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	2^522535-351457	157299	Enzo Doria	07/2015
2002	2^522226+2799079	157206	Enzo Doria	04/2016
2003	(134*10^157191-11)/3	157193	Robert Price	01/2022
2004	2^522134-1849451	157178	Enzo Doria	08/2015
2005	9*10^157152+71	157153	Robert Price	08/2020
2006	4*10^157150+93	157151	Robert Price	08/2018
2007	2^521401-29593	156958	Enzo Doria	08/2015
2008	7*10^156956+87	156957	Robert Price	07/2019
2009	2^521348-23397	156942	Enzo Doria	08/2013
2010	10^156902+34509	156903	Patrick De Geest	08/2021
2012	10^156902-80000001	156902	Robert Price	04/2021
2011	10^156902-69789	156902	Patrick De Geest	08/2021
2013	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
2014	65^86522+64	156857	Lelio R Paula	04/2016
2015	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
2016	2^520977-1858183	156830	Enzo Doria	10/2015
2017	(8*10^156718-101)/3	156719	Robert Price	08/2018
2018	(10^156640+7)/53	156639	Alfred Reich	07/2021
2019	2^520314-1849481	156631	Enzo Doria	08/2015
2020	(13*10^156522+89)/3	156523	Robert Price	09/2018
2021	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
2022	(4*10^156501+119)/3	156502	Robert Price	12/2021
2023	(83*10^156476-101)/9	156477	Robert Price	08/2021
2024	3*10^156435-97	156436	Robert Price	07/2018
2025	(8*10^156371-77)/3	156372	Robert Price	07/2018
2026	53^90679-52^90679	156356	Robert Price	01/2013
2027	2^519106-59141	156267	Enzo Doria	10/2015
2028	2^519053+6077	156251	Enzo Doria	02/2016
2029	2^518968-1860989	156225	Enzo Doria	11/2015
2030	(25*10^156221-7)/9	156222	Robert Price	05/2018
2031	2^518931-2782297	156214	Enzo Doria	09/2015
2032	2^518608-2939	156117	Yves Minet	09/2014
2033	10*27^109005+697	156027	Curtis Bright	05/2015
2034	(49*10^155933-319)/9	155934	Robert Price	10/2021
2035	2^517967-113485	155924	Enzo Doria	08/2014
2036	(103*10^155904+17)/3	155906	Robert Price	08/2020
2037	(8*10^155887-719)/9	155887	Robert Price	03/2021
2038	4*10^155853-39	155854	Robert Price	09/2020
2039	2^517698+4429	155843	Lelio R Paula	01/2013
2040	2^517543-113257	155796	Enzo Doria	07/2014
2041	(14*10^155740-143)/3	155741	Robert Price	11/2018
2042	31^104309-30^104309	155563	Henri Lifchitz	08/2013
2043	2^516742-39851	155555	Enzo Doria	09/2015
2044	(22*10^155543+47)/3	155544	Robert Price	06/2021
2045	(19*10^155504+131)/3	155505	Robert Price	06/2020
2046	7*10^155496+61	155497	Robert Price	08/2019
2047	2^516440+1878421	155464	Enzo Doria	08/2016
2048	2^515863-1867237	155291	Enzo Doria	03/2016
2049	2^515786-461861	155268	Enzo Doria	07/2015
2050	2^515644-113247	155225	Enzo Doria	07/2014
2051	(7*10^155203+107)/3	155204	Robert Price	02/2018
2052	10^155163+206871	155164	Patrick De Geest	05/2021
2053	10^155163-40001	155163	Robert Price	01/2021
2054	(17*10^155133-89)/9	155134	Robert Price	07/2018
2055	2^515227-114997	155099	Enzo Doria	06/2015
2057	EPrime(155025)	155025	Eric W. Weisstein	10/2010
2056	(14*10^155024-221)/9	155025	Robert Price	04/2018
2058	(4*10^155022+173)/3	155023	Robert Price	02/2018
2059	(266*10^154897+1)/3	154899	Robert Price	04/2020
2060	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
2061	(86*10^154853-221)/9	154854	Robert Price	09/2019
2062	2^514361+78167	154839	Enzo Doria	05/2016
2063	2^514281-115033	154815	Enzo Doria	06/2015
