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	2^775672+1866721	233501	Enzo Doria	03/2016
2002	2^775238+57	233370	Stefano Morozzi	05/2021
2003	(11^223999+1)/12	233270	Paul Bourdelais	02/2010
2004	U(1302049)	233238	Serge Batalov	07/2024
2005	2^774118+1885789	233033	Enzo Doria	04/2017
2006	21^176191-20^176191	232964	Jean-Louis Charton	01/2015
2007	2^773723+217523	232914	Enzo Doria	01/2024
2008	2^773679-113425	232901	Enzo Doria	08/2014
2009	(7*10^232620+23)/3	232621	Robert Price	05/2023
2010	10^232599+192489	232600	Patrick De Geest	12/2013
2011	10^232599-3	232599	Markus Tervooren	10/2010
2012	2^772552-458879	232562	Enzo Doria	04/2015
2013	2^772214+1874899	232460	Enzo Doria	06/2016
2014	2^771994-1862771	232394	Enzo Doria	12/2015
2015	2^771889+1876037	232362	Enzo Doria	07/2016
2016	2^771660+1866511	232293	Enzo Doria	02/2016
2017	5^332150-18188	232163	Enzo Doria	06/2014
2018	2^771227+61121	232163	Boyan Hu	05/2024
2019	2^770623+212543	231981	Enzo Doria	09/2023
2020	3^485977-2^485977	231870	Mike Oakes	09/2009
2021	2^770082-114161	231818	Enzo Doria	01/2015
2022	2^769791+25523	231731	Enzo Doria	11/2023
2023	7^274120-2	231659	Paul Bourdelais	08/2023
2024	(20^177967+1)/21	231540	Paul Bourdelais	05/2013
2025	2^769011+81	231496	Henri Lifchitz	01/2025
2026	(71^125029-1)/105024430	231453	Paul Vanderveen	06/2025
2027	(4*10^231254+23)/9	231254	Serge Batalov	11/2022
2028	2^768205+22217	231253	Enzo Doria	09/2023
2029	49262^49262-49247^49247	231163	Henri Lifchitz	11/2024
2030	2^767622-9221	231078	Lelio R Paula	01/2016
2031	2^767344+1880311	230994	Enzo Doria	09/2016
2032	8*10^230921-13	230922	Robert Price	08/2023
2033	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
2034	(10^230706+179)/9	230706	Serge Batalov	12/2014
2035	2^766309+1875257	230682	Enzo Doria	06/2016
2036	(26131^52441-1)/(26131^229-1)	230629	Ryan Propper	11/2023
2037	2^765635+1879883	230480	Enzo Doria	09/2016
2038	43^141090+141090	230467	Kellen Shenton	06/2023
2039	(26*10^230394-119)/3	230395	Robert Price	07/2023
2040	2^764348-113697	230092	Enzo Doria	09/2014
2041	2^764131+78863	230027	Enzo Doria	05/2016
2042	2^763701+60197	229897	Enzo Doria	03/2016
2043	4*10^229836+21	229837	Robert Price	12/2022
2044	2^763362+27799	229795	Enzo Doria	01/2024
2045	2^762841-25905	229639	Enzo Doria	10/2013
2046	2^762659+212633	229584	Enzo Doria	09/2023
2047	77*10^229211+3	229213	Robert Price	11/2023
2048	2^761117-113569	229120	Enzo Doria	08/2014
2049	(29022^51529-1)/(29022^227-1)	228947	Ryan Propper	11/2023
2050	(98^114859+1)/99	228709	Paul Bourdelais	12/2018
2051	5*3^479067-2^479067	228574	Jon Grantham	08/2023
2052	2^758645+216011	228375	Enzo Doria	12/2023
2053	(2^758231+1)/(32714694297653973236839266867)	228223	Gord Palameta	12/2018
2054	10^228208+111	228209	Boyan Hu	10/2024
2055	(298*10^228177-7)/3	228179	Robert Price	02/2023
2056	2^757985-2790013	228177	Enzo Doria	12/2015
2057	34*10^228129-9	228131	Robert Price	05/2023
2058	2^757038-1862081	227892	Enzo Doria	12/2015
2059	2^756839+95849	227832	Makoto Morimoto	10/2013
2061	(2^756839+6989)/756091	227826	Makoto Morimoto	09/2016
2060	(2^756839-50211)/(137*3203)	227826	Makoto Morimoto	08/2019
2062	2^756773-112723	227812	Enzo Doria	07/2014
