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 ?
1001	2^780408-113453	234927	Enzo Doria	08/2014
1002	2^780368-1864829	234915	Enzo Doria	01/2016
1003	2^779593-1836559	234681	Enzo Doria	05/2015
1004	(8713#+(549391#)/(8713#))/360295171	234487	Makoto Morimoto	11/2017
1005	(5^335429+1)/6	234455	Paul Bourdelais	08/2010
1006	2^778395-113617	234321	Enzo Doria	08/2014
1007	23*10^234025-7	234027	Robert Price	10/2022
1008	Phi(78125,5517)	233857	Anonymous	09/2022
1009	2^776245-2792353	233674	Enzo Doria	02/2016
1010	2^776060-114029	233618	Enzo Doria	11/2014
1011	2^775987-2789557	233596	Enzo Doria	12/2015
1012	2^775672+1866721	233501	Enzo Doria	03/2016
1013	2^775238+57	233370	Stefano Morozzi	05/2021
1014	(11^223999+1)/12	233270	Paul Bourdelais	02/2010
1015	2^774118+1885789	233033	Enzo Doria	04/2017
1016	21^176191-20^176191	232964	Jean-Louis Charton	01/2015
1017	2^773679-113425	232901	Enzo Doria	08/2014
1018	10^232599+192489	232600	Patrick De Geest	12/2013
1019	10^232599-3	232599	Markus Tervooren	10/2010
1020	2^772552-458879	232562	Enzo Doria	04/2015
1021	2^772214+1874899	232460	Enzo Doria	06/2016
1022	2^771994-1862771	232394	Enzo Doria	12/2015
1023	2^771889+1876037	232362	Enzo Doria	07/2016
1024	2^771660+1866511	232293	Enzo Doria	02/2016
1025	5^332150-18188	232163	Enzo Doria	06/2014
1026	3^485977-2^485977	231870	Mike Oakes	09/2009
1027	2^770082-114161	231818	Enzo Doria	01/2015
1028	(20^177967+1)/21	231540	Paul Bourdelais	05/2013
1029	(4*10^231254+23)/9	231254	Serge Batalov	11/2022
1030	2^767622-9221	231078	Lelio R Paula	01/2016
1031	2^767344+1880311	230994	Enzo Doria	09/2016
1032	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
1033	(10^230706+179)/9	230706	Serge Batalov	12/2014
1034	2^766309+1875257	230682	Enzo Doria	06/2016
1035	2^765635+1879883	230480	Enzo Doria	09/2016
1036	2^764348-113697	230092	Enzo Doria	09/2014
1037	2^764131+78863	230027	Enzo Doria	05/2016
1038	2^763701+60197	229897	Enzo Doria	03/2016
1039	4*10^229836+21	229837	Robert Price	12/2022
1040	2^762841-25905	229639	Enzo Doria	10/2013
1041	2^761117-113569	229120	Enzo Doria	08/2014
1042	(98^114859+1)/99	228709	Paul Bourdelais	12/2018
1043	(2^758231+1)/(32714694297653973236839266867)	228223	Gord Palameta	12/2018
1044	2^757985-2790013	228177	Enzo Doria	12/2015
1045	2^757038-1862081	227892	Enzo Doria	12/2015
1046	2^756839+95849	227832	Makoto Morimoto	10/2013
1047	(2^756839+6989)/756091	227826	Makoto Morimoto	09/2016
1048	(2^756839-50211)/(137*3203)	227826	Makoto Morimoto	08/2019
1049	2^756773-112723	227812	Enzo Doria	07/2014
1050	524309#+616367	227431	Makoto Morimoto	02/2016
1051	2^755097-114193	227307	Enzo Doria	12/2014
1052	7*10^227178+39	227179	Robert Price	01/2023
1053	2^754473-2791513	227120	Enzo Doria	01/2016
1054	2^754376+25	227090	Stefano Morozzi	05/2021
1055	2^754038+25	226989	Stefano Morozzi	05/2021
1056	2^751426-764321	226202	Enzo Doria	12/2013
1057	(18^180181-1)/17	226176	Andy Steward	04/2007
1058	2^750740-3	225996	Paul Bourdelais	03/2012
1059	2^750725+60227	225991	Enzo Doria	02/2016
1060	2^750525-113743	225931	Enzo Doria	09/2014
1061	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
1062	2^749444-1861889	225606	Enzo Doria	12/2015
