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	30^146021-29^146021	215691	Jean-Louis Charton	09/2018
1002	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
1003	227^91413-40	215372	Enzo Doria	04/2015
1004	2^714717+782897	215152	Enzo Doria	11/2016
1005	tau(373^15186)	214796	Nik Lygeros / Olivier Rozier / LR team	10/2013
1006	2^713241+1879157	214707	Enzo Doria	08/2016
1007	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
1008	2^712801-69553	214575	Enzo Doria	01/2016
1009	2^712603-25357	214515	Enzo Doria	09/2013
1010	2^711721-1846723	214250	Enzo Doria	07/2015
1011	2^710730-396765	213952	Enzo Doria	09/2013
1012	2^708468-114329	213271	Enzo Doria	02/2015
1013	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
1014	2^706838-69041	212780	Enzo Doria	11/2015
1015	2^704577-113871	212099	Enzo Doria	10/2014
1016	2^704110-2792441	211959	Enzo Doria	02/2016
1017	2^703943-1862947	211908	Enzo Doria	12/2015
1018	(60^119083+1)/61	211746	Paul Bourdelais	10/2018
1019	(10^211610-91)/9	211610	Serge Batalov	12/2014
1020	227^89797+2	211565	Lelio R Paula	08/2012
1021	2^702194-3	211382	Paul Bourdelais	03/2012
1022	2^702064+1874911	211343	Enzo Doria	07/2016
1023	2^701968-113873	211314	Enzo Doria	10/2014
1024	2^701713-113779	211237	Enzo Doria	09/2014
1025	2^701449-25201	211158	Enzo Doria	09/2013
1026	2^701403-2786977	211144	Enzo Doria	11/2015
1027	2^701189-25423	211079	Enzo Doria	09/2013
1028	2^701162-459161	211071	Enzo Doria	05/2015
1029	(24^152783-1)/23	210872	Paul Bourdelais	04/2018
1030	2^700400+9385	210842	Lelio R Paula	01/2014
1031	2^700131+1874693	210761	Enzo Doria	06/2016
1032	(2^700095+225414)/2	210750	Stefano Morozzi	04/2020
1033	(2^700090+278254)/2	210748	Stefano Morozzi	04/2020
1034	(2^700075+303666)/2	210744	Stefano Morozzi	04/2020
1035	(2^700073+75882)/2	210743	Stefano Morozzi	04/2020
1036	(2^700074+328890)/2	210743	Stefano Morozzi	04/2020
1037	(2^700052+79162)/2	210737	Stefano Morozzi	04/2020
1038	(2^700052+304458)/2	210737	Stefano Morozzi	04/2020
1039	(2^700048+376578)/2	210736	Stefano Morozzi	04/2020
1040	11^202357-1140	210734	Enzo Doria	12/2012
1041	(2^700021+25874)/2	210728	Stefano Morozzi	04/2020
1042	(2^700018+377518)/2	210727	Stefano Morozzi	04/2020
1043	2^699740+25	210643	Stefano Morozzi	05/2021
1044	2^698929-2788423	210399	Enzo Doria	11/2015
1045	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
1046	2^698316+1878601	210215	Enzo Doria	08/2016
1047	2^697036+1878751	209829	Enzo Doria	08/2016
1048	6^269407+5	209640	Paul Bourdelais	02/2021
1049	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
1050	2^696254-115151	209594	Enzo Doria	06/2015
1051	(35^135623+1)/36	209410	Paul Bourdelais	07/2018
1052	2^694633+1887257	209106	Enzo Doria	05/2017
1053	2^693959+180923	208903	Enzo Doria	07/2016
1054	2^693462-1847561	208753	Enzo Doria	07/2015
1055	2^690890-59981	207979	Enzo Doria	11/2015
1056	(38^131591+1)/39	207884	Paul Bourdelais	07/2018
1057	2^690163+1877063	207760	Enzo Doria	07/2016
1058	7^245608-2	207563	Paul Bourdelais	01/2021
1059	2^689286-29381	207496	Enzo Doria	08/2015
1060	2^689122-114521	207447	Enzo Doria	04/2015
1061	2^688373+6077	207221	Enzo Doria	02/2016
1062	2^688201+1875527	207170	Enzo Doria	07/2016
1063	(42^127609+1)/43	207140	Paul Bourdelais	07/2018