2063	(710^(2113887+1)+9*10^113887-7)/9	227775	Robert Price	08/2024
2064	(10^227542)/(227542^10)	227489	Henri Lifchitz	05/2025
2065	524309#+616367	227431	Makoto Morimoto	02/2016
2066	2^755404+226575	227400	Enzo Doria	09/2024
2067	2^755116+81	227313	Henri Lifchitz	11/2024
2068	2^755097-114193	227307	Enzo Doria	12/2014
2069	7*10^227178+39	227179	Robert Price	01/2023
2070	9*10^227153-89	227154	Robert Price	02/2023
2071	2^754473-2791513	227120	Enzo Doria	01/2016
2072	2^754376+25	227090	Stefano Morozzi	05/2021
2073	2^754138+213289	227019	Enzo Doria	09/2023
2074	2^754038+25	226989	Stefano Morozzi	05/2021
2075	2^753263+217133	226755	Enzo Doria	12/2023
2076	7*10^226479-9	226480	Robert Price	02/2023
2077	(10^226381+1)/14973418875371	226368	Alfred Reich	06/2025
2078	2^751655+33893	226271	Enzo Doria	06/2024
2079	2^751426-764321	226202	Enzo Doria	12/2013
2080	(18^180181-1)/17	226176	Andy Steward	04/2007
2081	2^750740-3	225996	Paul Bourdelais	03/2012
2082	2^750725+60227	225991	Enzo Doria	02/2016
2083	2^750525-113743	225931	Enzo Doria	09/2014
2084	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
2085	2^749444-1861889	225606	Enzo Doria	12/2015
2086	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
2087	(3^472721+1)/9422189991086734893916	225524	Paul Vanderveen	06/2025
2088	2^749096+1876861	225501	Enzo Doria	07/2016
2089	2^748895+26213	225440	Enzo Doria	12/2023
2090	(519643#+43033)/(2318712706283)	225379	Makoto Morimoto	08/2019
2091	2^748657+79607	225369	Enzo Doria	06/2016
2092	(2^746920-11)/5	224845	Stefano Morozzi	08/2022
2093	2^746653-291583	224765	Enzo Doria	07/2015
2094	2^746461-114043	224708	Enzo Doria	11/2014
2095	2^746302+25	224660	Stefano Morozzi	05/2021
2096	(202*10^224545-1)/3	224547	Robert Price	06/2023
2097	(19*10^224533-37)/9	224534	Alfred Reich	12/2023
2098	2^745674+213949	224471	Enzo Doria	10/2023
2099	2^745098-350471	224297	Enzo Doria	06/2015
2100	2^745039-4897	224280	Yves Minet	03/2021
2101	23*10^224232-7	224234	Robert Price	10/2022
2102	(154*10^224061-1)/9	224063	Serge Batalov	12/2014
2103	2^744211-1845787	224030	Enzo Doria	07/2015
2104	2^743773+37757	223898	Enzo Doria	10/2024
2105	2^743592-134579	223844	Hans Havermann	10/2018
2106	2^742452+3	223501	Paul Bourdelais	06/2019
2107	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
2108	47747^47747-2512^2512	223406	Henri Lifchitz	10/2024
2109	2^741651-461197	223260	Enzo Doria	07/2015
2110	10^223236-1001	223236	Robert Price	10/2022
2111	2^741362-1845251	223173	Enzo Doria	07/2015
2112	3^467546-5*2^467546	223077	Jon Grantham	08/2023
2113	2^740455-1863877	222900	Enzo Doria	12/2015
2114	2^740274+217519	222845	Enzo Doria	01/2024
2115	(14*10^222718-41)/9	222719	Serge Batalov	01/2023
2116	2^739636-2792219	222653	Enzo Doria	02/2016
2117	11^213654-180	222498	Enzo Doria	01/2013
2118	2^738957-1859743	222449	Enzo Doria	11/2015
2119	4*10^222253-21	222254	Robert Price	12/2022
2120	2^737825+57	222108	Stefano Morozzi	05/2021
2121	(54^128189+1)/55	222073	Paul Bourdelais	11/2018
2122	3^232689+1^232689+4^232689+1^232689+5^232689+9^232689	222042	Henri Lifchitz	03/2025
2123	2^737166+220099	221910	Enzo Doria	03/2024
2124	(10^221654+179)/9	221654	Serge Batalov	12/2014
2125	2^736281+79817	221643	Enzo Doria	06/2016
