzo Doria	08/2015
2065	(188*10^166611+7)/3	166613	Robert Price	03/2020
2066	2^553383-2784217	166585	Enzo Doria	10/2015
2067	2^553069+76427	166491	Enzo Doria	05/2016
2068	2*10^166458+51	166459	Robert Price	05/2018
2069	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
2070	11^159756-2424	166369	Mike Oakes	06/2010
2071	2^552649-361275	166364	Enzo Doria	05/2014
2072	2^552628-113669	166358	Enzo Doria	09/2014
2073	(19*10^166325+137)/3	166326	Robert Price	03/2022
2074	10^166324+550603	166325	Patrick De Geest	07/2018
2075	10^166324-801	166324	Robert Price	02/2018
2076	(85*10^166297-1)/3	166299	Robert Price	02/2020
2077	8*10^166227+87	166228	Robert Price	10/2019
2078	2^552137+1879397	166210	Enzo Doria	09/2016
2079	(103*10^166126+11)/3	166128	Robert Price	01/2021
2080	(22*10^166077+179)/3	166078	Robert Price	02/2022
2081	(23^121949-1)/22	166061	Paul Bourdelais	10/2017
2082	2^551542+19249	166031	Payam Samidoost	08/2002
2083	2^551535-23821	166029	Enzo Doria	08/2013
2084	2^551507-23557	166021	Enzo Doria	08/2013
2085	10^165947-7000000001	165947	Robert Price	12/2021
2086	4*10^165938-47	165939	Robert Price	10/2021
2087	7*10^165916-3	165917	Robert Price	08/2015
2088	(29*10^165796+67)/3	165797	Robert Price	12/2019
2089	81^86837-80^86837	165728	Robert Price	01/2015
2090	(71*10^165716-17)/9	165717	Serge Batalov	01/2023
2091	(71*10^165663-539)/9	165664	Robert Price	07/2019
2092	2^550270-69551	165648	Enzo Doria	12/2015
2093	(202*10^165569-13)/9	165571	Robert Price	01/2020
2094	2^550000-23625	165567	Enzo Doria	08/2013
2095	2^549675-1852057	165469	Enzo Doria	08/2015
2096	(529*10^165394-7)/9	165396	Robert Price	08/2021
2097	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
2098	(28*10^165358-1)/9	165359	Serge Batalov	10/2014
2099	2^549278+1879669	165350	Enzo Doria	09/2016
2100	(7*10^165350-439)/9	165350	Robert Price	02/2018
2101	2^549252-351269	165342	Enzo Doria	06/2015
2102	67*10^165327-9	165329	Robert Price	03/2021
2104	(14*10^165282+73)/3	165283	Robert Price	12/2018
2103	(8*10^165283-629)/9	165283	Robert Price	01/2022
2105	2^549049+2797607	165281	Enzo Doria	04/2016
2106	(218*10^165258+7)/9	165260	Robert Price	06/2022
2107	(7*10^165239+107)/3	165240	Robert Price	02/2018
2108	(44^100511-1)/43	165184	Paul Bourdelais	11/2017
2109	(7*10^165134+107)/3	165135	Robert Price	02/2018
2110	(301*10^165082+23)/9	165084	Robert Price	06/2021
2111	(23*10^165060-83)/3	165061	Robert Price	08/2019
2112	7*10^165023-27	165024	Robert Price	11/2022
2113	(76*10^164984+77)/9	164985	Robert Price	10/2019
2114	(4*10^164929-211)/9	164929	Robert Price	03/2022
2115	10^164878-500001	164878	Robert Price	03/2022
2116	9*10^164791-89	164792	Robert Price	04/2020
2117	2^547178-1856501	164717	Enzo Doria	10/2015
2118	11^158160-60	164707	Enzo Doria	07/2012
2119	(26*10^164643-167)/3	164644	Robert Price	10/2019
2120	(10^164643+83)/3	164643	Robert Price	08/2021
2121	2^546398-59201	164483	Enzo Doria	10/2015
2122	2^546332-114893	164463	Enzo Doria	05/2015
2123	(65*10^164427+277)/9	164428	Robert Price	08/2021
2124	2^545958+1876189	164350	Enzo Doria	07/2016
2125	2^545878-49841	164326	Enzo Doria	10/2015
2126	(10^164284+77)/3	164284	Robert Price	01/2018
2127	2^545668-4019	164263	Yves Minet	04/2017
