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	7*10^154038-57	154039	Robert Price	06/2020
2002	2^511658-114371	154025	Enzo Doria	02/2015
2003	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
2004	2^511580-1846679	154001	Enzo Doria	07/2015
2005	(259*10^153998-1)/3	154000	Robert Price	12/2020
2006	2^511541-113713	153990	Enzo Doria	09/2014
2007	49958^32768+49957^32768	153965	Kellen Shenton	11/2020
2008	10^153935+970801	153936	Patrick De Geest	05/2021
2009	10^153935-1000001	153935	Robert Price	08/2020
2010	(16*10^153868-73)/3	153869	Robert Price	07/2020
2011	9*10^153851-67	153852	Robert Price	11/2020
2012	2^511077-112723	153850	Enzo Doria	06/2014
2013	69^83653-68^83653	153826	Robert Price	12/2013
2014	2^510963-113707	153816	Enzo Doria	09/2014
2015	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
2016	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
2017	2*10^153746-3	153747	Robert Price	07/2015
2018	2^510626+1179379	153714	Enzo Doria	05/2016
2019	(7*10^153664+113)/3	153665	Robert Price	02/2018
2020	2^510420+81121	153652	Enzo Doria	07/2016
2021	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
2022	2^509894-459161	153494	Enzo Doria	05/2015
2023	2^509841+71657	153478	Enzo Doria	04/2016
2024	9*10^153446+41	153447	Robert Price	08/2020
2025	2^509533-1846723	153385	Enzo Doria	07/2015
2026	2^509468-39989	153366	Enzo Doria	09/2015
2027	70^83117-69^83117	153360	Robert Price	01/2014
2028	(112*10^153025-1)/3	153027	Serge Batalov	12/2014
2029	(19*10^153010+131)/3	153011	Robert Price	06/2020
2030	2^508174-1855151	152976	Enzo Doria	09/2015
2031	181^67757-2	152974	Lelio R Paula	12/2017
2032	2^508160-1864829	152972	Enzo Doria	01/2016
2033	10^152960+412563	152961	Patrick De Geest	05/2021
2034	10^152960-50000000001	152960	Robert Price	12/2020
2035	10^152960-423749	152960	Patrick De Geest	05/2021
2036	(71*10^152933-143)/9	152934	Robert Price	10/2021
2037	2^507857-1848199	152881	Enzo Doria	07/2015
2038	2^507638-115361	152815	Enzo Doria	07/2015
2039	2^507551-114025	152789	Enzo Doria	11/2014
2040	(6^196337+1)/7	152780	Paul Bourdelais	02/2010
2041	(22*10^152670-13)/9	152671	Robert Price	06/2018
2042	2^506451-22339	152457	Enzo Doria	07/2013
2043	2^505995-113185	152320	Enzo Doria	07/2014
2044	(4*10^152253+149)/9	152253	Robert Price	04/2018
2045	578^55117-577^55117	152230	Jean-Louis Charton	08/2012
2046	2^505431-505431	152150	Henri Lifchitz	04/2005
2047	(203*10^152143+1)/3	152145	Robert Price	03/2020
2048	2^505053+73097	152037	Enzo Doria	04/2016
2049	22*10^151998+3	152000	Robert Price	01/2020
2050	(238*10^151979-1)/3	151981	Robert Price	04/2020
2051	(2^504793-7)/46765	151954	Lelio R Paula	12/2017
2052	350377#+797581	151937	Nicolas PALAU	08/2017
2053	2^504618-343991	151906	Enzo Doria	07/2015
2054	2^504212-461939	151783	Enzo Doria	07/2015
2055	7*10^151772-41	151773	Robert Price	08/2021
2056	2^504054-2231	151736	Yves Minet	10/2011
2057	(28*10^151682+191)/3	151683	Robert Price	02/2020
2058	2^503475-933075	151562	Paul Bourdelais	06/2021
2059	2^503361-39883	151527	Enzo Doria	09/2015
2060	2^503225+382667	151486	Enzo Doria	10/2016
2061	(844*10^151396-7)/9	151398	Robert Price	05/2021
2062	(26*10^151391-503)/9	151392	Robert Price	07/2018
2063	2^502769+1877567	151349	Enzo Doria	08/2016
2064	2^502576-4019	151291	Yves Minet	10/2011