2064	2^514194-3311	154788	Yves Minet	12/2014
2065	(14*10^154773+37)/3	154774	Robert Price	12/2018
2066	6*10^154742-31	154743	Robert Price	07/2020
2067	(14*10^154645+139)/9	154646	Robert Price	11/2021
2068	5*10^154618-79	154619	Robert Price	03/2021
2069	(167*10^154595+1)/3	154597	Robert Price	04/2021
2070	2^513437+1879337	154560	Enzo Doria	09/2016
2071	2^513306-113201	154521	Enzo Doria	07/2014
2072	(10^154494-13)/3	154494	Robert Price	12/2017
2073	2^513042-113787	154442	Enzo Doria	09/2014
2074	(151*10^154434-7)/9	154436	Robert Price	01/2020
2075	(14*10^154413+139)/9	154414	Robert Price	11/2021
2076	2^512628-114053	154317	Enzo Doria	11/2014
2077	2^512529-49783	154287	Enzo Doria	10/2015
2078	(355573#+6991)/(6991*2031599)	154285	Makoto Morimoto	06/2019
2079	2^512315-115297	154223	Enzo Doria	06/2015
2080	(7*10^154211+173)/9	154211	Robert Price	01/2022
2081	2^512168+79561	154178	Enzo Doria	06/2016
2082	(77*10^154175+67)/9	154176	Robert Price	12/2021
2083	(5*10^154158-311)/9	154158	Robert Price	12/2021
2084	(89*10^154103-737)/9	154104	Robert Price	01/2022
2085	4*10^154078-57	154079	Robert Price	10/2018
2086	(355049#+1859)/(111310148891*62587751)	154051	Makoto Morimoto	06/2019
2087	7*10^154038-57	154039	Robert Price	06/2020
2088	2^511658-114371	154025	Enzo Doria	02/2015
2089	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
2090	2^511580-1846679	154001	Enzo Doria	07/2015
2091	(259*10^153998-1)/3	154000	Robert Price	12/2020
2092	2^511541-113713	153990	Enzo Doria	09/2014
2093	49958^32768+49957^32768	153965	Kellen Shenton	11/2020
2094	10^153935+970801	153936	Patrick De Geest	05/2021
2095	10^153935-1000001	153935	Robert Price	08/2020
2096	(16*10^153868-73)/3	153869	Robert Price	07/2020
2097	9*10^153851-67	153852	Robert Price	11/2020
2098	2^511077-112723	153850	Enzo Doria	06/2014
2099	69^83653-68^83653	153826	Robert Price	12/2013
2100	2^510963-113707	153816	Enzo Doria	09/2014
2101	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
2102	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
2103	2*10^153746-3	153747	Robert Price	07/2015
2104	2^510626+1179379	153714	Enzo Doria	05/2016
2105	(7*10^153664+113)/3	153665	Robert Price	02/2018
2106	2^510420+81121	153652	Enzo Doria	07/2016
2107	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
2108	2^509894-459161	153494	Enzo Doria	05/2015
2109	2^509841+71657	153478	Enzo Doria	04/2016
2110	9*10^153446+41	153447	Robert Price	08/2020
2111	2^509533-1846723	153385	Enzo Doria	07/2015
2112	2^509468-39989	153366	Enzo Doria	09/2015
2113	70^83117-69^83117	153360	Robert Price	01/2014
2114	(112*10^153025-1)/3	153027	Serge Batalov	12/2014
2115	(19*10^153010+131)/3	153011	Robert Price	06/2020
2116	2^508174-1855151	152976	Enzo Doria	09/2015
2117	181^67757-2	152974	Lelio R Paula	12/2017
2118	2^508160-1864829	152972	Enzo Doria	01/2016
2119	10^152960+412563	152961	Patrick De Geest	05/2021
2120	10^152960-50000000001	152960	Robert Price	12/2020
2121	10^152960-423749	152960	Patrick De Geest	05/2021
2122	(71*10^152933-143)/9	152934	Robert Price	10/2021
2123	2^507857-1848199	152881	Enzo Doria	07/2015
2124	2^507638-115361	152815	Enzo Doria	07/2015
2125	2^507551-114025	152789	Enzo Doria	11/2014
2126	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
2127	(22*10^152670-13)/9	152671	Robert Price	06/2018
