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	2^769791+25523	231731	Enzo Doria	11/2023
2002	7^274120-2	231659	Paul Bourdelais	08/2023
2003	(20^177967+1)/21	231540	Paul Bourdelais	05/2013
2004	2^769011+81	231496	Henri Lifchitz	01/2025
2005	(71^125029-1)/105024430	231453	Paul Vanderveen	06/2025
2006	(4*10^231254+23)/9	231254	Serge Batalov	11/2022
2007	2^768205+22217	231253	Enzo Doria	09/2023
2008	49262^49262-49247^49247	231163	Henri Lifchitz	11/2024
2009	2^767622-9221	231078	Lelio R Paula	01/2016
2010	2^767344+1880311	230994	Enzo Doria	09/2016
2011	8*10^230921-13	230922	Robert Price	08/2023
2012	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
2013	(10^230706+179)/9	230706	Serge Batalov	12/2014
2014	2^766309+1875257	230682	Enzo Doria	06/2016
2015	(26131^52441-1)/(26131^229-1)	230629	Ryan Propper	11/2023
2016	2^765635+1879883	230480	Enzo Doria	09/2016
2017	43^141090+141090	230467	Kellen Shenton	06/2023
2018	(26*10^230394-119)/3	230395	Robert Price	07/2023
2019	2^764348-113697	230092	Enzo Doria	09/2014
2020	2^764131+78863	230027	Enzo Doria	05/2016
2021	2^763701+60197	229897	Enzo Doria	03/2016
2022	4*10^229836+21	229837	Robert Price	12/2022
2023	2^763362+27799	229795	Enzo Doria	01/2024
2024	2^762841-25905	229639	Enzo Doria	10/2013
2025	2^762659+212633	229584	Enzo Doria	09/2023
2026	77*10^229211+3	229213	Robert Price	11/2023
2027	2^761117-113569	229120	Enzo Doria	08/2014
2028	(29022^51529-1)/(29022^227-1)	228947	Ryan Propper	11/2023
2029	(98^114859+1)/99	228709	Paul Bourdelais	12/2018
2030	5*3^479067-2^479067	228574	Jon Grantham	08/2023
2031	2^758645+216011	228375	Enzo Doria	12/2023
2032	(2^758231+1)/(32714694297653973236839266867)	228223	Gord Palameta	12/2018
2033	10^228208+111	228209	Boyan Hu	10/2024
2034	(298*10^228177-7)/3	228179	Robert Price	02/2023
2035	2^757985-2790013	228177	Enzo Doria	12/2015
2036	34*10^228129-9	228131	Robert Price	05/2023
2037	2^757038-1862081	227892	Enzo Doria	12/2015
2038	2^756839+95849	227832	Makoto Morimoto	10/2013
2040	(2^756839+6989)/756091	227826	Makoto Morimoto	09/2016
2039	(2^756839-50211)/(137*3203)	227826	Makoto Morimoto	08/2019
2041	2^756773-112723	227812	Enzo Doria	07/2014
2042	(710^(2113887+1)+9*10^113887-7)/9	227775	Robert Price	08/2024
2043	(10^227542)/(227542^10)	227489	Henri Lifchitz	05/2025
2044	524309#+616367	227431	Makoto Morimoto	02/2016
2045	2^755404+226575	227400	Enzo Doria	09/2024
2046	2^755116+81	227313	Henri Lifchitz	11/2024
2047	2^755097-114193	227307	Enzo Doria	12/2014
2048	7*10^227178+39	227179	Robert Price	01/2023
2049	9*10^227153-89	227154	Robert Price	02/2023
2050	2^754473-2791513	227120	Enzo Doria	01/2016
2051	2^754376+25	227090	Stefano Morozzi	05/2021
2052	2^754138+213289	227019	Enzo Doria	09/2023
2053	2^754038+25	226989	Stefano Morozzi	05/2021
2054	2^753263+217133	226755	Enzo Doria	12/2023
2055	7*10^226479-9	226480	Robert Price	02/2023
2056	(10^226381+1)/14973418875371	226368	Alfred Reich	06/2025
2057	2^751655+33893	226271	Enzo Doria	06/2024
2058	2^751426-764321	226202	Enzo Doria	12/2013
2059	(18^180181-1)/17	226176	Andy Steward	04/2007
2060	2^750740-3	225996	Paul Bourdelais	03/2012
2061	2^750725+60227	225991	Enzo Doria	02/2016
2062	2^750525-113743	225931	Enzo Doria	09/2014
