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	(14*10^243724-197)/3	243725	Robert Price	03/2023
1002	2^808767-3295	243464	Yves Minet	12/2016
1003	2^808621-113809	243420	Enzo Doria	09/2014
1004	2^807724+1879621	243150	Enzo Doria	09/2016
1005	(23*10^242909+91)/3	242910	Robert Price	03/2023
1006	2*10^242822-91	242823	Robert Price	02/2023
1007	20^186554-3	242713	Paul Bourdelais	12/2020
1008	2^805843-113611	242583	Enzo Doria	08/2014
1009	2^805745-459763	242554	Enzo Doria	05/2015
1010	2^805353+782687	242436	Enzo Doria	11/2016
1011	6^311257+5	242206	Paul Bourdelais	02/2021
1012	2^804277-417933	242112	Enzo Doria	01/2014
1013	2^803468-269039	241868	Enzo Doria	10/2013
1014	2^803172+80851	241779	Enzo Doria	07/2016
1015	3^506233-2	241535	Robert Price	11/2013
1016	2^802025-25999	241434	Enzo Doria	10/2013
1017	(3^505823+3^252912+1)/7	241339	Serge Batalov	03/2014
1018	2^801303+1872923	241217	Enzo Doria	05/2016
1019	2^800579-1862947	240999	Enzo Doria	12/2015
1020	3^504206+2	240568	Luke W. Richards	03/2018
1021	2^798973-26283	240515	Enzo Doria	10/2013
1022	2^798671-69487	240424	Enzo Doria	12/2015
1023	2^797220+79831	239988	Enzo Doria	06/2016
1024	2^796910-26001	239894	Enzo Doria	10/2013
1025	2^796598+653119	239800	Enzo Doria	12/2016
1026	2^796432-1859729	239750	Enzo Doria	11/2015
1027	2^796002-1852211	239621	Enzo Doria	08/2015
1028	2^795709+75767	239533	Enzo Doria	04/2016
1029	2^795708+81721	239532	Enzo Doria	08/2016
1030	2^795468-2786249	239460	Enzo Doria	10/2015
1031	2^795442+80779	239452	Enzo Doria	07/2016
1032	2^795075-1852057	239342	Enzo Doria	08/2015
1033	(86^123677+1)/87	239252	Paul Bourdelais	01/2019
1034	2^794043+1875023	239031	Enzo Doria	06/2016
1035	2^793347-69577	238822	Enzo Doria	01/2016
1036	2^792988-344429	238714	Enzo Doria	08/2015
1037	2^792700-2786369	238627	Enzo Doria	11/2015
1038	2^792663-1844797	238616	Enzo Doria	06/2015
1039	2^792605-291943	238598	Enzo Doria	07/2015
1040	(2^792061-2^396031+1)/5	238434	Thomas Ritschel	03/2014
1041	4*10^238163+21	238164	Robert Price	12/2022
1042	(26*10^238157-77)/3	238158	Robert Price	03/2023
1043	2^789373+1869377	237625	Enzo Doria	05/2016
1044	((10^59387+1)^3(10^59387+1+10^29694)-(10^118774+10^59387)(10^29694-1)+10^178161)/27961	237544	Serge Batalov	04/2015
1045	2^788942+1866409	237496	Enzo Doria	02/2016
1046	2^788844-114329	237466	Enzo Doria	01/2015
1047	2^788705-1859713	237424	Enzo Doria	11/2015
1048	2^786180+1871971	236664	Enzo Doria	05/2016
1049	11^227092-90	236492	Enzo Doria	11/2012
1050	2^785260+1866361	236387	Enzo Doria	02/2016
1051	2^785220+1880611	236375	Enzo Doria	10/2016
1052	(2^784689-15)/7	236215	Stefano Morozzi	08/2022
1053	19^184650-2	236122	Robert Price	10/2014
1054	10^236059+216513	236060	Patrick De Geest	04/2016
1055	10^236059-20909	236059	Robert Price	09/2015
1056	2^783893-21	235976	Stefano Morozzi	07/2022
1057	(87^121487-1)/86	235625	Paul Bourdelais	12/2018
1058	2^782634-113981	235597	Enzo Doria	11/2014
1059	2^782423+1879733	235533	Enzo Doria	09/2016
1060	2^781682-2789543	235310	Enzo Doria	12/2015
1061	2^780408-113453	234927	Enzo Doria	08/2014
1062	7*10^234915+9	234916	Robert Price	04/2023
1063	2^780368-1864829	234915	Enzo Doria	01/2016