1063	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
1064	2^749096+1876861	225501	Enzo Doria	07/2016
1065	(519643#+43033)/(2318712706283)	225379	Makoto Morimoto	08/2019
1066	2^748657+79607	225369	Enzo Doria	06/2016
1067	(2^746920-11)/5	224845	Stefano Morozzi	08/2022
1068	2^746653-291583	224765	Enzo Doria	07/2015
1069	2^746461-114043	224708	Enzo Doria	11/2014
1070	2^746302+25	224660	Stefano Morozzi	05/2021
1071	2^745098-350471	224297	Enzo Doria	06/2015
1072	2^745039-4897	224280	Yves Minet	03/2021
1073	23*10^224232-7	224234	Robert Price	10/2022
1074	(154*10^224061-1)/9	224063	Serge Batalov	12/2014
1075	2^744211-1845787	224030	Enzo Doria	07/2015
1076	2^743592-134579	223844	Hans Havermann	10/2018
1077	2^742452+3	223501	Paul Bourdelais	06/2019
1078	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
1079	2^741651-461197	223260	Enzo Doria	07/2015
1080	10^223236-1001	223236	Robert Price	10/2022
1081	2^741362-1845251	223173	Enzo Doria	07/2015
1082	2^740455-1863877	222900	Enzo Doria	12/2015
1083	(14*10^222718-41)/9	222719	Serge Batalov	01/2023
1084	2^739636-2792219	222653	Enzo Doria	02/2016
1085	11^213654-180	222498	Enzo Doria	01/2013
1086	2^738957-1859743	222449	Enzo Doria	11/2015
1087	4*10^222253-21	222254	Robert Price	12/2022
1088	2^737825+57	222108	Stefano Morozzi	05/2021
1089	(54^128189+1)/55	222073	Paul Bourdelais	11/2018
1090	(10^221654+179)/9	221654	Serge Batalov	12/2014
1091	2^736281+79817	221643	Enzo Doria	06/2016
1092	10^221631+247617	221632	Patrick De Geest	10/2013
1093	10^221631-9	221631	Alexander Gramolin	02/2011
1094	10^221628+7	221629	Alfred Reich	04/2021
1095	2^735970-1839821	221550	Enzo Doria	06/2015
1096	2^735367+60293	221368	Enzo Doria	03/2016
1097	(29^151153+1)/30	221045	Paul Bourdelais	09/2017
1098	2^733264-2784089	220735	Enzo Doria	10/2015
1099	2^733114-24555	220690	Enzo Doria	09/2013
1100	2^731891-636259	220322	Enzo Doria	12/2013
1101	2^731124-25539	220091	Enzo Doria	09/2013
1102	2^730972-462029	220045	Enzo Doria	07/2015
1103	2^730833+1868627	220003	Enzo Doria	04/2016
1104	2^730645-2787133	219947	Enzo Doria	11/2015
1105	2^730547-25581	219917	Enzo Doria	09/2013
1106	(113*13^197420-5)/12	219916	Anonymous	11/2022
1107	2^730460+82291	219891	Enzo Doria	09/2016
1108	(2^730339+1)/(3278390620037943469324347)	219831	Gord Palameta	12/2018
1109	L(1051849)	219824	Renaud Lifchitz	03/2009
1110	8*10^219740-3	219741	Serge Batalov	01/2023
1111	11^210961-240	219694	Enzo Doria	01/2013
1112	2^729611-113437	219635	Enzo Doria	08/2014
1113	7^259710-2	219481	Paul Bourdelais	01/2021
1114	F(1049897)	219416	Henri Lifchitz	10/2008
1115	2^728604+1879321	219332	Enzo Doria	10/2016
1116	33^144412+2	219292	Robert Price	04/2015
1117	2^728277-183313	219234	Hans Havermann	10/2018
1118	2^727998-1862711	219150	Enzo Doria	12/2015
1119	(29*10^219124+91)/3	219125	Robert Price	12/2022
1120	2^727729-114073	219069	Enzo Doria	12/2014
1121	2^727496-1851809	218999	Enzo Doria	08/2015
1122	2^726591+2793143	218726	Enzo Doria	02/2016
1123	2^725534-2791931	218408	Enzo Doria	02/2016
1124	Phi(220531,10)/2686456812680882641	217774	Makoto Kamada	10/2020
1125	2^722184+1877821	217400	Enzo Doria	08/2016
1126	(109*10^217360-1)/9	217362	Serge Batalov	12/2014