2063	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
2064	2^749444-1861889	225606	Enzo Doria	12/2015
2065	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
2066	(3^472721+1)/9422189991086734893916	225524	Paul Vanderveen	06/2025
2067	2^749096+1876861	225501	Enzo Doria	07/2016
2068	2^748895+26213	225440	Enzo Doria	12/2023
2069	(519643#+43033)/(2318712706283)	225379	Makoto Morimoto	08/2019
2070	2^748657+79607	225369	Enzo Doria	06/2016
2071	(2^746920-11)/5	224845	Stefano Morozzi	08/2022
2072	2^746653-291583	224765	Enzo Doria	07/2015
2073	2^746461-114043	224708	Enzo Doria	11/2014
2074	2^746302+25	224660	Stefano Morozzi	05/2021
2075	(202*10^224545-1)/3	224547	Robert Price	06/2023
2076	(19*10^224533-37)/9	224534	Alfred Reich	12/2023
2077	2^745674+213949	224471	Enzo Doria	10/2023
2078	2^745098-350471	224297	Enzo Doria	06/2015
2079	2^745039-4897	224280	Yves Minet	03/2021
2080	23*10^224232-7	224234	Robert Price	10/2022
2081	(154*10^224061-1)/9	224063	Serge Batalov	12/2014
2082	2^744211-1845787	224030	Enzo Doria	07/2015
2083	2^743773+37757	223898	Enzo Doria	10/2024
2084	2^743592-134579	223844	Hans Havermann	10/2018
2085	2^742452+3	223501	Paul Bourdelais	06/2019
2086	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
2087	47747^47747-2512^2512	223406	Henri Lifchitz	10/2024
2088	2^741651-461197	223260	Enzo Doria	07/2015
2089	10^223236-1001	223236	Robert Price	10/2022
2090	2^741362-1845251	223173	Enzo Doria	07/2015
2091	3^467546-5*2^467546	223077	Jon Grantham	08/2023
2092	2^740455-1863877	222900	Enzo Doria	12/2015
2093	2^740274+217519	222845	Enzo Doria	01/2024
2094	(14*10^222718-41)/9	222719	Serge Batalov	01/2023
2095	2^739636-2792219	222653	Enzo Doria	02/2016
2096	11^213654-180	222498	Enzo Doria	01/2013
2097	2^738957-1859743	222449	Enzo Doria	11/2015
2098	4*10^222253-21	222254	Robert Price	12/2022
2099	2^737825+57	222108	Stefano Morozzi	05/2021
2100	(54^128189+1)/55	222073	Paul Bourdelais	11/2018
2101	3^232689+1^232689+4^232689+1^232689+5^232689+9^232689	222042	Henri Lifchitz	03/2025
2102	2^737166+220099	221910	Enzo Doria	03/2024
2103	(10^221654+179)/9	221654	Serge Batalov	12/2014
2104	2^736281+79817	221643	Enzo Doria	06/2016
2105	10^221631+247617	221632	Patrick De Geest	10/2013
2106	10^221631-9	221631	Alexander Gramolin	02/2011
2107	10^221628+7	221629	Alfred Reich	04/2021
2108	2^735970-1839821	221550	Enzo Doria	06/2015
2109	2^735367+60293	221368	Enzo Doria	03/2016
2110	77*10^221343+3	221345	Robert Price	11/2023
2111	299^299^299-582	221328	Henri Lifchitz	03/2025
2112	(241^92821-1)/240	221099	Anonymous	04/2024
2113	(202*10^221092-1)/3	221094	Robert Price	06/2023
2114	(5^316297-1)/220142716	221074	Paul Vanderveen	05/2025
2115	(29^151153+1)/30	221045	Paul Bourdelais	09/2017
2116	2^734228+24751	221025	Enzo Doria	10/2023
2117	(28*10^220800+173)/3	220801	Robert Price	07/2024
2118	2^733264-2784089	220735	Enzo Doria	10/2015
2119	2^733114-24555	220690	Enzo Doria	09/2013
2120	2^731891-636259	220322	Enzo Doria	12/2013
2121	98*10^220185-9	220187	Robert Price	05/2023
2122	418319^39164+418318	220161	Alfred Reich	11/2023
2123	2^4^182829+182829^4^2	220149	Henri Lifchitz	03/2025
2124	2^731124-25539	220091	Enzo Doria	09/2013
2125	2^730972-462029	220045	Enzo Doria	07/2015
