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	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
2002	(203*10^162689+1)/3	162691	Robert Price	03/2020
2003	3*10^162620-59	162621	Robert Price	09/2018
2004	3^340694-112960	162553	Enzo Doria	07/2014
2005	2^539807-114081	162499	Enzo Doria	12/2014
2006	414^62093+62093^414	162498	Norbert Schneider	03/2022
2007	2^539654-114893	162453	Enzo Doria	05/2015
2008	9*10^162449-71	162450	Robert Price	11/2020
2009	2^539617-1851583	162441	Enzo Doria	08/2015
2010	(91*10^162410+11)/3	162412	Robert Price	02/2020
2011	2^539346+81049	162360	Enzo Doria	07/2016
2012	2^539220-115499	162322	Enzo Doria	07/2015
2013	2^539217-113713	162321	Enzo Doria	09/2014
2014	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
2015	4*10^162263-39	162264	Robert Price	09/2020
2016	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
2017	(10^162138+11)/3	162138	Serge Batalov	07/2015
2018	(61*10^162100-403)/9	162101	Robert Price	10/2021
2019	2^538473-112723	162097	Enzo Doria	06/2014
2020	2^538157+79337	162002	Enzo Doria	06/2016
2021	2^538136-114749	161996	Enzo Doria	05/2015
2022	2^538104+1531	161986	Lelio R Paula	01/2013
2023	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
2024	2^537815-22737	161899	Enzo Doria	07/2013
2025	2^537804-39839	161896	Enzo Doria	09/2015
2026	(754*10^161816-7)/9	161818	Robert Price	05/2020
2027	2^537458-59201	161791	Enzo Doria	10/2015
2028	2*10^161766+51	161767	Robert Price	05/2018
2029	(7*10^161760+131)/3	161761	Robert Price	06/2020
2030	2^537209-49849	161717	Enzo Doria	10/2015
2031	(58*10^161691+329)/9	161692	Robert Price	05/2019
2032	23*10^161668-3	161670	Robert Price	10/2021
2033	2^536937+1879397	161635	Enzo Doria	09/2016
2034	34*10^161593-9	161595	Robert Price	06/2020
2035	(31*10^161582-1)/3	161584	Robert Price	02/2020
2036	2^536569-22881	161524	Enzo Doria	07/2013
2037	(46*10^161505+593)/9	161506	Robert Price	04/2022
2038	10^161253+573493	161254	Patrick De Geest	07/2018
2039	10^161253-8001	161253	Robert Price	03/2018
2040	97*10^161247-3	161249	Robert Price	05/2020
2041	7*10^161192-9	161193	Robert Price	10/2015
2042	2^535415-19	161176	Stefano Morozzi	07/2022
2043	2^535269-113803	161133	Enzo Doria	09/2014
2044	2^535205-23295	161113	Enzo Doria	08/2013
2045	(49*10^161105+437)/9	161106	Robert Price	09/2021
2046	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
2047	2^534429-19	160880	Stefano Morozzi	07/2022
2048	2^534359-23229	160859	Enzo Doria	08/2013
2049	457^60454+60454^457	160803	Norbert Schneider	07/2021
2050	8*10^160782+53	160783	Robert Price	08/2020
2051	67^88037-66^88037	160763	Robert Price	10/2013
2052	(88*10^160761-637)/9	160762	Robert Price	11/2020
2053	2^533948-1852559	160735	Enzo Doria	08/2015
2054	2^533665-23335	160650	Enzo Doria	08/2013
2055	(19*10^160619+77)/3	160620	Robert Price	05/2019
2056	2^533350-5	160555	Stefano Morozzi	07/2022
2057	(38*10^160508+151)/9	160509	Robert Price	03/2022
2058	3^336353-2^336353	160482	Mike Oakes	10/2007
2059	2*10^160339-63	160340	Robert Price	01/2022
2060	(91*10^160249+11)/3	160251	Robert Price	02/2020
2061	(772*10^160239-7)/9	160241	Robert Price	06/2022
2062	(2*10^160226+187)/9	160226	Robert Price	06/2022
2063	2^532253+1868417	160225	Enzo Doria	04/2016