2065	5*10^151257+41	151258	Robert Price	03/2019
2066	2^502290-2792501	151205	Enzo Doria	02/2016
2067	2^502181+1868417	151172	Enzo Doria	04/2016
2068	6*10^151063-77	151064	Robert Price	09/2021
2069	2^501781-1850503	151052	Enzo Doria	08/2015
2070	(5*10^151007+37)/3	151008	Robert Price	03/2018
2071	2^501627-991	151005	Yves Minet	02/2014
2072	2^501577-115333	150990	Enzo Doria	07/2015
2073	8*10^150975+3	150976	Robert Price	08/2015
2074	2^501512-113669	150971	Enzo Doria	09/2014
2075	(12^139739+1)/13	150803	Paul Bourdelais	09/2011
2076	(31^101111-1)/30	150792	Alexander Zhirkov	11/2010
2077	2^500899-500899	150786	Henri Lifchitz	04/2005
2078	2^500832+1876801	150766	Enzo Doria	07/2016
2079	(23*10^150763-59)/9	150764	Robert Price	05/2018
2080	2^500699+1884953	150726	Enzo Doria	02/2017
2081	(13*10^150675-37)/3	150676	Robert Price	01/2019
2082	(2^500527+lucasV(1,2,500527)+1)/4	150674	Mike Oakes	11/2016
2083	2^500337-71101	150617	Enzo Doria	04/2016
2084	(74*10^150616+133)/9	150617	Robert Price	06/2019
2085	4*10^150577+91	150578	Robert Price	08/2018
2086	2^500160+80071	150564	Enzo Doria	06/2016
2087	(2^500120+5)/9	150551	Lelio R Paula	12/2017
2088	(43*10^150515-421)/9	150516	Robert Price	01/2019
2089	(10^150551-1)/9/385207015049/57498437921/7808738631274081	150512	Maksym Voznyy	08/2014
2090	(10^150551-1)/1556587827131683185788921941743157225041	150512	Robert Price	07/2016
2091	2^499861-29503	150474	Enzo Doria	08/2015
2092	2^499653-113533	150411	Enzo Doria	08/2014
2093	(14*10^150391-191)/3	150392	Robert Price	10/2020
2094	2^499534-221	150375	Yves Minet	06/2012
2095	(28*10^150294+41)/3	150295	Robert Price	07/2021
2096	2^499225+49727	150282	Enzo Doria	09/2016
2097	2^499054-29261	150231	Enzo Doria	07/2015
2098	(844*10^150196-7)/9	150198	Robert Price	05/2021
2099	2^498907-933075	150186	Paul Bourdelais	06/2021
2100	(2^498898-7)/9	150183	Lelio R Paula	10/2015
2101	3*10^150182+17	150183	Robert Price	07/2018
2102	5*10^150175+63	150176	Robert Price	09/2020
2103	2^498623+1866983	150101	Enzo Doria	03/2016
2104	(25*10^150050-403)/9	150051	Robert Price	12/2020
2105	numbpart(18140942830)	150033	Serge Batalov	04/2017
2106	10^150029+4381	150030	Patrick De Geest	05/2016
2107	10^150029-41	150029	Serge Batalov	12/2014
2108	10^150000+1158603	150001	Patrick De Geest	09/2018
2109	10^150000-245703	150000	Patrick De Geest	09/2018
2110	(38*10^149999+691)/9	150000	Robert Price	10/2018
2111	2^498238-53	149985	Lelio R Paula	12/2017
2112	45728^1905+1905^45728	149984	Hans Havermann	10/2020
2113	5*10^149907+23	149908	Robert Price	03/2019
2114	39347^6442+6442^39347	149874	Hans Havermann	09/2020
2115	2^497850+81049	149868	Enzo Doria	07/2016
2116	37228^10575+10575^37228	149816	Hans Havermann	10/2020
2117	(5*2^497673+1)/2743	149812	Lelio R Paula	10/2015
2118	(5*2^497671+1)/373703	149810	Lelio R Paula	10/2015
2119	(2*10^149803-143)/3	149803	Robert Price	03/2018
2120	33845^26604+26604^33845	149763	Hans Havermann	09/2020
2121	2^497434-2784191	149743	Enzo Doria	10/2015
2122	(865*10^149737-1)/9	149739	Robert Price	04/2020
2123	10^149695-7000001	149695	Robert Price	06/2021
2124	38237^8214+8214^38237	149681	Hans Havermann	09/2020
2125	(23*10^149655+19)/3	149656	Robert Price	07/2019
2126	2^497068-113579	149633	Enzo Doria	08/2014
2127	2^497037+73727	149624	Enzo Doria	04/2016
2128	11*10^149618+3	149620	Robert Price	07/2021