2126	2^730833+1868627	220003	Enzo Doria	04/2016
2127	2^730645-2787133	219947	Enzo Doria	11/2015
2128	2^730547-25581	219917	Enzo Doria	09/2013
2129	(113*13^197420-5)/12	219916	Anonymous	11/2022
2130	(13^197420*113-5)/12	219916	Eric Chen	10/2023
2131	2^730460+82291	219891	Enzo Doria	09/2016
2132	(5*10^219847-101)/3	219848	Robert Price	08/2023
2133	(2^730339+1)/(3278390620037943469324347)	219831	Gord Palameta	12/2018
2134	L(1051849)	219824	Renaud Lifchitz	03/2009
2135	3*2^730149+5	219798	Jon Grantham	07/2023
2136	8*10^219740-3	219741	Serge Batalov	01/2023
2137	11^210961-240	219694	Enzo Doria	01/2013
2138	(26*10^219639-77)/3	219640	Robert Price	03/2023
2139	2^729611-113437	219635	Enzo Doria	08/2014
2140	7^259710-2	219481	Paul Bourdelais	01/2021
2141	F(1049897)	219416	Henri Lifchitz	10/2008
2142	(1488^69151-1)/1487	219386	Alexander Zhirkov	02/2023
2143	2^728604+1879321	219332	Enzo Doria	10/2016
2144	33^144412+2	219292	Robert Price	04/2015
2145	2^728277-183313	219234	Hans Havermann	10/2018
2146	2^727998-1862711	219150	Enzo Doria	12/2015
2147	(29*10^219124+91)/3	219125	Robert Price	12/2022
2148	2^727729-114073	219069	Enzo Doria	12/2014
2149	2^727496-1851809	218999	Enzo Doria	08/2015
2150	2^727025+25907	218857	Enzo Doria	12/2023
2151	2^726591+2793143	218726	Enzo Doria	02/2016
2152	(7*10^218644+17)/3	218645	Robert Price	06/2023
2153	2^725534-2791931	218408	Enzo Doria	02/2016
2154	Phi(220531,10)/2686456812680882641	217774	Makoto Kamada	10/2020
2155	2^722184+1877821	217400	Enzo Doria	08/2016
2156	(109*10^217360-1)/9	217362	Serge Batalov	12/2014
2157	2^721721-4453	217260	Yves Minet	03/2021
2158	10^216950+49	216951	Robert Price	02/2023
2159	281*499979#/46410-2702372	216849	Robert Smith	08/2016
2160	281*499979#/46410+2400766	216849	Robert Smith	08/2016
2161	tau(311^15786)	216429	Nik Lygeros / Olivier Rozier / LR team	10/2013
2162	2^718756-114107	216368	Enzo Doria	12/2014
2163	2^717672+121	216041	Stefano Morozzi	05/2021
2164	2^717305+80327	215931	Enzo Doria	07/2016
2165	2^717069-59773	215860	Enzo Doria	10/2015
2166	10^215802+33	215803	Robert Price	08/2023
2167	30^146021-29^146021	215691	Jean-Louis Charton	09/2018
2168	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
2169	2^716428+215011	215667	Enzo Doria	11/2023
2170	(13*10^215592-43)/3	215593	Robert Price	08/2023
2171	p(41292)#+p(41292+1)	215450	Henri Lifchitz	11/2024
2172	(29^147319-1)/466757843690852	215425	Paul Vanderveen	06/2025
2173	227^91413-40	215372	Enzo Doria	04/2015
2174	(2^715008-21)/5	215239	Stefano Morozzi	08/2022
2175	2^714717+782897	215152	Enzo Doria	11/2016
2176	(19^168013-1)/80910356454	214837	Paul Vanderveen	05/2025
2177	tau(373^15186)	214796	Nik Lygeros / Olivier Rozier / LR team	10/2013
2178	2^713241+1879157	214707	Enzo Doria	08/2016
2179	(23*10^214633+91)/3	214634	Robert Price	03/2023
2180	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
2181	2^712801-69553	214575	Enzo Doria	01/2016
2182	2^712603-25357	214515	Enzo Doria	09/2013
2183	2^711721-1846723	214250	Enzo Doria	07/2015
2184	2^710730-396765	213952	Enzo Doria	09/2013
2185	(19*10^213934-37)/9	213935	Alfred Reich	12/2023
2186	(19*10^213730-37)/9	213731	Alfred Reich	12/2023
2187	(713^74897-1)/712	213685	Jinyuan Wang	08/2023