2128	2^506451-22339	152457	Enzo Doria	07/2013
2129	2^505995-113185	152320	Enzo Doria	07/2014
2130	(4*10^152253+149)/9	152253	Robert Price	04/2018
2131	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
2132	2^505431-505431	152150	Henri Lifchitz	04/2005
2133	(203*10^152143+1)/3	152145	Robert Price	03/2020
2134	2^505053+73097	152037	Enzo Doria	04/2016
2135	22*10^151998+3	152000	Robert Price	01/2020
2136	(238*10^151979-1)/3	151981	Robert Price	04/2020
2137	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
2138	350377#+797581	151937	Nicolas PALAU	08/2017
2139	2^504618-343991	151906	Enzo Doria	07/2015
2140	2^504212-461939	151783	Enzo Doria	07/2015
2141	7*10^151772-41	151773	Robert Price	08/2021
2142	2^504054-2231	151736	Yves Minet	10/2011
2143	(28*10^151682+191)/3	151683	Robert Price	02/2020
2144	2^503475-933075	151562	Paul Bourdelais	06/2021
2145	2^503361-39883	151527	Enzo Doria	09/2015
2146	2^503225+382667	151486	Enzo Doria	10/2016
2147	(844*10^151396-7)/9	151398	Robert Price	05/2021
2148	(26*10^151391-503)/9	151392	Robert Price	07/2018
2149	2^502769+1877567	151349	Enzo Doria	08/2016
2150	2^502576-4019	151291	Yves Minet	10/2011
2151	5*10^151257+41	151258	Robert Price	03/2019
2152	2^502290-2792501	151205	Enzo Doria	02/2016
2153	2^502181+1868417	151172	Enzo Doria	04/2016
2154	6*10^151063-77	151064	Robert Price	09/2021
2155	2^501781-1850503	151052	Enzo Doria	08/2015
2156	(5*10^151007+37)/3	151008	Robert Price	03/2018
2157	2^501627-991	151005	Yves Minet	02/2014
2158	2^501577-115333	150990	Enzo Doria	07/2015
2159	8*10^150975+3	150976	Robert Price	08/2015
2160	2^501512-113669	150971	Enzo Doria	09/2014
2161	(83*10^150908+493)/9	150909	Robert Price	12/2021
2162	2*10^150818+83	150819	Robert Price	12/2021
2163	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
2164	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
2165	2^500899-500899	150786	Henri Lifchitz	04/2005
2166	2^500832+1876801	150766	Enzo Doria	07/2016
2167	(23*10^150763-59)/9	150764	Robert Price	05/2018
2168	2^500699+1884953	150726	Enzo Doria	02/2017
2169	(13*10^150675-37)/3	150676	Robert Price	01/2019
2170	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
2171	2^500337-71101	150617	Enzo Doria	04/2016
2172	(74*10^150616+133)/9	150617	Robert Price	06/2019
2173	4*10^150577+91	150578	Robert Price	08/2018
2174	2^500160+80071	150564	Enzo Doria	06/2016
2175	(2^500120+5)/9	150551	Lelio R Paula	12/2017
2176	(43*10^150515-421)/9	150516	Robert Price	01/2019
2177	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
2178	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
2179	2^499861-29503	150474	Enzo Doria	08/2015
2180	2^499653-113533	150411	Enzo Doria	08/2014
2181	(14*10^150391-191)/3	150392	Robert Price	10/2020
2182	2^499534-221	150375	Yves Minet	06/2012
2183	(28*10^150294+41)/3	150295	Robert Price	07/2021
2184	2^499225+49727	150282	Enzo Doria	09/2016
2185	(695*10^150274+7)/9	150276	Robert Price	12/2021
2186	2^499054-29261	150231	Enzo Doria	07/2015
2187	(844*10^150196-7)/9	150198	Robert Price	05/2021
2188	2^498907-933075	150186	Paul Bourdelais	06/2021
2189	(2^498898-7)/9	150183	Lelio R Paula	10/2015
2190	3*10^150182+17	150183	Robert Price	07/2018
2191	5*10^150175+63	150176	Robert Price	09/2020
