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	2^737825+57	222108	Stefano Morozzi	05/2021
1002	(54^128189+1)/55	222073	Paul Bourdelais	11/2018
1003	(10^221654+179)/9	221654	Serge Batalov	12/2014
1004	2^736281+79817	221643	Enzo Doria	06/2016
1005	10^221631+247617	221632	Patrick De Geest	10/2013
1006	10^221631-9	221631	Alexander Gramolin	02/2011
1007	10^221628+7	221629	Alfred Reich	04/2021
1008	2^735970-1839821	221550	Enzo Doria	06/2015
1009	2^735367+60293	221368	Enzo Doria	03/2016
1010	(29^151153+1)/30	221045	Paul Bourdelais	09/2017
1011	2^733264-2784089	220735	Enzo Doria	10/2015
1012	2^733114-24555	220690	Enzo Doria	09/2013
1013	2^731891-636259	220322	Enzo Doria	12/2013
1014	2^731124-25539	220091	Enzo Doria	09/2013
1015	2^730972-462029	220045	Enzo Doria	07/2015
1016	2^730833+1868627	220003	Enzo Doria	04/2016
1017	2^730645-2787133	219947	Enzo Doria	11/2015
1018	2^730547-25581	219917	Enzo Doria	09/2013
1019	2^730460+82291	219891	Enzo Doria	09/2016
1020	(2^730339+1)/(3278390620037943469324347)	219831	Gord Palameta	12/2018
1021	L(1051849)	219824	Renaud Lifchitz	03/2009
1022	11^210961-240	219694	Enzo Doria	01/2013
1023	2^729611-113437	219635	Enzo Doria	08/2014
1024	7^259710-2	219481	Paul Bourdelais	01/2021
1025	F(1049897)	219416	Henri Lifchitz	10/2008
1026	2^728604+1879321	219332	Enzo Doria	10/2016
1027	33^144412+2	219292	Robert Price	04/2015
1028	2^728277-183313	219234	Hans Havermann	10/2018
1029	2^727998-1862711	219150	Enzo Doria	12/2015
1030	2^727729-114073	219069	Enzo Doria	12/2014
1031	2^727496-1851809	218999	Enzo Doria	08/2015
1032	2^726591+2793143	218726	Enzo Doria	02/2016
1033	2^725534-2791931	218408	Enzo Doria	02/2016
1034	Phi(220531,10)/2686456812680882641	217774	Makoto Kamada	10/2020
1035	2^722184+1877821	217400	Enzo Doria	08/2016
1036	(109*10^217360-1)/9	217362	Serge Batalov	12/2014
1037	2^721721-4453	217260	Yves Minet	03/2021
1038	281*499979#/46410-2702372	216849	Robert Smith	08/2016
1039	281*499979#/46410+2400766	216849	Robert Smith	08/2016
1040	tau(311^15786)	216429	Nik Lygeros / Olivier Rozier / LR team	10/2013
1041	2^718756-114107	216368	Enzo Doria	12/2014
1042	2^717672+121	216041	Stefano Morozzi	05/2021
1043	2^717305+80327	215931	Enzo Doria	07/2016
1044	2^717069-59773	215860	Enzo Doria	10/2015
1045	30^146021-29^146021	215691	Jean-Louis Charton	09/2018
1046	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
1047	227^91413-40	215372	Enzo Doria	04/2015
1048	(2^715008-21)/5	215239	Stefano Morozzi	08/2022
1049	2^714717+782897	215152	Enzo Doria	11/2016
1050	tau(373^15186)	214796	Nik Lygeros / Olivier Rozier / LR team	10/2013
1051	2^713241+1879157	214707	Enzo Doria	08/2016
1052	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
1053	2^712801-69553	214575	Enzo Doria	01/2016
1054	2^712603-25357	214515	Enzo Doria	09/2013
1055	2^711721-1846723	214250	Enzo Doria	07/2015
1056	2^710730-396765	213952	Enzo Doria	09/2013
1057	2^708468-114329	213271	Enzo Doria	02/2015
1058	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
1059	2^706838-69041	212780	Enzo Doria	11/2015
1060	2^704577-113871	212099	Enzo Doria	10/2014
1061	(2^704548-19)/3	212090	Stefano Morozzi	08/2022
1062	2^704110-2792441	211959	Enzo Doria	02/2016
1063	2^703943-1862947	211908	Enzo Doria	12/2015
