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	(26*10^164643-167)/3	164644	Robert Price	10/2019
2002	(10^164643+83)/3	164643	Robert Price	08/2021
2003	2^546398-59201	164483	Enzo Doria	10/2015
2004	2^546332-114893	164463	Enzo Doria	05/2015
2005	(65*10^164427+277)/9	164428	Robert Price	08/2021
2006	2^545958+1876189	164350	Enzo Doria	07/2016
2007	2^545878-49841	164326	Enzo Doria	10/2015
2008	(10^164284+77)/3	164284	Robert Price	01/2018
2009	2^545668-4019	164263	Yves Minet	04/2017
2010	10^164216+780639	164217	Patrick De Geest	08/2021
2012	10^164216-50000000001	164216	Robert Price	12/2020
2011	10^164216-891051	164216	Patrick De Geest	08/2021
2013	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
2014	(16*10^164122+197)/3	164123	Robert Price	04/2019
2015	2^545185+76757	164118	Enzo Doria	05/2016
2016	2^545076-114329	164085	Enzo Doria	01/2015
2017	(2*10^164043-143)/3	164043	Robert Price	03/2018
2018	(29^112153+1)/30	164011	Lelio R Paula	03/2017
2019	2^544757+1874777	163989	Enzo Doria	06/2016
2020	2^544444-457199	163894	Enzo Doria	01/2015
2021	2^544264-343529	163840	Enzo Doria	07/2015
2022	7*10^163780+9	163781	Robert Price	09/2015
2023	2^543989+2793047	163758	Enzo Doria	02/2016
2024	(28*10^163709+113)/3	163710	Robert Price	03/2020
2025	(23*10^163523+301)/9	163524	Robert Price	06/2021
2026	(68*10^163521-329)/9	163522	Robert Price	03/2021
2027	35820^35899+35899^35820	163489	Norbert Schneider	11/2021
2028	2^542870-69551	163421	Enzo Doria	12/2015
2029	2^542395+72533	163278	Enzo Doria	04/2016
2030	2^542072-3683	163180	Yves Minet	03/2017
2031	(682*10^163106-7)/9	163108	Robert Price	08/2021
2032	2^541779-1867357	163092	Enzo Doria	04/2016
2033	(29*10^163056+313)/9	163057	Robert Price	04/2021
2034	8*10^162924+9	162925	Robert Price	12/2015
2035	2^540905+81557	162829	Enzo Doria	08/2016
2036	2^540628-2939	162746	Yves Minet	09/2014
2037	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
2038	(203*10^162689+1)/3	162691	Robert Price	03/2020
2039	3*10^162620-59	162621	Robert Price	09/2018
2040	3^340694-112960	162553	Enzo Doria	07/2014
2041	2^539807-114081	162499	Enzo Doria	12/2014
2042	414^62093+62093^414	162498	Norbert Schneider	03/2022
2043	2^539654-114893	162453	Enzo Doria	05/2015
2044	9*10^162449-71	162450	Robert Price	11/2020
2045	2^539617-1851583	162441	Enzo Doria	08/2015
2046	(509*10^162422+31)/9	162424	Robert Price	08/2022
2047	(91*10^162410+11)/3	162412	Robert Price	02/2020
2048	2^539346+81049	162360	Enzo Doria	07/2016
2049	2^539220-115499	162322	Enzo Doria	07/2015
2050	2^539217-113713	162321	Enzo Doria	09/2014
2051	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
2052	4*10^162263-39	162264	Robert Price	09/2020
2053	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
2054	(10^162138+11)/3	162138	Serge Batalov	07/2015
2055	(61*10^162100-403)/9	162101	Robert Price	10/2021
2056	2^538473-112723	162097	Enzo Doria	06/2014
2057	2^538157+79337	162002	Enzo Doria	06/2016
2058	2^538136-114749	161996	Enzo Doria	05/2015
2059	2^538104+1531	161986	Lelio R Paula	01/2013
2060	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
2061	2^537815-22737	161899	Enzo Doria	07/2013
2062	2^537804-39839	161896	Enzo Doria	09/2015
2063	(754*10^161816-7)/9	161818	Robert Price	05/2020