2129	34942^19067+19067^34942	149562	Hans Havermann	09/2020
2130	33696^27449+27449^33696	149561	Hans Havermann	09/2020
2131	2^496773+77747	149544	Enzo Doria	05/2016
2132	(7*10^149483-493)/9	149483	Robert Price	04/2021
2133	(206*10^149459+7)/3	149461	Robert Price	07/2020
2134	34589^20940+20940^34589	149459	Hans Havermann	09/2020
2135	2^496477-113485	149455	Enzo Doria	08/2014
2136	((10^74703-1)10000/9+7481)10^74703+(10^74703-1)/9	149410	Hans Havermann	09/2019
2137	2^496270-49451	149393	Enzo Doria	10/2015
2138	2^496238-1865081	149383	Enzo Doria	01/2016
2139	33831^26030+26030^33831	149380	Hans Havermann	09/2020
2140	34131^23780+23780^34131	149365	Hans Havermann	09/2020
2141	(5*10^149335-53)/3	149336	Robert Price	09/2020
2142	2^495968-1853699	149302	Enzo Doria	09/2015
2143	2^495935-4117	149292	Yves Minet	02/2018
2144	35816^14709+14709^35816	149267	Hans Havermann	09/2020
2145	(10^149264+7)/191/2683/80557	149254	Alfred Reich	07/2021
2146	2^495712-396765	149225	Enzo Doria	07/2013
2147	(21*2^495676-1)/4835	149211	Lelio R Paula	10/2015
2148	2^495420+1880701	149137	Enzo Doria	10/2016
2149	2^495337-1847293	149112	Enzo Doria	07/2015
2150	(2^495193-7)/5	149068	Lelio R Paula	10/2015
2151	33282^30097+30097^33282	149055	Hans Havermann	09/2020
2152	37384^9705+9705^37384	149050	Hans Havermann	09/2020
2153	34808^19143+19143^34808	149049	Hans Havermann	09/2020
2154	413^56963-412^56963	149013	Jean-Louis Charton	08/2012
2155	47^89113-46^89113	149006	Robert Price	10/2012
2156	2^494916+87855	148985	Lelio R Paula	01/2016
2157	6*10^148982+73	148983	Robert Price	04/2019
2158	10^148934+1530019	148935	Patrick De Geest	02/2021
2159	10^148934-1000000001	148934	Robert Price	11/2020
2160	10^148934-512057	148934	Patrick De Geest	02/2021
2161	39000^6571+6571^39000	148888	Hans Havermann	10/2020
2162	2^494586-2791991	148886	Enzo Doria	02/2016
2163	8*10^148860-3	148861	Ray Chandler	04/2011
2164	38262^7769+7769^38262	148854	Hans Havermann	10/2020
2165	2^494333-286183	148810	Enzo Doria	06/2015
2166	2^494144-264119	148753	Enzo Doria	05/2014
2167	36502^11823+11823^36502	148663	Hans Havermann	11/2020
2168	(5*2^493838-1)/3721	148658	Lelio R Paula	10/2015
2169	64239^206+206^64239	148641	Hans Havermann	10/2020
2170	(23*2^493761-1)/555	148636	Lelio R Paula	10/2015
2171	(23*10^148627-137)/3	148628	Robert Price	08/2021
2172	(151*10^148601-1)/3	148603	Robert Price	03/2020
2173	2^493636+82081	148600	Enzo Doria	09/2016
2174	((((((((((((((34251^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	148593	Serge Batalov	07/2016
2175	177487#+(519643#)/(177487#)	148558	Makoto Morimoto	11/2017
2176	(2*10^148460-23)/3	148460	Robert Price	04/2018
2177	(28*10^148445+101)/3	148446	Robert Price	09/2020
2178	36203^12556+12556^36203	148391	Hans Havermann	10/2020
2179	33912^23749+23749^33912	148387	Hans Havermann	10/2020
2180	(8*10^148328+1)/9	148328	Serge Batalov	05/2010
2181	34294^21117+21117^34294	148309	Hans Havermann	10/2020
2182	(71*10^148306-539)/9	148307	Robert Price	07/2019
2183	38042^7875+7875^38042	148222	Hans Havermann	10/2020
2184	5^211959-12874	148153	Enzo Doria	05/2014
2185	34142^21831+21831^34142	148145	Hans Havermann	10/2020
2186	10^148112+34059	148113	Patrick De Geest	05/2021
2187	10^148112-70000001	148112	Robert Price	03/2021
2188	10^148112-106593	148112	Patrick De Geest	05/2021