1064	(60^119083+1)/61	211746	Paul Bourdelais	10/2018
1065	(10^211610-91)/9	211610	Serge Batalov	12/2014
1066	227^89797+2	211565	Lelio R Paula	08/2012
1067	2^702194-3	211382	Paul Bourdelais	03/2012
1068	2^702064+1874911	211343	Enzo Doria	07/2016
1069	2^701968-113873	211314	Enzo Doria	10/2014
1070	2^701713-113779	211237	Enzo Doria	09/2014
1071	2^701449-25201	211158	Enzo Doria	09/2013
1072	2^701403-2786977	211144	Enzo Doria	11/2015
1073	2^701189-25423	211079	Enzo Doria	09/2013
1074	2^701162-459161	211071	Enzo Doria	05/2015
1075	(24^152783-1)/23	210872	Paul Bourdelais	04/2018
1076	2^700400+9385	210842	Lelio R Paula	01/2014
1077	2^700304-17	210813	Stefano Morozzi	07/2022
1078	2^700131+1874693	210761	Enzo Doria	06/2016
1079	(2^700095+225414)/2	210750	Stefano Morozzi	04/2020
1080	(2^700090+278254)/2	210748	Stefano Morozzi	04/2020
1081	(2^700075+303666)/2	210744	Stefano Morozzi	04/2020
1082	(2^700073+75882)/2	210743	Stefano Morozzi	04/2020
1083	(2^700074+328890)/2	210743	Stefano Morozzi	04/2020
1084	(2^700052+79162)/2	210737	Stefano Morozzi	04/2020
1085	(2^700052+304458)/2	210737	Stefano Morozzi	04/2020
1086	(2^700048+376578)/2	210736	Stefano Morozzi	04/2020
1087	11^202357-1140	210734	Enzo Doria	12/2012
1088	(2^700021+25874)/2	210728	Stefano Morozzi	04/2020
1089	(2^700018+377518)/2	210727	Stefano Morozzi	04/2020
1090	2^699740+25	210643	Stefano Morozzi	05/2021
1091	2^698929-2788423	210399	Enzo Doria	11/2015
1092	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
1093	2^698316+1878601	210215	Enzo Doria	08/2016
1094	2^697036+1878751	209829	Enzo Doria	08/2016
1095	6^269407+5	209640	Paul Bourdelais	02/2021
1096	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
1097	2^696254-115151	209594	Enzo Doria	06/2015
1098	(35^135623+1)/36	209410	Paul Bourdelais	07/2018
1099	2^694633+1887257	209106	Enzo Doria	05/2017
1100	2^693959+180923	208903	Enzo Doria	07/2016
1101	(2^693747-11)/3	208839	Stefano Morozzi	08/2022
1102	2^693462-1847561	208753	Enzo Doria	07/2015
1103	2^690890-59981	207979	Enzo Doria	11/2015
1104	(38^131591+1)/39	207884	Paul Bourdelais	07/2018
1105	2^690163+1877063	207760	Enzo Doria	07/2016
1106	7^245608-2	207563	Paul Bourdelais	01/2021
1107	2^689286-29381	207496	Enzo Doria	08/2015
1108	2^689122-114521	207447	Enzo Doria	04/2015
1109	2^688373+6077	207221	Enzo Doria	02/2016
1110	2^688201+1875527	207170	Enzo Doria	07/2016
1111	(42^127609+1)/43	207140	Paul Bourdelais	07/2018
1112	2^687619+81563	206994	Enzo Doria	08/2016
1113	2^686572-1845299	206679	Enzo Doria	07/2015
1114	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
1115	(2^685739+1)/(3*87774593)	206420	Gord Palameta	08/2018
1116	2^685578+3	206380	Paul Bourdelais	04/2012
1117	2^684836-49349	206157	Enzo Doria	10/2015
1118	(73^110603-1)/72	206088	Paul Bourdelais	06/2018
1119	2^684163-2790967	205954	Enzo Doria	12/2015
1120	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
1121	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
1122	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
1123	2^681545+467	205166	Lelio R Paula	11/2013
1124	2^681306+81049	205094	Enzo Doria	07/2016
1125	2^680697+1877057	204911	Enzo Doria	07/2016
1126	2^680415+71783	204826	Enzo Doria	04/2016