2128	10^164216+780639	164217	Patrick De Geest	08/2021
2130	10^164216-50000000001	164216	Robert Price	12/2020
2129	10^164216-891051	164216	Patrick De Geest	08/2021
2131	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
2132	(16*10^164122+197)/3	164123	Robert Price	04/2019
2133	2^545185+76757	164118	Enzo Doria	05/2016
2134	2^545076-114329	164085	Enzo Doria	01/2015
2135	(2*10^164043-143)/3	164043	Robert Price	03/2018
2136	(29^112153+1)/30	164011	Lelio R Paula	03/2017
2137	2^544757+1874777	163989	Enzo Doria	06/2016
2138	2^544444-457199	163894	Enzo Doria	01/2015
2139	2^544264-343529	163840	Enzo Doria	07/2015
2140	7*10^163780+9	163781	Robert Price	09/2015
2141	2^543989+2793047	163758	Enzo Doria	02/2016
2142	(28*10^163709+113)/3	163710	Robert Price	03/2020
2143	(23*10^163523+301)/9	163524	Robert Price	06/2021
2144	(68*10^163521-329)/9	163522	Robert Price	03/2021
2145	35820^35899+35899^35820	163489	Norbert Schneider	11/2021
2146	2^542870-69551	163421	Enzo Doria	12/2015
2147	2^542395+72533	163278	Enzo Doria	04/2016
2148	2^542072-3683	163180	Yves Minet	03/2017
2149	(682*10^163106-7)/9	163108	Robert Price	08/2021
2150	2^541779-1867357	163092	Enzo Doria	04/2016
2151	(29*10^163056+313)/9	163057	Robert Price	04/2021
2152	8*10^162924+9	162925	Robert Price	12/2015
2153	2^540905+81557	162829	Enzo Doria	08/2016
2154	2^540628-2939	162746	Yves Minet	09/2014
2155	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
2156	(203*10^162689+1)/3	162691	Robert Price	03/2020
2157	3*10^162620-59	162621	Robert Price	09/2018
2158	3^340694-112960	162553	Enzo Doria	07/2014
2159	2^539807-114081	162499	Enzo Doria	12/2014
2160	414^62093+62093^414	162498	Norbert Schneider	03/2022
2161	2^539654-114893	162453	Enzo Doria	05/2015
2162	9*10^162449-71	162450	Robert Price	11/2020
2163	2^539617-1851583	162441	Enzo Doria	08/2015
2164	(509*10^162422+31)/9	162424	Robert Price	08/2022
2165	(91*10^162410+11)/3	162412	Robert Price	02/2020
2166	2^539346+81049	162360	Enzo Doria	07/2016
2167	2^539220-115499	162322	Enzo Doria	07/2015
2168	2^539217-113713	162321	Enzo Doria	09/2014
2169	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
2170	4*10^162263-39	162264	Robert Price	09/2020
2171	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
2172	(10^162138+11)/3	162138	Serge Batalov	07/2015
2173	(61*10^162100-403)/9	162101	Robert Price	10/2021
2174	2^538473-112723	162097	Enzo Doria	06/2014
2175	2^538157+79337	162002	Enzo Doria	06/2016
2176	2^538136-114749	161996	Enzo Doria	05/2015
2177	2^538104+1531	161986	Lelio R Paula	01/2013
2178	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
2179	2^537815-22737	161899	Enzo Doria	07/2013
2180	2^537804-39839	161896	Enzo Doria	09/2015
2181	(754*10^161816-7)/9	161818	Robert Price	05/2020
2182	2^537458-59201	161791	Enzo Doria	10/2015
2183	2*10^161766+51	161767	Robert Price	05/2018
2184	(7*10^161760+131)/3	161761	Robert Price	06/2020
2185	2^537209-49849	161717	Enzo Doria	10/2015
2186	(58*10^161691+329)/9	161692	Robert Price	05/2019
2187	23*10^161668-3	161670	Robert Price	10/2021
2188	2^536937+1879397	161635	Enzo Doria	09/2016
2189	34*10^161593-9	161595	Robert Price	06/2020
2190	(31*10^161582-1)/3	161584	Robert Price	02/2020