2064	2^532108-291989	160181	Enzo Doria	07/2015
2065	(28*10^160171-79)/3	160172	Robert Price	02/2021
2066	(26*10^160166-131)/3	160167	Robert Price	10/2019
2067	55*10^160145+9	160147	Robert Price	03/2022
2068	(17*10^160143+67)/3	160144	Robert Price	01/2019
2069	(19*10^159921-49)/3	159922	Robert Price	05/2019
2070	2^531110-1853771	159881	Enzo Doria	09/2015
2071	(275^65536+53^65536)/2	159864	Kellen Shenton	11/2020
2072	2^530992-1845299	159845	Enzo Doria	07/2015
2073	2^530810+25	159790	Stefano Morozzi	04/2021
2074	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
2075	2^530417-113833	159672	Enzo Doria	09/2014
2076	2^530406-69701	159669	Enzo Doria	02/2016
2077	5*10^159656+41	159657	Robert Price	03/2019
2078	8*10^159614+29	159615	Robert Price	11/2021
2079	7^188858-188858^7	159604	Norbert Schneider	05/2018
2080	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
2081	(17*10^159438-377)/9	159439	Robert Price	03/2018
2082	(203*10^159381+1)/3	159383	Robert Price	03/2020
2083	89*10^159258-9	159260	Robert Price	05/2020
2084	2^528944-461315	159229	Enzo Doria	07/2015
2085	(13*10^159147+161)/3	159148	Robert Price	11/2018
2086	2^528620-113879	159131	Enzo Doria	10/2014
2087	(47*10^159083+259)/9	159084	Robert Price	03/2022
2088	2^528000-23307	158944	Enzo Doria	08/2013
2089	(29*10^158909+61)/9	158910	Robert Price	08/2018
2090	2^527817+1876817	158889	Enzo Doria	07/2016
2091	2^527774-49451	158876	Enzo Doria	10/2015
2092	2^527745-291553	158868	Enzo Doria	07/2015
2093	(91*10^158862+11)/3	158864	Robert Price	02/2020
2094	2^527644-1856999	158837	Enzo Doria	10/2015
2095	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
2096	2^527573-1863253	158816	Enzo Doria	12/2015
2097	2^527553-23401	158810	Enzo Doria	08/2013
2098	(49*10^158783+437)/9	158784	Robert Price	09/2021
2099	10^158755+310207	158756	Patrick De Geest	08/2021
2100	10^158755-50001	158755	Robert Price	08/2020
2101	(61*10^158748-619)/9	158749	Robert Price	03/2022
2102	11^152420-210	158730	Enzo Doria	09/2012
2103	(13*10^158694+401)/9	158695	Robert Price	01/2018
2104	2^527052-69059	158659	Enzo Doria	11/2015
2105	2^526849-113233	158598	Enzo Doria	07/2014
2106	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016
2107	(299*10^158544-17)/3	158546	Robert Price	04/2020
2108	2^526658-3551	158540	Yves Minet	03/2017
2109	7*10^158465-11	158466	Robert Price	06/2019
2110	2^526375-23115	158455	Enzo Doria	08/2013
2111	(77*10^158407-293)/9	158408	Robert Price	09/2019
2112	2^526028-112793	158351	Enzo Doria	07/2014
2113	(229*10^158339-1)/3	158341	Robert Price	07/2020
2114	2^525690-9221	158249	Lelio R Paula	01/2013
2115	2*10^158242-7	158243	Robert Price	10/2015
2116	2^525667-525667^2	158242	Henri Lifchitz	12/2017
2117	(56*10^158230+187)/9	158231	Robert Price	10/2021
2118	10^158209-7000000001	158209	Robert Price	12/2021
2119	2^525186-1857431	158097	Enzo Doria	10/2015
2120	2^524515-23245	157895	Enzo Doria	08/2013
2121	2^524499-109087	157890	Enzo Doria	04/2014
2122	2^18067*(2^506221+1)-1	157827	Makoto Morimoto	05/2014
2123	2^524288+189093	157827	Makoto Morimoto	01/2016
2124	2^524288-164073	157827	Matthias Baur	03/2020
2125	(2^(2^19)-9333)/(1923463121331973)	157814	Makoto Morimoto	09/2017
2126	(10^157792+359)/9	157792	Serge Batalov	12/2014