1064	2^687619+81563	206994	Enzo Doria	08/2016
1065	2^686572-1845299	206679	Enzo Doria	07/2015
1066	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
1067	(2^685739+1)/(3*87774593)	206420	Gord Palameta	08/2018
1068	2^685578+3	206380	Paul Bourdelais	04/2012
1069	2^684836-49349	206157	Enzo Doria	10/2015
1070	(73^110603-1)/72	206088	Paul Bourdelais	06/2018
1071	2^684163-2790967	205954	Enzo Doria	12/2015
1072	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
1073	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
1074	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
1075	2^681545+467	205166	Lelio R Paula	11/2013
1076	2^681306+81049	205094	Enzo Doria	07/2016
1077	2^680697+1877057	204911	Enzo Doria	07/2016
1078	2^680415+71783	204826	Enzo Doria	04/2016
1079	2^679860-459995	204659	Enzo Doria	06/2015
1080	2^679593+1879547	204578	Enzo Doria	09/2016
1081	2^678651+1875023	204295	Enzo Doria	07/2016
1082	2^678561+678561	204268	Henri Lifchitz	05/2006
1083	2^678101-114043	204129	Enzo Doria	11/2014
1084	2^678028+1875631	204107	Enzo Doria	06/2016
1085	2^676992-59783	203795	Enzo Doria	10/2015
1086	2^676972+1866871	203789	Enzo Doria	03/2016
1087	2^676761-9	203726	Robert Price	01/2017
1088	2^676563-2792407	203666	Enzo Doria	02/2016
1089	2^676306-114713	203589	Enzo Doria	04/2015
1090	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
1091	10247^50678-50678^10247	203250	Norbert Schneider	03/2022
1092	2^674627-25161	203083	Enzo Doria	09/2013
1093	2^674603-69337	203076	Enzo Doria	12/2015
1094	2^674459+74213	203033	Enzo Doria	04/2016
1095	2^674116-458879	202930	Enzo Doria	04/2015
1096	2^674076-114755	202918	Enzo Doria	04/2015
1097	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
1098	(467617#+14534)/(2^21343)	202603	Makoto Morimoto	06/2019
1099	2^672556-1835519	202460	Enzo Doria	04/2015
1100	2^671446-351401	202126	Enzo Doria	07/2015
1101	2^671373+77747	202104	Enzo Doria	05/2016
1102	2^670726-114845	201909	Enzo Doria	05/2015
1103	2^670539-25045	201853	Enzo Doria	09/2013
1104	43284^43519-43519^43284	201769	Norbert Schneider	08/2018
1105	2^670213+282317	201755	Enzo Doria	09/2016
1106	2^670133+89	201731	Stefano Morozzi	05/2021
1107	2^669854-113501	201647	Enzo Doria	08/2014
1108	2^669718+81619	201606	Enzo Doria	08/2016
1109	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
1110	2^668938-1839821	201371	Enzo Doria	06/2015
1111	2^668492+1879303	201237	Enzo Doria	08/2016
1112	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
1113	10194^50161-50161^10194	201063	Norbert Schneider	09/2020
1114	2^667894+1875589	201057	Enzo Doria	06/2016
1115	2^667569-1836559	200959	Enzo Doria	05/2015
1116	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
1117	2^666430+782569	200616	Enzo Doria	10/2016
1118	(86^103471+1)/87	200163	Paul Bourdelais	05/2018
1119	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
1120	103(10^100000+33798)^2-4707(10^100000+33798)+50383	200003	Robert Price	01/2018
1121	numbpart(32235776596)	200002	Serge Batalov	04/2017
1122	(10^200001+149)/3	200001	Serge Batalov	12/2014
1123	10^200000+571791	200001	Patrick De Geest	08/2019
1124	(3^419180-621444)/3	200000	Stefano Morozzi	06/2019
1125	(3^419180-1941384)/3	200000	Stefano Morozzi	08/2019