1064	2^779593-1836559	234681	Enzo Doria	05/2015
1065	(8713#+(549391#)/(8713#))/360295171	234487	Makoto Morimoto	11/2017
1066	(5^335429+1)/6	234455	Paul Bourdelais	08/2010
1067	2^778395-113617	234321	Enzo Doria	08/2014
1068	23*10^234025-7	234027	Robert Price	10/2022
1069	Phi(78125,5517)	233857	Anonymous	09/2022
1070	2^776245-2792353	233674	Enzo Doria	02/2016
1071	2^776060-114029	233618	Enzo Doria	11/2014
1072	2^775987-2789557	233596	Enzo Doria	12/2015
1073	2*10^233564-91	233565	Robert Price	02/2023
1074	2^775672+1866721	233501	Enzo Doria	03/2016
1075	2^775238+57	233370	Stefano Morozzi	05/2021
1076	(11^223999+1)/12	233270	Paul Bourdelais	02/2010
1077	2^774118+1885789	233033	Enzo Doria	04/2017
1078	21^176191-20^176191	232964	Jean-Louis Charton	01/2015
1079	2^773679-113425	232901	Enzo Doria	08/2014
1080	(7*10^232620+23)/3	232621	Robert Price	05/2023
1081	10^232599+192489	232600	Patrick De Geest	12/2013
1082	10^232599-3	232599	Markus Tervooren	10/2010
1083	2^772552-458879	232562	Enzo Doria	04/2015
1084	2^772214+1874899	232460	Enzo Doria	06/2016
1085	2^771994-1862771	232394	Enzo Doria	12/2015
1086	2^771889+1876037	232362	Enzo Doria	07/2016
1087	2^771660+1866511	232293	Enzo Doria	02/2016
1088	5^332150-18188	232163	Enzo Doria	06/2014
1089	3^485977-2^485977	231870	Mike Oakes	09/2009
1090	2^770082-114161	231818	Enzo Doria	01/2015
1091	(20^177967+1)/21	231540	Paul Bourdelais	05/2013
1092	(4*10^231254+23)/9	231254	Serge Batalov	11/2022
1093	2^767622-9221	231078	Lelio R Paula	01/2016
1094	2^767344+1880311	230994	Enzo Doria	09/2016
1095	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
1096	(10^230706+179)/9	230706	Serge Batalov	12/2014
1097	2^766309+1875257	230682	Enzo Doria	06/2016
1098	2^765635+1879883	230480	Enzo Doria	09/2016
1099	2^764348-113697	230092	Enzo Doria	09/2014
1100	2^764131+78863	230027	Enzo Doria	05/2016
1101	2^763701+60197	229897	Enzo Doria	03/2016
1102	4*10^229836+21	229837	Robert Price	12/2022
1103	2^762841-25905	229639	Enzo Doria	10/2013
1104	2^761117-113569	229120	Enzo Doria	08/2014
1105	(98^114859+1)/99	228709	Paul Bourdelais	12/2018
1106	(2^758231+1)/(32714694297653973236839266867)	228223	Gord Palameta	12/2018
1107	(298*10^228177-7)/3	228179	Robert Price	02/2023
1108	2^757985-2790013	228177	Enzo Doria	12/2015
1109	34*10^228129-9	228131	Robert Price	05/2023
1110	2^757038-1862081	227892	Enzo Doria	12/2015
1111	2^756839+95849	227832	Makoto Morimoto	10/2013
1113	(2^756839+6989)/756091	227826	Makoto Morimoto	09/2016
1112	(2^756839-50211)/(137*3203)	227826	Makoto Morimoto	08/2019
1114	2^756773-112723	227812	Enzo Doria	07/2014
1115	524309#+616367	227431	Makoto Morimoto	02/2016
1116	2^755097-114193	227307	Enzo Doria	12/2014
1117	7*10^227178+39	227179	Robert Price	01/2023
1118	9*10^227153-89	227154	Robert Price	02/2023
1119	2^754473-2791513	227120	Enzo Doria	01/2016
1120	2^754376+25	227090	Stefano Morozzi	05/2021
1121	2^754038+25	226989	Stefano Morozzi	05/2021
1122	7*10^226479-9	226480	Robert Price	02/2023
1123	2^751426-764321	226202	Enzo Doria	12/2013
1124	(18^180181-1)/17	226176	Andy Steward	04/2007
1125	2^750740-3	225996	Paul Bourdelais	03/2012
1126	2^750725+60227	225991	Enzo Doria	02/2016