1127	2^679860-459995	204659	Enzo Doria	06/2015
1128	2^679593+1879547	204578	Enzo Doria	09/2016
1129	2^678651+1875023	204295	Enzo Doria	07/2016
1130	2^678561+678561	204268	Henri Lifchitz	05/2006
1131	2^678101-114043	204129	Enzo Doria	11/2014
1132	2^678028+1875631	204107	Enzo Doria	06/2016
1133	2^676992-59783	203795	Enzo Doria	10/2015
1134	2^676972+1866871	203789	Enzo Doria	03/2016
1135	2^676761-9	203726	Robert Price	01/2017
1136	2^676592-23	203675	Stefano Morozzi	07/2022
1137	2^676563-2792407	203666	Enzo Doria	02/2016
1138	2^676306-114713	203589	Enzo Doria	04/2015
1139	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
1140	10247^50678-50678^10247	203250	Norbert Schneider	03/2022
1141	2^674627-25161	203083	Enzo Doria	09/2013
1142	2^674603-69337	203076	Enzo Doria	12/2015
1143	2^674459+74213	203033	Enzo Doria	04/2016
1144	2^674116-458879	202930	Enzo Doria	04/2015
1145	2^674076-114755	202918	Enzo Doria	04/2015
1146	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
1147	(2^673184-7)/3	202649	Stefano Morozzi	08/2022
1148	(467617#+14534)/(2^21343)	202603	Makoto Morimoto	06/2019
1149	2^672556-1835519	202460	Enzo Doria	04/2015
1150	2^671446-351401	202126	Enzo Doria	07/2015
1151	2^671373+77747	202104	Enzo Doria	05/2016
1152	2^670726-114845	201909	Enzo Doria	05/2015
1153	2^670539-25045	201853	Enzo Doria	09/2013
1154	43284^43519-43519^43284	201769	Norbert Schneider	08/2018
1155	2^670213+282317	201755	Enzo Doria	09/2016
1156	2^670133+89	201731	Stefano Morozzi	05/2021
1157	2^669854-113501	201647	Enzo Doria	08/2014
1158	2^669718+81619	201606	Enzo Doria	08/2016
1159	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
1160	2^668938-1839821	201371	Enzo Doria	06/2015
1161	2^668492+1879303	201237	Enzo Doria	08/2016
1162	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
1163	10194^50161-50161^10194	201063	Norbert Schneider	09/2020
1164	2^667894+1875589	201057	Enzo Doria	06/2016
1165	2^667569-1836559	200959	Enzo Doria	05/2015
1166	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
1167	2^666430+782569	200616	Enzo Doria	10/2016
1168	(86^103471+1)/87	200163	Paul Bourdelais	05/2018
1169	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
1170	103(10^100000+33798)^2-4707(10^100000+33798)+50383	200003	Robert Price	01/2018
1171	numbpart(32235776596)	200002	Serge Batalov	04/2017
1172	(10^200001+149)/3	200001	Serge Batalov	12/2014
1173	10^200000+571791	200001	Patrick De Geest	08/2019
1174	(3^419180-621444)/3	200000	Stefano Morozzi	06/2019
1175	(3^419180-1941384)/3	200000	Stefano Morozzi	08/2019
1176	10^200000-45557	200000	Patrick De Geest	08/2019
1177	(10^200000-1)/9-10^58838	200000	Akihiko Yoshida	04/2020
1178	92*10^199980-9	199982	Robert Price	12/2021
1179	(85*10^199951-139)/9	199952	Robert Price	08/2021
1180	(10^199926+7)/29/373/2339	199919	Alfred Reich	08/2021
1181	23*10^199833-9	199835	Robert Price	10/2021
1182	(299*10^199801-17)/3	199803	Robert Price	04/2020
1183	6*10^199788+77	199789	Robert Price	06/2020
1184	(23*10^199615+37)/3	199616	Robert Price	02/2022
1185	(17*10^199607-167)/3	199608	Robert Price	05/2022
1186	2^663020-933075	199589	Paul Bourdelais	06/2021
1187	(14*10^199447+73)/3	199448	Robert Price	12/2018
1188	(2^662424-15)/7	199409	Stefano Morozzi	08/2022
1189	2^662103-29287	199313	Enzo Doria	08/2015