1126	10^200000-45557	200000	Patrick De Geest	08/2019
1127	(10^200000-1)/9-10^58838	200000	Akihiko Yoshida	04/2020
1128	92*10^199980-9	199982	Robert Price	12/2021
1129	(85*10^199951-139)/9	199952	Robert Price	08/2021
1130	(10^199926+7)/29/373/2339	199919	Alfred Reich	08/2021
1131	23*10^199833-9	199835	Robert Price	10/2021
1132	(299*10^199801-17)/3	199803	Robert Price	04/2020
1133	6*10^199788+77	199789	Robert Price	06/2020
1134	(23*10^199615+37)/3	199616	Robert Price	02/2022
1135	(17*10^199607-167)/3	199608	Robert Price	05/2022
1136	2^663020-933075	199589	Paul Bourdelais	06/2021
1137	(14*10^199447+73)/3	199448	Robert Price	12/2018
1138	2^662103-29287	199313	Enzo Doria	08/2015
1139	(2*10^199283+457)/9	199283	Robert Price	01/2018
1140	(10^199248-19)/9	199248	Robert Price	01/2018
1141	(83*10^199213+529)/9	199214	Robert Price	12/2021
1142	(194*10^199146-17)/3	199148	Robert Price	09/2020
1143	(151*10^199003-1)/3	199005	Robert Price	03/2020
1144	9*10^198946-73	198947	Robert Price	01/2021
1145	45*10^198931-7	198933	Robert Price	07/2020
1146	2^660482-2891	198825	Yves Minet	05/2016
1147	2^659583+1879223	198555	Enzo Doria	08/2016
1148	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
1149	(49*10^198403+311)/9	198404	Robert Price	06/2019
1150	96*10^198376-7	198378	Robert Price	03/2021
1151	(10^198375+7)/59/1201/87589	198366	Alfred Reich	08/2021
1152	2^658828-29819	198327	Enzo Doria	08/2015
1153	2^658776-2791229	198312	Enzo Doria	01/2016
1154	(35*10^198294-377)/9	198295	Robert Price	07/2018
1155	(4*10^198268+137)/3	198269	Robert Price	03/2018
1156	2^658544-1854029	198242	Enzo Doria	09/2015
1157	(62*10^198229-233)/9	198230	Robert Price	02/2022
1158	(26*10^198200-41)/3	198201	Robert Price	02/2022
1159	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
1160	2*10^197959-37	197960	Robert Price	11/2021
1161	(232*10^197897+17)/3	197899	Robert Price	04/2021
1162	(4*10^197778+173)/3	197779	Robert Price	02/2018
1163	78*10^197702-7	197704	Robert Price	10/2020
1164	(17*10^197640-23)/3	197641	Robert Price	03/2021
1165	(29*10^197629-77)/3	197630	Robert Price	02/2020
1166	2^656462+1874419	197615	Enzo Doria	06/2016
1167	(89^101363+1)/90	197595	Paul Bourdelais	11/2017
1168	2^655893-344563	197444	Enzo Doria	07/2015
1169	2^655875+71333	197439	Enzo Doria	04/2016
1170	2^655845-9	197430	Robert Price	01/2017
1171	(299*10^197426+1)/3	197428	Robert Price	04/2020
1172	2^655682-1849121	197380	Enzo Doria	08/2015
1173	4*10^197268-89	197269	Robert Price	11/2018
1174	(11*10^197198-89)/3	197199	Robert Price	05/2021
1175	2^655045-49603	197189	Enzo Doria	10/2015
1176	2^655000-2784089	197175	Enzo Doria	10/2015
1177	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
1178	(154*10^197005+17)/9	197007	Robert Price	06/2022
1179	2^654400-39719	196995	Enzo Doria	09/2015
1180	(14*10^196965-221)/9	196966	Robert Price	04/2018
1181	2^654216-459995	196939	Enzo Doria	06/2015
1182	(17*10^196921+31)/3	196922	Robert Price	01/2019
1183	(14*10^196885-89)/3	196886	Robert Price	05/2020
1184	3*10^196881-59	196882	Robert Price	09/2018
1185	2^653851+82295	196829	Enzo Doria	09/2016
1186	(38*10^196792+691)/9	196793	Robert Price	10/2018
1187	(65*10^196768+493)/9	196769	Robert Price	08/2021
1188	2^653636-29429	196765	Enzo Doria	08/2015