1127	2^721721-4453	217260	Yves Minet	03/2021
1128	281*499979#/46410-2702372	216849	Robert Smith	08/2016
1129	281*499979#/46410+2400766	216849	Robert Smith	08/2016
1130	tau(311^15786)	216429	Nik Lygeros / Olivier Rozier / LR team	10/2013
1131	2^718756-114107	216368	Enzo Doria	12/2014
1132	2^717672+121	216041	Stefano Morozzi	05/2021
1133	2^717305+80327	215931	Enzo Doria	07/2016
1134	2^717069-59773	215860	Enzo Doria	10/2015
1135	30^146021-29^146021	215691	Jean-Louis Charton	09/2018
1136	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
1137	227^91413-40	215372	Enzo Doria	04/2015
1138	(2^715008-21)/5	215239	Stefano Morozzi	08/2022
1139	2^714717+782897	215152	Enzo Doria	11/2016
1140	tau(373^15186)	214796	Nik Lygeros / Olivier Rozier / LR team	10/2013
1141	2^713241+1879157	214707	Enzo Doria	08/2016
1142	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
1143	2^712801-69553	214575	Enzo Doria	01/2016
1144	2^712603-25357	214515	Enzo Doria	09/2013
1145	2^711721-1846723	214250	Enzo Doria	07/2015
1146	2^710730-396765	213952	Enzo Doria	09/2013
1147	2^708468-114329	213271	Enzo Doria	02/2015
1148	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
1149	2^706838-69041	212780	Enzo Doria	11/2015
1150	22*10^212339+7	212341	Robert Price	10/2022
1151	2^704577-113871	212099	Enzo Doria	10/2014
1152	(2^704548-19)/3	212090	Stefano Morozzi	08/2022
1153	2^704110-2792441	211959	Enzo Doria	02/2016
1154	2^703943-1862947	211908	Enzo Doria	12/2015
1155	(60^119083+1)/61	211746	Paul Bourdelais	10/2018
1156	(184*10^211682-1)/3	211684	Robert Price	12/2022
1157	(10^211610-91)/9	211610	Serge Batalov	12/2014
1158	227^89797+2	211565	Lelio R Paula	08/2012
1159	2^702194-3	211382	Paul Bourdelais	03/2012
1160	2^702064+1874911	211343	Enzo Doria	07/2016
1161	2^701968-113873	211314	Enzo Doria	10/2014
1162	(14*10^211262-41)/9	211263	Serge Batalov	01/2023
1163	2^701713-113779	211237	Enzo Doria	09/2014
1164	2^701449-25201	211158	Enzo Doria	09/2013
1165	2^701403-2786977	211144	Enzo Doria	11/2015
1166	2^701189-25423	211079	Enzo Doria	09/2013
1167	2^701162-459161	211071	Enzo Doria	05/2015
1168	(24^152783-1)/23	210872	Paul Bourdelais	04/2018
1169	2^700400+9385	210842	Lelio R Paula	01/2014
1170	2^700304-17	210813	Stefano Morozzi	07/2022
1171	2^700131+1874693	210761	Enzo Doria	06/2016
1172	(2^700095+225414)/2	210750	Stefano Morozzi	04/2020
1173	(2^700090+278254)/2	210748	Stefano Morozzi	04/2020
1174	(2^700075+303666)/2	210744	Stefano Morozzi	04/2020
1175	(2^700073+75882)/2	210743	Stefano Morozzi	04/2020
1176	(2^700074+328890)/2	210743	Stefano Morozzi	04/2020
1177	(2^700052+79162)/2	210737	Stefano Morozzi	04/2020
1178	(2^700052+304458)/2	210737	Stefano Morozzi	04/2020
1179	(2^700048+376578)/2	210736	Stefano Morozzi	04/2020
1180	11^202357-1140	210734	Enzo Doria	12/2012
1181	(2^700021+25874)/2	210728	Stefano Morozzi	04/2020
1182	(2^700018+377518)/2	210727	Stefano Morozzi	04/2020
1183	2^699740+25	210643	Stefano Morozzi	05/2021
1184	2^698929-2788423	210399	Enzo Doria	11/2015
1185	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
1186	2^698316+1878601	210215	Enzo Doria	08/2016
1187	2^697036+1878751	209829	Enzo Doria	08/2016
1188	6^269407+5	209640	Paul Bourdelais	02/2021