2064	2^537458-59201	161791	Enzo Doria	10/2015
2065	2*10^161766+51	161767	Robert Price	05/2018
2066	(7*10^161760+131)/3	161761	Robert Price	06/2020
2067	2^537209-49849	161717	Enzo Doria	10/2015
2068	(58*10^161691+329)/9	161692	Robert Price	05/2019
2069	23*10^161668-3	161670	Robert Price	10/2021
2070	2^536937+1879397	161635	Enzo Doria	09/2016
2071	34*10^161593-9	161595	Robert Price	06/2020
2072	(31*10^161582-1)/3	161584	Robert Price	02/2020
2073	2^536569-22881	161524	Enzo Doria	07/2013
2074	(46*10^161505+593)/9	161506	Robert Price	04/2022
2075	10^161253+573493	161254	Patrick De Geest	07/2018
2076	10^161253-8001	161253	Robert Price	03/2018
2077	97*10^161247-3	161249	Robert Price	05/2020
2078	7*10^161192-9	161193	Robert Price	10/2015
2079	2^535415-19	161176	Stefano Morozzi	07/2022
2080	2^535269-113803	161133	Enzo Doria	09/2014
2081	2^535205-23295	161113	Enzo Doria	08/2013
2082	(49*10^161105+437)/9	161106	Robert Price	09/2021
2083	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
2084	2^534429-19	160880	Stefano Morozzi	07/2022
2085	2^534359-23229	160859	Enzo Doria	08/2013
2086	457^60454+60454^457	160803	Norbert Schneider	07/2021
2087	8*10^160782+53	160783	Robert Price	08/2020
2088	67^88037-66^88037	160763	Robert Price	10/2013
2089	(88*10^160761-637)/9	160762	Robert Price	11/2020
2090	2^533948-1852559	160735	Enzo Doria	08/2015
2091	2^533665-23335	160650	Enzo Doria	08/2013
2092	(19*10^160619+77)/3	160620	Robert Price	05/2019
2093	2^533350-5	160555	Stefano Morozzi	07/2022
2094	(38*10^160508+151)/9	160509	Robert Price	03/2022
2095	3^336353-2^336353	160482	Mike Oakes	10/2007
2096	2*10^160339-63	160340	Robert Price	01/2022
2097	(91*10^160249+11)/3	160251	Robert Price	02/2020
2098	(772*10^160239-7)/9	160241	Robert Price	06/2022
2099	(2*10^160226+187)/9	160226	Robert Price	06/2022
2100	2^532253+1868417	160225	Enzo Doria	04/2016
2101	2^532108-291989	160181	Enzo Doria	07/2015
2102	(28*10^160171-79)/3	160172	Robert Price	02/2021
2103	(26*10^160166-131)/3	160167	Robert Price	10/2019
2104	55*10^160145+9	160147	Robert Price	03/2022
2105	(17*10^160143+67)/3	160144	Robert Price	01/2019
2106	(19*10^159921-49)/3	159922	Robert Price	05/2019
2107	2^531110-1853771	159881	Enzo Doria	09/2015
2108	(275^65536+53^65536)/2	159864	Kellen Shenton	11/2020
2109	2^530992-1845299	159845	Enzo Doria	07/2015
2110	2^530810+25	159790	Stefano Morozzi	04/2021
2111	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
2112	2^530417-113833	159672	Enzo Doria	09/2014
2113	2^530406-69701	159669	Enzo Doria	02/2016
2114	5*10^159656+41	159657	Robert Price	03/2019
2115	8*10^159614+29	159615	Robert Price	11/2021
2116	7^188858-188858^7	159604	Norbert Schneider	05/2018
2117	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
2118	(17*10^159438-377)/9	159439	Robert Price	03/2018
2119	(203*10^159381+1)/3	159383	Robert Price	03/2020
2120	89*10^159258-9	159260	Robert Price	05/2020
2121	2^528944-461315	159229	Enzo Doria	07/2015
2122	(13*10^159147+161)/3	159148	Robert Price	11/2018
2123	2^528620-113879	159131	Enzo Doria	10/2014
2124	(47*10^159083+259)/9	159084	Robert Price	03/2022
2125	2^528000-23307	158944	Enzo Doria	08/2013
2126	(29*10^158909+61)/9	158910	Robert Price	08/2018