2188	2^709773+25907	213663	Enzo Doria	12/2023
2189	2^708468-114329	213271	Enzo Doria	02/2015
2190	2^708293+27557	213218	Enzo Doria	01/2024
2191	379*10^213199+9	213202	Jason Yuen	01/2025
2192	2^707277+28997	212912	Enzo Doria	02/2024
2193	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
2194	2^706838-69041	212780	Enzo Doria	11/2015
2195	2^705653+25907	212423	Enzo Doria	12/2023
2196	22*10^212339+7	212341	Robert Price	10/2022
2197	2^704577-113871	212099	Enzo Doria	10/2014
2198	(2^704548-19)/3	212090	Stefano Morozzi	08/2022
2199	2^704110-2792441	211959	Enzo Doria	02/2016
2200	2^704084+28531	211951	Enzo Doria	02/2024
2201	2^703943-1862947	211908	Enzo Doria	12/2015
2202	(60^119083+1)/61	211746	Paul Bourdelais	10/2018
2203	(184*10^211682-1)/3	211684	Robert Price	12/2022
2204	(10^211610-91)/9	211610	Serge Batalov	12/2014
2205	227^89797+2	211565	Lelio R Paula	08/2012
2206	2^702194-3	211382	Paul Bourdelais	03/2012
2207	2^702064+1874911	211343	Enzo Doria	07/2016
2208	2^701968-113873	211314	Enzo Doria	10/2014
2209	(14*10^211262-41)/9	211263	Serge Batalov	01/2023
2210	2^701713-113779	211237	Enzo Doria	09/2014
2211	2^701616-216803	211208	Enzo Doria	01/2024
2212	2^701449-25201	211158	Enzo Doria	09/2013
2213	2^701403-2786977	211144	Enzo Doria	11/2015
2214	2^701189-25423	211079	Enzo Doria	09/2013
2215	2^701162-459161	211071	Enzo Doria	05/2015
2216	2^700793+219407	210960	Enzo Doria	03/2024
2217	(24^152783-1)/23	210872	Paul Bourdelais	04/2018
2218	2^700400+9385	210842	Lelio R Paula	01/2014
2219	2^700304-17	210813	Stefano Morozzi	07/2022
2220	2^700131+1874693	210761	Enzo Doria	06/2016
2221	(2^700095+225414)/2	210750	Stefano Morozzi	04/2020
2222	(2^700090+278254)/2	210748	Stefano Morozzi	04/2020
2223	(2^700075+303666)/2	210744	Stefano Morozzi	04/2020
2224	(2^700073+75882)/2	210743	Stefano Morozzi	04/2020
2225	(2^700074+328890)/2	210743	Stefano Morozzi	04/2020
2226	(2^700052+79162)/2	210737	Stefano Morozzi	04/2020
2227	(2^700052+304458)/2	210737	Stefano Morozzi	04/2020
2228	(2^700048+376578)/2	210736	Stefano Morozzi	04/2020
2229	11^202357-1140	210734	Enzo Doria	12/2012
2230	(2^700021+25874)/2	210728	Stefano Morozzi	04/2020
2231	(2^700018+377518)/2	210727	Stefano Morozzi	04/2020
2232	2^699999+300729	210721	Norman Luhn	09/2023
2233	(238*10^210712-1)/3	210714	Robert Price	09/2023
2234	2^699740+25	210643	Stefano Morozzi	05/2021
2235	(23*10^210525-143)/3	210526	Robert Price	12/2023
2236	2^698929-2788423	210399	Enzo Doria	11/2015
2237	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
2238	2^698316+1878601	210215	Enzo Doria	08/2016
2239	34*10^210097-9	210099	Robert Price	05/2023
2240	(19*10^210011-49)/3	210012	Robert Price	06/2023
2241	6*10^209846-91	209847	Robert Price	05/2023
2242	2^697036+1878751	209829	Enzo Doria	08/2016
2243	2^696813+28607	209762	Enzo Doria	02/2024
2244	(238*10^209715-1)/3	209717	Robert Price	09/2023
2245	6^269407+5	209640	Paul Bourdelais	02/2021
2246	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
2247	2^696254-115151	209594	Enzo Doria	06/2015
2248	2^695841+225	209470	Henri Lifchitz	01/2025
2249	(35^135623+1)/36	209410	Paul Bourdelais	07/2018
2250	7*10^209161+39	209162	Robert Price	01/2023

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