2126	10^221631+247617	221632	Patrick De Geest	10/2013
2127	10^221631-9	221631	Alexander Gramolin	02/2011
2128	10^221628+7	221629	Alfred Reich	04/2021
2129	2^735970-1839821	221550	Enzo Doria	06/2015
2130	2^735367+60293	221368	Enzo Doria	03/2016
2131	77*10^221343+3	221345	Robert Price	11/2023
2132	299^299^299-582	221328	Henri Lifchitz	03/2025
2133	(241^92821-1)/240	221099	Anonymous	04/2024
2134	(202*10^221092-1)/3	221094	Robert Price	06/2023
2135	(5^316297-1)/220142716	221074	Paul Vanderveen	05/2025
2136	(29^151153+1)/30	221045	Paul Bourdelais	09/2017
2137	2^734228+24751	221025	Enzo Doria	10/2023
2138	(28*10^220800+173)/3	220801	Robert Price	07/2024
2139	2^733264-2784089	220735	Enzo Doria	10/2015
2140	2^733114-24555	220690	Enzo Doria	09/2013
2141	2^731891-636259	220322	Enzo Doria	12/2013
2142	98*10^220185-9	220187	Robert Price	05/2023
2143	418319^39164+418318	220161	Alfred Reich	11/2023
2144	2^4^182829+182829^4^2	220149	Henri Lifchitz	03/2025
2145	2^731124-25539	220091	Enzo Doria	09/2013
2146	2^730972-462029	220045	Enzo Doria	07/2015
2147	2^730833+1868627	220003	Enzo Doria	04/2016
2148	2^730645-2787133	219947	Enzo Doria	11/2015
2149	2^730547-25581	219917	Enzo Doria	09/2013
2150	(113*13^197420-5)/12	219916	Anonymous	11/2022
2151	(13^197420*113-5)/12	219916	Eric Chen	10/2023
2152	2^730460+82291	219891	Enzo Doria	09/2016
2153	(5*10^219847-101)/3	219848	Robert Price	08/2023
2154	(2^730339+1)/(3278390620037943469324347)	219831	Gord Palameta	12/2018
2155	L(1051849)	219824	Renaud Lifchitz	03/2009
2156	3*2^730149+5	219798	Jon Grantham	07/2023
2157	8*10^219740-3	219741	Serge Batalov	01/2023
2158	11^210961-240	219694	Enzo Doria	01/2013
2159	(26*10^219639-77)/3	219640	Robert Price	03/2023
2160	2^729611-113437	219635	Enzo Doria	08/2014
2161	7^259710-2	219481	Paul Bourdelais	01/2021
2162	F(1049897)	219416	Henri Lifchitz	10/2008
2163	(1488^69151-1)/1487	219386	Alexander Zhirkov	02/2023
2164	2^728604+1879321	219332	Enzo Doria	10/2016
2165	33^144412+2	219292	Robert Price	04/2015
2166	2^728277-183313	219234	Hans Havermann	10/2018
2167	2^727998-1862711	219150	Enzo Doria	12/2015
2168	(29*10^219124+91)/3	219125	Robert Price	12/2022
2169	2^727729-114073	219069	Enzo Doria	12/2014
2170	2^727496-1851809	218999	Enzo Doria	08/2015
2171	2^727025+25907	218857	Enzo Doria	12/2023
2172	2^726591+2793143	218726	Enzo Doria	02/2016
2173	(7*10^218644+17)/3	218645	Robert Price	06/2023
2174	2^725534-2791931	218408	Enzo Doria	02/2016
2175	Phi(220531,10)/2686456812680882641	217774	Makoto Kamada	10/2020
2176	2^722184+1877821	217400	Enzo Doria	08/2016
2177	(109*10^217360-1)/9	217362	Serge Batalov	12/2014
2178	2^721721-4453	217260	Yves Minet	03/2021
2179	10^216950+49	216951	Robert Price	02/2023
2180	281*499979#/46410-2702372	216849	Robert Smith	08/2016
2181	281*499979#/46410+2400766	216849	Robert Smith	08/2016
2182	tau(311^15786)	216429	Nik Lygeros / Olivier Rozier / LR team	10/2013
2183	2^718756-114107	216368	Enzo Doria	12/2014
2184	2^717672+121	216041	Stefano Morozzi	05/2021
2185	2^717305+80327	215931	Enzo Doria	07/2016
2186	2^717069-59773	215860	Enzo Doria	10/2015
2187	10^215802+33	215803	Robert Price	08/2023
2188	30^146021-29^146021	215691	Jean-Louis Charton	09/2018