1127	2^750525-113743	225931	Enzo Doria	09/2014
1128	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
1129	2^749444-1861889	225606	Enzo Doria	12/2015
1130	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
1131	2^749096+1876861	225501	Enzo Doria	07/2016
1132	(519643#+43033)/(2318712706283)	225379	Makoto Morimoto	08/2019
1133	2^748657+79607	225369	Enzo Doria	06/2016
1134	(2^746920-11)/5	224845	Stefano Morozzi	08/2022
1135	2^746653-291583	224765	Enzo Doria	07/2015
1136	2^746461-114043	224708	Enzo Doria	11/2014
1137	2^746302+25	224660	Stefano Morozzi	05/2021
1138	2^745098-350471	224297	Enzo Doria	06/2015
1139	2^745039-4897	224280	Yves Minet	03/2021
1140	23*10^224232-7	224234	Robert Price	10/2022
1141	(154*10^224061-1)/9	224063	Serge Batalov	12/2014
1142	2^744211-1845787	224030	Enzo Doria	07/2015
1143	2^743592-134579	223844	Hans Havermann	10/2018
1144	2^742452+3	223501	Paul Bourdelais	06/2019
1145	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
1146	2^741651-461197	223260	Enzo Doria	07/2015
1147	10^223236-1001	223236	Robert Price	10/2022
1148	2^741362-1845251	223173	Enzo Doria	07/2015
1149	2^740455-1863877	222900	Enzo Doria	12/2015
1150	(14*10^222718-41)/9	222719	Serge Batalov	01/2023
1151	2^739636-2792219	222653	Enzo Doria	02/2016
1152	11^213654-180	222498	Enzo Doria	01/2013
1153	2^738957-1859743	222449	Enzo Doria	11/2015
1154	4*10^222253-21	222254	Robert Price	12/2022
1155	2^737825+57	222108	Stefano Morozzi	05/2021
1156	(54^128189+1)/55	222073	Paul Bourdelais	11/2018
1157	(10^221654+179)/9	221654	Serge Batalov	12/2014
1158	2^736281+79817	221643	Enzo Doria	06/2016
1159	10^221631+247617	221632	Patrick De Geest	10/2013
1160	10^221631-9	221631	Alexander Gramolin	02/2011
1161	10^221628+7	221629	Alfred Reich	04/2021
1162	2^735970-1839821	221550	Enzo Doria	06/2015
1163	2^735367+60293	221368	Enzo Doria	03/2016
1164	(29^151153+1)/30	221045	Paul Bourdelais	09/2017
1165	2^733264-2784089	220735	Enzo Doria	10/2015
1166	2^733114-24555	220690	Enzo Doria	09/2013
1167	2^731891-636259	220322	Enzo Doria	12/2013
1168	98*10^220185-9	220187	Robert Price	05/2023
1169	2^731124-25539	220091	Enzo Doria	09/2013
1170	2^730972-462029	220045	Enzo Doria	07/2015
1171	2^730833+1868627	220003	Enzo Doria	04/2016
1172	2^730645-2787133	219947	Enzo Doria	11/2015
1173	2^730547-25581	219917	Enzo Doria	09/2013
1174	(113*13^197420-5)/12	219916	Anonymous	11/2022
1175	2^730460+82291	219891	Enzo Doria	09/2016
1176	(2^730339+1)/(3278390620037943469324347)	219831	Gord Palameta	12/2018
1177	L(1051849)	219824	Renaud Lifchitz	03/2009
1178	8*10^219740-3	219741	Serge Batalov	01/2023
1179	11^210961-240	219694	Enzo Doria	01/2013
1180	(26*10^219639-77)/3	219640	Robert Price	03/2023
1181	2^729611-113437	219635	Enzo Doria	08/2014
1182	7^259710-2	219481	Paul Bourdelais	01/2021
1183	F(1049897)	219416	Henri Lifchitz	10/2008
1184	(1488^69151-1)/1487	219386	Alexander Zhirkov	02/2023
1185	2^728604+1879321	219332	Enzo Doria	10/2016
1186	33^144412+2	219292	Robert Price	04/2015
1187	2^728277-183313	219234	Hans Havermann	10/2018
1188	2^727998-1862711	219150	Enzo Doria	12/2015
1189	(29*10^219124+91)/3	219125	Robert Price	12/2022
1190	2^727729-114073	219069	Enzo Doria	12/2014