2127	2^527817+1876817	158889	Enzo Doria	07/2016
2128	2^527774-49451	158876	Enzo Doria	10/2015
2129	2^527745-291553	158868	Enzo Doria	07/2015
2130	(91*10^158862+11)/3	158864	Robert Price	02/2020
2131	2^527644-1856999	158837	Enzo Doria	10/2015
2132	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
2133	2^527573-1863253	158816	Enzo Doria	12/2015
2134	2^527553-23401	158810	Enzo Doria	08/2013
2135	(49*10^158783+437)/9	158784	Robert Price	09/2021
2136	10^158755+310207	158756	Patrick De Geest	08/2021
2137	10^158755-50001	158755	Robert Price	08/2020
2138	(61*10^158748-619)/9	158749	Robert Price	03/2022
2139	11^152420-210	158730	Enzo Doria	09/2012
2140	(13*10^158694+401)/9	158695	Robert Price	01/2018
2141	2^527052-69059	158659	Enzo Doria	11/2015
2142	2^526849-113233	158598	Enzo Doria	07/2014
2143	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016
2144	(299*10^158544-17)/3	158546	Robert Price	04/2020
2145	2^526658-3551	158540	Yves Minet	03/2017
2146	7*10^158465-11	158466	Robert Price	06/2019
2147	2^526375-23115	158455	Enzo Doria	08/2013
2148	(77*10^158407-293)/9	158408	Robert Price	09/2019
2149	2^526028-112793	158351	Enzo Doria	07/2014
2150	(229*10^158339-1)/3	158341	Robert Price	07/2020
2151	2^525690-9221	158249	Lelio R Paula	01/2013
2152	2*10^158242-7	158243	Robert Price	10/2015
2153	2^525667-525667^2	158242	Henri Lifchitz	12/2017
2154	(56*10^158230+187)/9	158231	Robert Price	10/2021
2155	10^158209-7000000001	158209	Robert Price	12/2021
2156	2^525186-1857431	158097	Enzo Doria	10/2015
2157	2^524515-23245	157895	Enzo Doria	08/2013
2158	2^524499-109087	157890	Enzo Doria	04/2014
2159	2^18067*(2^506221+1)-1	157827	Makoto Morimoto	05/2014
2160	2^524288+189093	157827	Makoto Morimoto	01/2016
2161	2^524288-164073	157827	Matthias Baur	03/2020
2162	(2^(2^19)-9333)/(1923463121331973)	157814	Makoto Morimoto	09/2017
2163	(10^157792+359)/9	157792	Serge Batalov	12/2014
2164	2^524154+25	157787	Stefano Morozzi	04/2021
2165	2^523924+1876591	157717	Enzo Doria	07/2016
2166	(17*10^157705+67)/3	157706	Robert Price	01/2019
2167	(46^94841+1)/47	157696	Robert Price	01/2014
2168	2^523774+77839	157672	Enzo Doria	05/2016
2169	2^523587+2799143	157616	Enzo Doria	04/2016
2170	2^523371+1872113	157551	Enzo Doria	05/2016
2171	8*10^157477+27	157478	Robert Price	09/2021
2172	(8*10^157368+49)/3	157369	Robert Price	05/2020
2173	(82*10^157319+449)/9	157320	Robert Price	11/2019
2174	2^522535-351457	157299	Enzo Doria	07/2015
2175	2^522226+2799079	157206	Enzo Doria	04/2016
2176	(134*10^157191-11)/3	157193	Robert Price	01/2022
2177	2^522134-1849451	157178	Enzo Doria	08/2015
2178	9*10^157152+71	157153	Robert Price	08/2020
2179	4*10^157150+93	157151	Robert Price	08/2018
2180	2^521401-29593	156958	Enzo Doria	08/2015
2181	7*10^156956+87	156957	Robert Price	07/2019
2182	2^521348-23397	156942	Enzo Doria	08/2013
2183	10^156902+34509	156903	Patrick De Geest	08/2021
2185	10^156902-80000001	156902	Robert Price	04/2021
2184	10^156902-69789	156902	Patrick De Geest	08/2021
2186	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
2187	65^86522+64	156857	Lelio R Paula	04/2016
2188	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
2189	2^520977-1858183	156830	Enzo Doria	10/2015