2189	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
2190	2^716428+215011	215667	Enzo Doria	11/2023
2191	(13*10^215592-43)/3	215593	Robert Price	08/2023
2192	p(41292)#+p(41292+1)	215450	Henri Lifchitz	11/2024
2193	(29^147319-1)/466757843690852	215425	Paul Vanderveen	06/2025
2194	227^91413-40	215372	Enzo Doria	04/2015
2195	(2^715008-21)/5	215239	Stefano Morozzi	08/2022
2196	2^714717+782897	215152	Enzo Doria	11/2016
2197	(19^168013-1)/80910356454	214837	Paul Vanderveen	05/2025
2198	tau(373^15186)	214796	Nik Lygeros / Olivier Rozier / LR team	10/2013
2199	2^713241+1879157	214707	Enzo Doria	08/2016
2200	(23*10^214633+91)/3	214634	Robert Price	03/2023
2201	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
2202	2^712801-69553	214575	Enzo Doria	01/2016
2203	2^712603-25357	214515	Enzo Doria	09/2013
2204	2^711721-1846723	214250	Enzo Doria	07/2015
2205	2^710730-396765	213952	Enzo Doria	09/2013
2206	(19*10^213934-37)/9	213935	Alfred Reich	12/2023
2207	(19*10^213730-37)/9	213731	Alfred Reich	12/2023
2208	(713^74897-1)/712	213685	Jinyuan Wang	08/2023
2209	2^709773+25907	213663	Enzo Doria	12/2023
2210	2^708468-114329	213271	Enzo Doria	02/2015
2211	2^708293+27557	213218	Enzo Doria	01/2024
2212	379*10^213199+9	213202	Jason Yuen	01/2025
2213	2^707277+28997	212912	Enzo Doria	02/2024
2214	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
2215	2^706838-69041	212780	Enzo Doria	11/2015
2216	2^705653+25907	212423	Enzo Doria	12/2023
2217	22*10^212339+7	212341	Robert Price	10/2022
2218	2^704577-113871	212099	Enzo Doria	10/2014
2219	(2^704548-19)/3	212090	Stefano Morozzi	08/2022
2220	2^704110-2792441	211959	Enzo Doria	02/2016
2221	2^704084+28531	211951	Enzo Doria	02/2024
2222	2^703943-1862947	211908	Enzo Doria	12/2015
2223	(60^119083+1)/61	211746	Paul Bourdelais	10/2018
2224	(184*10^211682-1)/3	211684	Robert Price	12/2022
2225	(10^211610-91)/9	211610	Serge Batalov	12/2014
2226	227^89797+2	211565	Lelio R Paula	08/2012
2227	2^702194-3	211382	Paul Bourdelais	03/2012
2228	2^702064+1874911	211343	Enzo Doria	07/2016
2229	2^701968-113873	211314	Enzo Doria	10/2014
2230	(14*10^211262-41)/9	211263	Serge Batalov	01/2023
2231	2^701713-113779	211237	Enzo Doria	09/2014
2232	2^701616-216803	211208	Enzo Doria	01/2024
2233	2^701449-25201	211158	Enzo Doria	09/2013
2234	2^701403-2786977	211144	Enzo Doria	11/2015
2235	2^701189-25423	211079	Enzo Doria	09/2013
2236	2^701162-459161	211071	Enzo Doria	05/2015
2237	2^700793+219407	210960	Enzo Doria	03/2024
2238	(24^152783-1)/23	210872	Paul Bourdelais	04/2018
2239	2^700400+9385	210842	Lelio R Paula	01/2014
2240	2^700304-17	210813	Stefano Morozzi	07/2022
2241	2^700131+1874693	210761	Enzo Doria	06/2016
2242	(2^700095+225414)/2	210750	Stefano Morozzi	04/2020
2243	(2^700090+278254)/2	210748	Stefano Morozzi	04/2020
2244	(2^700075+303666)/2	210744	Stefano Morozzi	04/2020
2245	(2^700073+75882)/2	210743	Stefano Morozzi	04/2020
2246	(2^700074+328890)/2	210743	Stefano Morozzi	04/2020
2247	(2^700052+79162)/2	210737	Stefano Morozzi	04/2020
2248	(2^700052+304458)/2	210737	Stefano Morozzi	04/2020
2249	(2^700048+376578)/2	210736	Stefano Morozzi	04/2020
2250	11^202357-1140	210734	Enzo Doria	12/2012

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