1189	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
1190	2^696254-115151	209594	Enzo Doria	06/2015
1191	(35^135623+1)/36	209410	Paul Bourdelais	07/2018
1192	7*10^209161+39	209162	Robert Price	01/2023
1193	2^694633+1887257	209106	Enzo Doria	05/2017
1194	2^693959+180923	208903	Enzo Doria	07/2016
1195	(2^693747-11)/3	208839	Stefano Morozzi	08/2022
1196	2^693462-1847561	208753	Enzo Doria	07/2015
1197	2^690890-59981	207979	Enzo Doria	11/2015
1198	(38^131591+1)/39	207884	Paul Bourdelais	07/2018
1199	2^690163+1877063	207760	Enzo Doria	07/2016
1200	7^245608-2	207563	Paul Bourdelais	01/2021
1201	(67*10^207556+23)/9	207557	Serge Batalov	01/2023
1202	2^689286-29381	207496	Enzo Doria	08/2015
1203	2^689122-114521	207447	Enzo Doria	04/2015
1204	2^688373+6077	207221	Enzo Doria	02/2016
1205	2^688201+1875527	207170	Enzo Doria	07/2016
1206	(42^127609+1)/43	207140	Paul Bourdelais	07/2018
1207	2^687619+81563	206994	Enzo Doria	08/2016
1208	2^686572-1845299	206679	Enzo Doria	07/2015
1209	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
1210	(2^685739+1)/(3*87774593)	206420	Gord Palameta	08/2018
1211	2^685578+3	206380	Paul Bourdelais	04/2012
1212	2^684836-49349	206157	Enzo Doria	10/2015
1213	(73^110603-1)/72	206088	Paul Bourdelais	06/2018
1214	2^684163-2790967	205954	Enzo Doria	12/2015
1215	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
1216	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
1217	(68*10^205510+13)/9	205511	Serge Batalov	01/2023
1218	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
1219	2^681545+467	205166	Lelio R Paula	11/2013
1220	2^681306+81049	205094	Enzo Doria	07/2016
1221	2^680697+1877057	204911	Enzo Doria	07/2016
1222	2^680415+71783	204826	Enzo Doria	04/2016
1223	2^679860-459995	204659	Enzo Doria	06/2015
1224	2^679593+1879547	204578	Enzo Doria	09/2016
1225	2^678651+1875023	204295	Enzo Doria	07/2016
1226	2^678561+678561	204268	Henri Lifchitz	05/2006
1227	2^678101-114043	204129	Enzo Doria	11/2014
1228	2^678028+1875631	204107	Enzo Doria	06/2016
1229	2^676992-59783	203795	Enzo Doria	10/2015
1230	2^676972+1866871	203789	Enzo Doria	03/2016
1231	2^676761-9	203726	Robert Price	01/2017
1232	2^676592-23	203675	Stefano Morozzi	07/2022
1233	2^676563-2792407	203666	Enzo Doria	02/2016
1234	2^676306-114713	203589	Enzo Doria	04/2015
1235	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
1236	10247^50678-50678^10247	203250	Norbert Schneider	03/2022
1237	2^674627-25161	203083	Enzo Doria	09/2013
1238	2^674603-69337	203076	Enzo Doria	12/2015
1239	2^674459+74213	203033	Enzo Doria	04/2016
1240	2^674116-458879	202930	Enzo Doria	04/2015
1241	2^674076-114755	202918	Enzo Doria	04/2015
1242	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
1243	(2^673184-7)/3	202649	Stefano Morozzi	08/2022
1244	(467617#+14534)/(2^21343)	202603	Makoto Morimoto	06/2019
1245	2^672556-1835519	202460	Enzo Doria	04/2015
1246	2^671446-351401	202126	Enzo Doria	07/2015
1247	2^671373+77747	202104	Enzo Doria	05/2016
1248	(2*10^202059+7)/9	202059	Rytis Slatkevicius	01/2023
1249	2^670726-114845	201909	Enzo Doria	05/2015
1250	2^670539-25045	201853	Enzo Doria	09/2013

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