1189	2^653601-69673	196754	Enzo Doria	02/2016
1190	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
1191	2^652786-1852571	196509	Enzo Doria	08/2015
1192	2^652752-1325	196498	Yves Minet	07/2015
1193	2^652470-1859141	196414	Enzo Doria	10/2015
1194	2^652307+1877483	196364	Enzo Doria	08/2016
1195	2^652293-115273	196360	Enzo Doria	06/2015
1196	(47*10^196281+403)/9	196282	Robert Price	03/2019
1197	(7*10^196125-31)/3	196126	Robert Price	12/2021
1198	6*10^196070+73	196071	Robert Price	04/2019
1199	2^651218-1868201	196037	Enzo Doria	04/2016
1200	2^651047-49687	195985	Enzo Doria	10/2015
1201	10^195968-700001	195968	Robert Price	08/2021
1202	(29*10^195875-197)/3	195876	Robert Price	08/2021
1203	(25*10^195808-97)/9	195809	Robert Price	01/2022
1204	2^650285-2785333	195756	Enzo Doria	10/2015
1205	(10^195732+7)/18089/49605893	195721	Alfred Reich	08/2021
1206	(69^106397-1)/68	195647	Paul Bourdelais	10/2017
1207	2^649811+1877573	195613	Enzo Doria	08/2016
1208	2^649662-170531	195568	Hans Havermann	10/2018
1209	2^649586+182839	195545	Enzo Doria	11/2016
1210	2^649537-1867363	195531	Enzo Doria	04/2016
1211	2^649536-1861499	195530	Enzo Doria	12/2015
1212	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
1213	2^649102-59351	195400	Enzo Doria	10/2015
1214	(2*10^195399+529)/9	195399	Robert Price	01/2018
1215	(202*10^195383-13)/9	195385	Robert Price	01/2020
1216	2^648988+1178971	195365	Enzo Doria	06/2016
1217	2^648975-114319	195361	Enzo Doria	02/2015
1218	(11*10^195350-137)/9	195351	Robert Price	01/2018
1219	2^648619-24835	195254	Enzo Doria	09/2013
1220	5*10^195250-21	195251	Robert Price	12/2021
1221	(14*10^195234-83)/3	195235	Robert Price	12/2018
1222	5*10^195221+81	195222	Robert Price	03/2019
1223	10^195143-5001	195143	Robert Price	12/2021
1224	2^648190-24737	195125	Enzo Doria	09/2013
1225	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
1226	(29*10^195098-197)/3	195099	Robert Price	08/2021
1227	10^195060+89701	195061	Patrick De Geest	02/2021
1229	10^195060-40000000001	195060	Robert Price	09/2020
1228	10^195060-110337	195060	Patrick De Geest	02/2021
1230	56*10^195032-3	195034	Robert Price	03/2020
1231	11^187185-90	194934	Enzo Doria	09/2012
1232	(86*10^194818-437)/9	194819	Robert Price	03/2021
1233	2^647068+77281	194787	Enzo Doria	05/2016
1234	2*10^194716-93	194717	Robert Price	12/2021
1235	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
1236	F(931517)	194676	Henri Lifchitz	09/2008
1237	4*10^194668+49	194669	Robert Price	01/2019
1238	2^646589+1179407	194643	Enzo Doria	06/2016
1239	2^646289-114621	194553	Enzo Doria	05/2015
1240	2^646236-39659	194537	Enzo Doria	09/2015
1241	(16*10^194536+53)/3	194537	Robert Price	03/2019
1242	2^646161-59833	194514	Enzo Doria	11/2015
1243	(17*10^194502+31)/3	194503	Robert Price	01/2019
1244	(19*10^194428+287)/9	194429	Robert Price	10/2021
1245	2*10^194413+3	194414	Robert Price	07/2015
1246	2^645360-1848599	194273	Enzo Doria	08/2015
1247	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
1248	2*10^193981-43	193982	Robert Price	04/2018
1249	2^644382+75169	193979	Enzo Doria	04/2016
1250	2^644304-1861409	193955	Enzo Doria	11/2015

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Probable Primes Top 10000

(290751 PRPs in the top)