2127	2^524154+25	157787	Stefano Morozzi	04/2021
2128	2^523924+1876591	157717	Enzo Doria	07/2016
2129	(17*10^157705+67)/3	157706	Robert Price	01/2019
2130	(46^94841+1)/47	157696	Robert Price	01/2014
2131	2^523774+77839	157672	Enzo Doria	05/2016
2132	2^523587+2799143	157616	Enzo Doria	04/2016
2133	2^523371+1872113	157551	Enzo Doria	05/2016
2134	8*10^157477+27	157478	Robert Price	09/2021
2135	(8*10^157368+49)/3	157369	Robert Price	05/2020
2136	(82*10^157319+449)/9	157320	Robert Price	11/2019
2137	2^522535-351457	157299	Enzo Doria	07/2015
2138	2^522226+2799079	157206	Enzo Doria	04/2016
2139	(134*10^157191-11)/3	157193	Robert Price	01/2022
2140	2^522134-1849451	157178	Enzo Doria	08/2015
2141	9*10^157152+71	157153	Robert Price	08/2020
2142	4*10^157150+93	157151	Robert Price	08/2018
2143	2^521401-29593	156958	Enzo Doria	08/2015
2144	7*10^156956+87	156957	Robert Price	07/2019
2145	2^521348-23397	156942	Enzo Doria	08/2013
2146	10^156902+34509	156903	Patrick De Geest	08/2021
2148	10^156902-80000001	156902	Robert Price	04/2021
2147	10^156902-69789	156902	Patrick De Geest	08/2021
2149	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
2150	65^86522+64	156857	Lelio R Paula	04/2016
2151	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
2152	2^520977-1858183	156830	Enzo Doria	10/2015
2153	(8*10^156718-101)/3	156719	Robert Price	08/2018
2154	(10^156640+7)/53	156639	Alfred Reich	07/2021
2155	2^520314-1849481	156631	Enzo Doria	08/2015
2156	(13*10^156522+89)/3	156523	Robert Price	09/2018
2157	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
2158	(4*10^156501+119)/3	156502	Robert Price	12/2021
2159	(83*10^156476-101)/9	156477	Robert Price	08/2021
2160	3*10^156435-97	156436	Robert Price	07/2018
2161	(8*10^156371-77)/3	156372	Robert Price	07/2018
2162	53^90679-52^90679	156356	Robert Price	01/2013
2163	(418*10^156309-31)/9	156311	Robert Price	05/2022
2164	2^519106-59141	156267	Enzo Doria	10/2015
2165	2^519053+6077	156251	Enzo Doria	02/2016
2166	2^518968-1860989	156225	Enzo Doria	11/2015
2167	(25*10^156221-7)/9	156222	Robert Price	05/2018
2168	2^518931-2782297	156214	Enzo Doria	09/2015
2169	2^518608-2939	156117	Yves Minet	09/2014
2170	10*27^109005+697	156027	Curtis Bright	05/2015
2171	(49*10^155933-319)/9	155934	Robert Price	10/2021
2172	2^517967-113485	155924	Enzo Doria	08/2014
2173	(103*10^155904+17)/3	155906	Robert Price	08/2020
2174	(8*10^155887-719)/9	155887	Robert Price	03/2021
2175	4*10^155853-39	155854	Robert Price	09/2020
2176	2^517698+4429	155843	Lelio R Paula	01/2013
2177	2^517543-113257	155796	Enzo Doria	07/2014
2178	(14*10^155740-143)/3	155741	Robert Price	11/2018
2179	31^104309-30^104309	155563	Henri Lifchitz	08/2013
2180	2^516742-39851	155555	Enzo Doria	09/2015
2181	(22*10^155543+47)/3	155544	Robert Price	06/2021
2182	(19*10^155504+131)/3	155505	Robert Price	06/2020
2183	7*10^155496+61	155497	Robert Price	08/2019
2184	2^516440+1878421	155464	Enzo Doria	08/2016
2185	2^515863-1867237	155291	Enzo Doria	03/2016
2186	2^515786-461861	155268	Enzo Doria	07/2015
2187	2^515644-113247	155225	Enzo Doria	07/2014
2188	(7*10^155203+107)/3	155204	Robert Price	02/2018
2189	10^155163+206871	155164	Patrick De Geest	05/2021
2190	10^155163-40001	155163	Robert Price	01/2021