2190	(8*10^156718-101)/3	156719	Robert Price	08/2018
2191	(10^156640+7)/53	156639	Alfred Reich	07/2021
2192	2^520314-1849481	156631	Enzo Doria	08/2015
2193	(16*10^156563-637)/9	156564	Robert Price	09/2022
2194	(13*10^156522+89)/3	156523	Robert Price	09/2018
2195	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
2196	(2^519925-5)/3	156513	Stefano Morozzi	08/2022
2197	(4*10^156501+119)/3	156502	Robert Price	12/2021
2198	(83*10^156476-101)/9	156477	Robert Price	08/2021
2199	3*10^156435-97	156436	Robert Price	07/2018
2200	(8*10^156371-77)/3	156372	Robert Price	07/2018
2201	53^90679-52^90679	156356	Robert Price	01/2013
2202	(418*10^156309-31)/9	156311	Robert Price	05/2022
2203	2^519106-59141	156267	Enzo Doria	10/2015
2204	2^519053+6077	156251	Enzo Doria	02/2016
2205	2^518968-1860989	156225	Enzo Doria	11/2015
2206	(25*10^156221-7)/9	156222	Robert Price	05/2018
2207	2^518931-2782297	156214	Enzo Doria	09/2015
2208	2^518608-2939	156117	Yves Minet	09/2014
2209	10*27^109005+697	156027	Curtis Bright	05/2015
2210	(49*10^155933-319)/9	155934	Robert Price	10/2021
2211	2^517967-113485	155924	Enzo Doria	08/2014
2212	(103*10^155904+17)/3	155906	Robert Price	08/2020
2213	(8*10^155887-719)/9	155887	Robert Price	03/2021
2214	4*10^155853-39	155854	Robert Price	09/2020
2215	2^517698+4429	155843	Lelio R Paula	01/2013
2216	2^517543-113257	155796	Enzo Doria	07/2014
2217	(14*10^155740-143)/3	155741	Robert Price	11/2018
2218	31^104309-30^104309	155563	Henri Lifchitz	08/2013
2219	2^516742-39851	155555	Enzo Doria	09/2015
2220	(22*10^155543+47)/3	155544	Robert Price	06/2021
2221	(19*10^155504+131)/3	155505	Robert Price	06/2020
2222	7*10^155496+61	155497	Robert Price	08/2019
2223	2^516440+1878421	155464	Enzo Doria	08/2016
2224	2^515863-1867237	155291	Enzo Doria	03/2016
2225	2^515786-461861	155268	Enzo Doria	07/2015
2226	2^515644-113247	155225	Enzo Doria	07/2014
2227	(7*10^155203+107)/3	155204	Robert Price	02/2018
2228	10^155163+206871	155164	Patrick De Geest	05/2021
2229	10^155163-40001	155163	Robert Price	01/2021
2230	(17*10^155133-89)/9	155134	Robert Price	07/2018
2231	2^515227-114997	155099	Enzo Doria	06/2015
2233	EPrime(155025)	155025	Eric W. Weisstein	10/2010
2232	(14*10^155024-221)/9	155025	Robert Price	04/2018
2234	(4*10^155022+173)/3	155023	Robert Price	02/2018
2235	(266*10^154897+1)/3	154899	Robert Price	04/2020
2236	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
2237	(86*10^154853-221)/9	154854	Robert Price	09/2019
2238	2^514361+78167	154839	Enzo Doria	05/2016
2239	2^514281-115033	154815	Enzo Doria	06/2015
2240	2^514194-3311	154788	Yves Minet	12/2014
2241	(14*10^154773+37)/3	154774	Robert Price	12/2018
2242	(16*10^154748+131)/3	154749	Robert Price	03/2022
2243	6*10^154742-31	154743	Robert Price	07/2020
2244	(14*10^154645+139)/9	154646	Robert Price	11/2021
2245	5*10^154618-79	154619	Robert Price	03/2021
2246	(167*10^154595+1)/3	154597	Robert Price	04/2021
2247	2^513437+1879337	154560	Enzo Doria	09/2016
2248	2^513306-113201	154521	Enzo Doria	07/2014
2249	(10^154494-13)/3	154494	Robert Price	12/2017
2250	2^513042-113787	154442	Enzo Doria	09/2014

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PRP Records

Probable Primes Top 10000

(291192 PRPs in the top)