2191	2^536569-22881	161524	Enzo Doria	07/2013
2192	(46*10^161505+593)/9	161506	Robert Price	04/2022
2193	10^161253+573493	161254	Patrick De Geest	07/2018
2194	10^161253-8001	161253	Robert Price	03/2018
2195	97*10^161247-3	161249	Robert Price	05/2020
2196	7*10^161192-9	161193	Robert Price	10/2015
2197	2^535415-19	161176	Stefano Morozzi	07/2022
2198	2^535269-113803	161133	Enzo Doria	09/2014
2199	2^535205-23295	161113	Enzo Doria	08/2013
2200	(49*10^161105+437)/9	161106	Robert Price	09/2021
2201	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
2202	2^534429-19	160880	Stefano Morozzi	07/2022
2203	2^534359-23229	160859	Enzo Doria	08/2013
2204	10^160836-1001	160836	Robert Price	10/2022
2205	457^60454+60454^457	160803	Norbert Schneider	07/2021
2206	8*10^160782+53	160783	Robert Price	08/2020
2207	67^88037-66^88037	160763	Robert Price	10/2013
2208	(88*10^160761-637)/9	160762	Robert Price	11/2020
2209	2^533948-1852559	160735	Enzo Doria	08/2015
2210	2^533665-23335	160650	Enzo Doria	08/2013
2211	(19*10^160619+77)/3	160620	Robert Price	05/2019
2212	2^533350-5	160555	Stefano Morozzi	07/2022
2213	(38*10^160508+151)/9	160509	Robert Price	03/2022
2214	3^336353-2^336353	160482	Mike Oakes	10/2007
2215	2*10^160339-63	160340	Robert Price	01/2022
2216	(91*10^160249+11)/3	160251	Robert Price	02/2020
2217	(772*10^160239-7)/9	160241	Robert Price	06/2022
2218	(2*10^160226+187)/9	160226	Robert Price	06/2022
2219	2^532253+1868417	160225	Enzo Doria	04/2016
2220	2^532108-291989	160181	Enzo Doria	07/2015
2221	(28*10^160171-79)/3	160172	Robert Price	02/2021
2222	(26*10^160166-131)/3	160167	Robert Price	10/2019
2223	55*10^160145+9	160147	Robert Price	03/2022
2224	(17*10^160143+67)/3	160144	Robert Price	01/2019
2225	(19*10^159921-49)/3	159922	Robert Price	05/2019
2226	2^531110-1853771	159881	Enzo Doria	09/2015
2227	(275^65536+53^65536)/2	159864	Kellen Shenton	11/2020
2228	2^530992-1845299	159845	Enzo Doria	07/2015
2229	2^530810+25	159790	Stefano Morozzi	04/2021
2230	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
2231	2^530417-113833	159672	Enzo Doria	09/2014
2232	2^530406-69701	159669	Enzo Doria	02/2016
2233	5*10^159656+41	159657	Robert Price	03/2019
2234	8*10^159614+29	159615	Robert Price	11/2021
2235	7^188858-188858^7	159604	Norbert Schneider	05/2018
2236	7*10^159553-27	159554	Robert Price	11/2022
2237	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
2238	(17*10^159438-377)/9	159439	Robert Price	03/2018
2239	(203*10^159381+1)/3	159383	Robert Price	03/2020
2240	89*10^159258-9	159260	Robert Price	05/2020
2241	2^528944-461315	159229	Enzo Doria	07/2015
2242	(13*10^159147+161)/3	159148	Robert Price	11/2018
2243	2^528620-113879	159131	Enzo Doria	10/2014
2244	(47*10^159083+259)/9	159084	Robert Price	03/2022
2245	2^528000-23307	158944	Enzo Doria	08/2013
2246	(29*10^158909+61)/9	158910	Robert Price	08/2018
2247	2^527817+1876817	158889	Enzo Doria	07/2016
2248	2^527774-49451	158876	Enzo Doria	10/2015
2249	2^527745-291553	158868	Enzo Doria	07/2015
2250	(91*10^158862+11)/3	158864	Robert Price	02/2020

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PRP Records

Probable Primes Top 10000

(291910 PRPs in the top)