2191	(17*10^155133-89)/9	155134	Robert Price	07/2018
2192	2^515227-114997	155099	Enzo Doria	06/2015
2194	EPrime(155025)	155025	Eric W. Weisstein	10/2010
2193	(14*10^155024-221)/9	155025	Robert Price	04/2018
2195	(4*10^155022+173)/3	155023	Robert Price	02/2018
2196	(266*10^154897+1)/3	154899	Robert Price	04/2020
2197	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
2198	(86*10^154853-221)/9	154854	Robert Price	09/2019
2199	2^514361+78167	154839	Enzo Doria	05/2016
2200	2^514281-115033	154815	Enzo Doria	06/2015
2201	2^514194-3311	154788	Yves Minet	12/2014
2202	(14*10^154773+37)/3	154774	Robert Price	12/2018
2203	(16*10^154748+131)/3	154749	Robert Price	03/2022
2204	6*10^154742-31	154743	Robert Price	07/2020
2205	(14*10^154645+139)/9	154646	Robert Price	11/2021
2206	5*10^154618-79	154619	Robert Price	03/2021
2207	(167*10^154595+1)/3	154597	Robert Price	04/2021
2208	2^513437+1879337	154560	Enzo Doria	09/2016
2209	2^513306-113201	154521	Enzo Doria	07/2014
2210	(10^154494-13)/3	154494	Robert Price	12/2017
2211	2^513042-113787	154442	Enzo Doria	09/2014
2212	(151*10^154434-7)/9	154436	Robert Price	01/2020
2213	(118*10^154428+11)/3	154430	Robert Price	03/2022
2214	(14*10^154413+139)/9	154414	Robert Price	11/2021
2215	(77*10^154389-149)/9	154390	Robert Price	03/2022
2216	2^512628-114053	154317	Enzo Doria	11/2014
2217	2^512529-49783	154287	Enzo Doria	10/2015
2218	(355573#+6991)/(6991*2031599)	154285	Makoto Morimoto	06/2019
2219	2^512315-115297	154223	Enzo Doria	06/2015
2220	(47*10^154221+241)/9	154222	Robert Price	06/2022
2221	(7*10^154211+173)/9	154211	Robert Price	01/2022
2222	2^512168+79561	154178	Enzo Doria	06/2016
2223	(77*10^154175+67)/9	154176	Robert Price	12/2021
2224	(5*10^154158-311)/9	154158	Robert Price	12/2021
2225	(89*10^154103-737)/9	154104	Robert Price	01/2022
2226	4*10^154078-57	154079	Robert Price	10/2018
2227	(355049#+1859)/(111310148891*62587751)	154051	Makoto Morimoto	06/2019
2228	7*10^154038-57	154039	Robert Price	06/2020
2229	2^511658-114371	154025	Enzo Doria	02/2015
2230	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
2231	2^511580-1846679	154001	Enzo Doria	07/2015
2232	(259*10^153998-1)/3	154000	Robert Price	12/2020
2233	2^511541-113713	153990	Enzo Doria	09/2014
2234	49958^32768+49957^32768	153965	Kellen Shenton	11/2020
2235	10^153935+970801	153936	Patrick De Geest	05/2021
2236	10^153935-1000001	153935	Robert Price	08/2020
2237	(16*10^153868-73)/3	153869	Robert Price	07/2020
2238	9*10^153851-67	153852	Robert Price	11/2020
2239	2^511077-112723	153850	Enzo Doria	06/2014
2240	69^83653-68^83653	153826	Robert Price	12/2013
2241	2^510963-113707	153816	Enzo Doria	09/2014
2242	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
2243	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
2244	2*10^153746-3	153747	Robert Price	07/2015
2245	2^510626+1179379	153714	Enzo Doria	05/2016
2246	(7*10^153664+113)/3	153665	Robert Price	02/2018
2247	2^510420+81121	153652	Enzo Doria	07/2016
2248	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
2249	2^509894-459161	153494	Enzo Doria	05/2015
2250	(74*10^153489+673)/9	153490	Robert Price	02/2022

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PRP Records

Probable Primes Top 10000

(290974 PRPs in the top)