1191	2^727496-1851809	218999	Enzo Doria	08/2015
1192	2^726591+2793143	218726	Enzo Doria	02/2016
1193	2^725534-2791931	218408	Enzo Doria	02/2016
1194	Phi(220531,10)/2686456812680882641	217774	Makoto Kamada	10/2020
1195	2^722184+1877821	217400	Enzo Doria	08/2016
1196	(109*10^217360-1)/9	217362	Serge Batalov	12/2014
1197	2^721721-4453	217260	Yves Minet	03/2021
1198	10^216950+49	216951	Robert Price	02/2023
1199	281*499979#/46410-2702372	216849	Robert Smith	08/2016
1200	281*499979#/46410+2400766	216849	Robert Smith	08/2016
1201	tau(311^15786)	216429	Nik Lygeros / Olivier Rozier / LR team	10/2013
1202	2^718756-114107	216368	Enzo Doria	12/2014
1203	2^717672+121	216041	Stefano Morozzi	05/2021
1204	2^717305+80327	215931	Enzo Doria	07/2016
1205	2^717069-59773	215860	Enzo Doria	10/2015
1206	30^146021-29^146021	215691	Jean-Louis Charton	09/2018
1207	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
1208	227^91413-40	215372	Enzo Doria	04/2015
1209	(2^715008-21)/5	215239	Stefano Morozzi	08/2022
1210	2^714717+782897	215152	Enzo Doria	11/2016
1211	tau(373^15186)	214796	Nik Lygeros / Olivier Rozier / LR team	10/2013
1212	2^713241+1879157	214707	Enzo Doria	08/2016
1213	(23*10^214633+91)/3	214634	Robert Price	03/2023
1214	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
1215	2^712801-69553	214575	Enzo Doria	01/2016
1216	2^712603-25357	214515	Enzo Doria	09/2013
1217	2^711721-1846723	214250	Enzo Doria	07/2015
1218	2^710730-396765	213952	Enzo Doria	09/2013
1219	2^708468-114329	213271	Enzo Doria	02/2015
1220	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
1221	2^706838-69041	212780	Enzo Doria	11/2015
1222	22*10^212339+7	212341	Robert Price	10/2022
1223	2^704577-113871	212099	Enzo Doria	10/2014
1224	(2^704548-19)/3	212090	Stefano Morozzi	08/2022
1225	2^704110-2792441	211959	Enzo Doria	02/2016
1226	2^703943-1862947	211908	Enzo Doria	12/2015
1227	(60^119083+1)/61	211746	Paul Bourdelais	10/2018
1228	(184*10^211682-1)/3	211684	Robert Price	12/2022
1229	(10^211610-91)/9	211610	Serge Batalov	12/2014
1230	227^89797+2	211565	Lelio R Paula	08/2012
1231	2^702194-3	211382	Paul Bourdelais	03/2012
1232	2^702064+1874911	211343	Enzo Doria	07/2016
1233	2^701968-113873	211314	Enzo Doria	10/2014
1234	(14*10^211262-41)/9	211263	Serge Batalov	01/2023
1235	2^701713-113779	211237	Enzo Doria	09/2014
1236	2^701449-25201	211158	Enzo Doria	09/2013
1237	2^701403-2786977	211144	Enzo Doria	11/2015
1238	2^701189-25423	211079	Enzo Doria	09/2013
1239	2^701162-459161	211071	Enzo Doria	05/2015
1240	(24^152783-1)/23	210872	Paul Bourdelais	04/2018
1241	2^700400+9385	210842	Lelio R Paula	01/2014
1242	2^700304-17	210813	Stefano Morozzi	07/2022
1243	2^700131+1874693	210761	Enzo Doria	06/2016
1244	(2^700095+225414)/2	210750	Stefano Morozzi	04/2020
1245	(2^700090+278254)/2	210748	Stefano Morozzi	04/2020
1246	(2^700075+303666)/2	210744	Stefano Morozzi	04/2020
1247	(2^700073+75882)/2	210743	Stefano Morozzi	04/2020
1248	(2^700074+328890)/2	210743	Stefano Morozzi	04/2020
1249	(2^700052+79162)/2	210737	Stefano Morozzi	04/2020
1250	(2^700052+304458)/2	210737	Stefano Morozzi	04/2020

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