1190	(2*10^199283+457)/9	199283	Robert Price	01/2018
1191	(10^199248-19)/9	199248	Robert Price	01/2018
1192	(83*10^199213+529)/9	199214	Robert Price	12/2021
1193	(194*10^199146-17)/3	199148	Robert Price	09/2020
1194	(151*10^199003-1)/3	199005	Robert Price	03/2020
1195	9*10^198946-73	198947	Robert Price	01/2021
1196	45*10^198931-7	198933	Robert Price	07/2020
1197	2^660482-2891	198825	Yves Minet	05/2016
1198	2^659589-21	198557	Stefano Morozzi	07/2022
1199	2^659583+1879223	198555	Enzo Doria	08/2016
1200	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
1201	(49*10^198403+311)/9	198404	Robert Price	06/2019
1202	96*10^198376-7	198378	Robert Price	03/2021
1203	(10^198375+7)/59/1201/87589	198366	Alfred Reich	08/2021
1204	2^658828-29819	198327	Enzo Doria	08/2015
1205	2^658776-2791229	198312	Enzo Doria	01/2016
1206	(35*10^198294-377)/9	198295	Robert Price	07/2018
1207	(4*10^198268+137)/3	198269	Robert Price	03/2018
1208	2^658544-1854029	198242	Enzo Doria	09/2015
1209	(62*10^198229-233)/9	198230	Robert Price	02/2022
1210	(26*10^198200-41)/3	198201	Robert Price	02/2022
1211	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
1212	2*10^197959-37	197960	Robert Price	11/2021
1213	(232*10^197897+17)/3	197899	Robert Price	04/2021
1214	(4*10^197778+173)/3	197779	Robert Price	02/2018
1215	78*10^197702-7	197704	Robert Price	10/2020
1216	(17*10^197640-23)/3	197641	Robert Price	03/2021
1217	(29*10^197629-77)/3	197630	Robert Price	02/2020
1218	2^656462+1874419	197615	Enzo Doria	06/2016
1219	(89^101363+1)/90	197595	Paul Bourdelais	11/2017
1220	2^655893-344563	197444	Enzo Doria	07/2015
1221	2^655875+71333	197439	Enzo Doria	04/2016
1222	2^655845-9	197430	Robert Price	01/2017
1223	(299*10^197426+1)/3	197428	Robert Price	04/2020
1224	2^655682-1849121	197380	Enzo Doria	08/2015
1225	4*10^197268-89	197269	Robert Price	11/2018
1226	(11*10^197198-89)/3	197199	Robert Price	05/2021
1227	2^655045-49603	197189	Enzo Doria	10/2015
1228	2^655000-2784089	197175	Enzo Doria	10/2015
1229	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
1230	(154*10^197005+17)/9	197007	Robert Price	06/2022
1231	2^654400-39719	196995	Enzo Doria	09/2015
1232	(14*10^196965-221)/9	196966	Robert Price	04/2018
1233	2^654216-459995	196939	Enzo Doria	06/2015
1234	(17*10^196921+31)/3	196922	Robert Price	01/2019
1235	(14*10^196885-89)/3	196886	Robert Price	05/2020
1236	3*10^196881-59	196882	Robert Price	09/2018
1237	2^653851+82295	196829	Enzo Doria	09/2016
1238	(38*10^196792+691)/9	196793	Robert Price	10/2018
1239	(65*10^196768+493)/9	196769	Robert Price	08/2021
1241	2^653636-29429	196765	Enzo Doria	08/2015
1240	2^653638-11	196765	Stefano Morozzi	07/2022
1242	2^653601-69673	196754	Enzo Doria	02/2016
1243	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
1244	2^652786-1852571	196509	Enzo Doria	08/2015
1245	2^652752-1325	196498	Yves Minet	07/2015
1246	2^652470-1859141	196414	Enzo Doria	10/2015
1247	2^652307+1877483	196364	Enzo Doria	08/2016
1248	2^652293-115273	196360	Enzo Doria	06/2015
1249	(47*10^196281+403)/9	196282	Robert Price	03/2019
1250	(7*10^196125-31)/3	196126	Robert Price	12/2021

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Probable Primes Top 10000

(291192 PRPs in the top)