2192	(77*10^150128+67)/9	150129	Robert Price	12/2021
2193	2^498623+1866983	150101	Enzo Doria	03/2016
2194	(25*10^150050-403)/9	150051	Robert Price	12/2020
2195	numbpart(18140942830)	150033	Serge Batalov	04/2017
2196	10^150029+4381	150030	Patrick De Geest	05/2016
2197	10^150029-41	150029	Serge Batalov	12/2014
2198	10^150000+1158603	150001	Patrick De Geest	09/2018
2199	10^150000-245703	150000	Patrick De Geest	09/2018
2200	(38*10^149999+691)/9	150000	Robert Price	10/2018
2201	2^498238-53	149985	Lelio R Paula	12/2017
2202	45728^1905+1905^45728	149984	Hans Havermann	10/2020
2203	5*10^149907+23	149908	Robert Price	03/2019
2204	39347^6442+6442^39347	149874	Hans Havermann	09/2020
2205	2^497850+81049	149868	Enzo Doria	07/2016
2206	37228^10575+10575^37228	149816	Hans Havermann	10/2020
2207	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
2208	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
2209	(2*10^149803-143)/3	149803	Robert Price	03/2018
2210	33845^26604+26604^33845	149763	Hans Havermann	09/2020
2211	2^497434-2784191	149743	Enzo Doria	10/2015
2212	(865*10^149737-1)/9	149739	Robert Price	04/2020
2213	10^149695-7000001	149695	Robert Price	06/2021
2214	38237^8214+8214^38237	149681	Hans Havermann	09/2020
2215	(23*10^149655+19)/3	149656	Robert Price	07/2019
2216	2^497068-113579	149633	Enzo Doria	08/2014
2217	2^497037+73727	149624	Enzo Doria	04/2016
2218	11*10^149618+3	149620	Robert Price	07/2021
2219	34942^19067+19067^34942	149562	Hans Havermann	09/2020
2220	33696^27449+27449^33696	149561	Hans Havermann	09/2020
2221	2^496773+77747	149544	Enzo Doria	05/2016
2222	(7*10^149483-493)/9	149483	Robert Price	04/2021
2223	(206*10^149459+7)/3	149461	Robert Price	07/2020
2224	34589^20940+20940^34589	149459	Hans Havermann	09/2020
2225	2^496477-113485	149455	Enzo Doria	08/2014
2226	((10^74703-1)10000/9+7481)10^74703+(10^74703-1)/9	149410	Hans Havermann	09/2019
2227	2^496270-49451	149393	Enzo Doria	10/2015
2228	2^496238-1865081	149383	Enzo Doria	01/2016
2229	33831^26030+26030^33831	149380	Hans Havermann	09/2020
2230	34131^23780+23780^34131	149365	Hans Havermann	09/2020
2231	(5*10^149335-53)/3	149336	Robert Price	09/2020
2232	2^495968-1853699	149302	Enzo Doria	09/2015
2233	2^495935-4117	149292	Yves Minet	02/2018
2234	35816^14709+14709^35816	149267	Hans Havermann	09/2020
2235	(10^149264+7)/191/2683/80557	149254	Alfred Reich	07/2021
2236	2^495712-396765	149225	Enzo Doria	07/2013
2237	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
2238	2^495420+1880701	149137	Enzo Doria	10/2016
2239	2^495337-1847293	149112	Enzo Doria	07/2015
2240	(2^495193-7)/5	149068	Lelio R Paula	10/2015
2241	2^495163+111546435	149059	Paul Bourdelais	10/2021
2242	33282^30097+30097^33282	149055	Hans Havermann	09/2020
2243	37384^9705+9705^37384	149050	Hans Havermann	09/2020
2244	34808^19143+19143^34808	149049	Hans Havermann	09/2020
2245	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
2246	47^89113-46^89113	149006	Robert Price	10/2012
2247	2^494916+87855	148985	Lelio R Paula	01/2016
2248	6*10^148982+73	148983	Robert Price	04/2019
2249	10^148934+1530019	148935	Patrick De Geest	02/2021
2250	10^148934-1000000001	148934	Robert Price	11/2020

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PRP Records

Probable Primes Top 10000

(288949 PRPs in the top)