2189	36303^12016+12016^36303	148108	Hans Havermann	10/2020
2190	(16*10^148071+41)/3	148072	Robert Price	03/2019
2191	187^65175-2	148068	Lelio R Paula	11/2017
2192	2^491851+1871453	148062	Enzo Doria	05/2016
2193	(68*10^148060-257)/9	148061	Robert Price	07/2019
2194	(151*10^148020-1)/3	148022	Robert Price	03/2020
2195	39153^6032+6032^39153	148017	Hans Havermann	10/2020
2196	36798^10507+10507^36798	147983	Hans Havermann	12/2020
2197	(26*10^147973-23)/3	147974	Robert Price	12/2019
2198	2^491521-1865323	147963	Enzo Doria	02/2016
2199	(2^491476+7)/71	147948	Lelio R Paula	10/2015
2200	2^491391-7807	147924	Lelio R Paula	01/2013
2201	39736^5279+5279^39736	147920	Hans Havermann	11/2020
2202	2^491370-113297	147918	Enzo Doria	07/2014
2203	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
2204	44368^2155+2155^44368	147899	Hans Havermann	12/2020
2205	(17*10^147890+79)/3	147891	Robert Price	04/2019
2206	94*10^147871-3	147873	Robert Price	05/2020
2207	10^147843+620967	147844	Patrick De Geest	05/2021
2208	10^147843-50000000001	147843	Robert Price	12/2020
2209	10^147843-182891	147843	Patrick De Geest	05/2021
2210	35805^13346+13346^35805	147709	Hans Havermann	11/2020
2211	2^490660-17	147704	Lelio R Paula	12/2017
2212	(229*10^147699-1)/3	147701	Robert Price	07/2020
2213	40656^4289+4289^40656	147678	Hans Havermann	11/2020
2214	2^490550+1179439	147671	Enzo Doria	06/2016
2215	(23*10^147649-59)/9	147650	Robert Price	05/2018
2216	2^490303+2793653	147596	Enzo Doria	03/2016
2217	199^64181-2	147543	Lelio R Paula	11/2017
2218	32849^30958+30958^32849	147518	Hans Havermann	11/2020
2219	2^489871-286987	147466	Enzo Doria	07/2015
2220	2^489864-351899	147464	Enzo Doria	07/2015
2221	175^65724-2	147422	Lelio R Paula	11/2017
2222	2^489712+1874851	147419	Enzo Doria	06/2016
2223	34473^18830+18830^34473	147367	Hans Havermann	11/2020
2224	63^81896-2	147359	Lelio R Paula	10/2017
2225	34580^18237+18237^34580	147344	Hans Havermann	11/2020
2226	(11*10^147313-107)/3	147314	Robert Price	09/2018
2227	2^489305-59815	147296	Enzo Doria	10/2015
2228	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
2229	2*10^147264-61	147265	Robert Price	10/2021
2230	2*10^147260+29	147261	Robert Price	02/2021
2231	33556^24457+24457^33556	147258	Hans Havermann	11/2020
2232	2^489125+80357	147242	Enzo Doria	06/2016
2233	32835^30452+30452^32835	147220	Hans Havermann	12/2020
2234	(148*10^147139-1)/3	147141	Robert Price	03/2020
2235	34338^19255+19255^34338	147123	Hans Havermann	11/2020
2236	2^488648-112799	147098	Enzo Doria	07/2014
2237	2^488627-350317	147092	Enzo Doria	06/2015
2238	33432^25075+25075^33432	147076	Hans Havermann	12/2020
2239	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
2240	2^488280-2165	146987	Yves Minet	07/2014
2241	2^488278+45	146987	Lelio R Paula	12/2017
2242	2^487927-39	146881	Lelio R Paula	12/2017
2243	(7*10^146860-13)/3	146861	Robert Price	07/2018
2244	(26*10^146856-77)/3	146857	Robert Price	11/2019
2245	32948^28611+28611^32948	146834	Hans Havermann	11/2020
2246	42596^2799+2799^42596	146829	Hans Havermann	12/2020
2247	2^487726-1863341	146821	Enzo Doria	12/2015
2248	43838^2229+2229^43838	146775	Hans Havermann	11/2020
2249	35005^15594+15594^35005	146775	Hans Havermann	11/2020
2250	(167*10^146764+7)/3	146766	Robert Price	04/2021

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