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	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
1002	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
1004	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
1003	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
1005	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
1006	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
1007	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
1008	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
1009	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
1010	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
1011	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
1013	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
1012	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
1014	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
1015	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
1016	2^624077-112723	187866	Enzo Doria	07/2014
1017	2^624008+1874941	187846	Enzo Doria	06/2016
1018	2^623870+78679	187804	Enzo Doria	05/2016
1019	2^623714-114035	187757	Enzo Doria	11/2014
1020	2^623651-1834251	187738	Enzo Doria	07/2015
1021	(7*10^187645+53)/3	187646	Robert Price	05/2018
1022	2^623146+1879609	187586	Enzo Doria	09/2016
1023	(5*10^187471+91)/3	187472	Robert Price	04/2018
1024	2^622500+81931	187392	Enzo Doria	08/2016
1025	2^622300-1861739	187331	Enzo Doria	12/2015
1026	(38*10^187281+349)/9	187282	Robert Price	10/2018
1027	2^622052+76771	187257	Enzo Doria	05/2016
1028	2^622005-24091	187243	Enzo Doria	08/2013
1029	2^621879-351787	187205	Enzo Doria	07/2015
1030	(23*10^187164-143)/3	187165	Robert Price	12/2019
1031	2^621700+79411	187151	Enzo Doria	06/2016
1032	(2*10^187062-71)/3	187062	Robert Price	12/2017
1033	2^620929-113203	186919	Enzo Doria	07/2014
1034	10^186842+168223	186843	Patrick De Geest	07/2018
1035	10^186842-8001	186842	Robert Price	03/2018
1036	2^620347-1777	186744	Lelio R Paula	07/2013
1037	11^179143-4170	186559	Enzo Doria	12/2012
1038	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
1039	2^619297-2792353	186427	Enzo Doria	02/2016
1040	(49*10^186409+383)/9	186410	Robert Price	04/2019
1041	2^618940-460139	186320	Enzo Doria	06/2015
1042	2^618046+74179	186051	Enzo Doria	04/2016
1043	3*10^186019+11	186020	Robert Price	07/2018
1044	(16*10^185978-19)/3	185979	Robert Price	02/2019
1045	2*10^185930-3	185931	Robert Price	07/2015
1046	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
1047	4*10^185905+91	185906	Robert Price	08/2018
1048	(37*10^185811+377)/9	185812	Robert Price	11/2018
1049	2^617250+9385	185811	Lelio R Paula	07/2013
1050	39^116749+2	185756	Robert Price	04/2015
1051	2^616924-39719	185713	Enzo Doria	09/2015
1052	2^616712+1867621	185649	Enzo Doria	04/2016
1053	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
1054	8*10^185529-67	185530	Robert Price	08/2019
1055	4*10^185355+9	185356	Robert Price	05/2015
1056	2^615622+76639	185321	Enzo Doria	05/2016
1057	2^615591+1879223	185312	Enzo Doria	08/2016
1058	2^615503+1876643	185285	Enzo Doria	07/2016
1059	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
1060	(4*10^185221-91)/3	185222	Robert Price	03/2018
1061	2^614783-2790097	185069	Enzo Doria	12/2015
1062	2^614745-29323	185057	Enzo Doria	07/2015
1063	(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840	185052	Serge Batalov	07/2013
1064	(49*10^184993-67)/9	184994	Robert Price	03/2019
1065	(14*10^184950+211)/9	184951	Robert Price	04/2018
1066	2^614315+81353	184928	Enzo Doria	08/2016
1067	2^614294-1849961	184921	Enzo Doria	08/2015
1068	2^614266+1877809	184913	Enzo Doria	08/2016
1069	2^613715-1860727	184747	Enzo Doria	11/2015
1070	2*10^184723+41	184724	Robert Price	05/2018
1071	2^613487-349987	184678	Enzo Doria	07/2015
1072	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
1073	14^161089-161089^14	184629	Serge Batalov	05/2016
1074	2^613033-114621	184542	Enzo Doria	05/2015
1075	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
1076	2^612341-1604809	184334	Enzo Doria	05/2015
1077	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
1078	(14*10^184150+37)/3	184151	Robert Price	12/2018
1079	2^611731-4837	184150	Yves Minet	08/2018
1080	3*10^184124-7	184125	Robert Price	08/2015
1081	2^611628-24537	184119	Enzo Doria	08/2013
1082	3*10^184110+13	184111	Robert Price	07/2018
1083	2^611460+71881	184068	Enzo Doria	04/2016
1084	4*10^184004-63	184005	Robert Price	10/2018
1085	2^610982-1867301	183924	Enzo Doria	03/2016
1086	3*10^183872-49	183873	Robert Price	07/2018
1087	2^610597+1178897	183809	Enzo Doria	05/2016
1088	(17*10^183764+31)/3	183765	Robert Price	01/2019
1089	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
1090	2^610401+1277	183750	Lelio R Paula	07/2013
1091	2^610356-1849019	183736	Enzo Doria	08/2015
1092	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
1093	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
1094	(4*10^183659+149)/9	183659	Robert Price	04/2018
1095	2^609846-1834251	183582	Enzo Doria	07/2015
1096	11^176176-240	183469	Enzo Doria	11/2012
1097	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
1098	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
1099	2^608965-113989	183317	Enzo Doria	10/2014
1100	A005165(43592)	183312	Serge Batalov	07/2017
1101	(61*10^183294+119)/9	183295	Robert Price	05/2019
1102	2^608814-461261	183272	Enzo Doria	06/2015
1103	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
1104	2^608541-608541^2	183190	Henri Lifchitz	02/2018
1105	2^608293+143807	183115	Enzo Doria	10/2016
1106	2^608164-462419	183076	Enzo Doria	08/2015
1107	2^607950-1862303	183012	Enzo Doria	12/2015
1108	(46*10^182896+683)/9	182897	Robert Price	03/2019
1109	2^607101+1871987	182756	Enzo Doria	05/2016
1110	2^606869-69175	182686	Enzo Doria	11/2015
1111	3*10^182614-11	182615	Robert Price	07/2018
1112	2^606560-357	182593	Enzo Doria	05/2014
1113	2^605687+1866983	182330	Enzo Doria	03/2016
1114	2^605655-114445	182321	Enzo Doria	02/2015
1115	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
1116	(14*10^182177-221)/9	182178	Robert Price	04/2018
1117	2^605174-112751	182176	Enzo Doria	06/2014
1118	2^604761+1874507	182052	Enzo Doria	06/2016
1119	2^604705+1871957	182035	Enzo Doria	05/2016
1120	(14*10^182000+229)/9	182001	Robert Price	03/2018
1121	(10^181996+41)/3	181996	Robert Price	12/2017
1122	(5*10^181950-101)/3	181951	Robert Price	04/2018
1123	2^603915+75233	181797	Enzo Doria	04/2016
1124	11^174145-360	181354	Enzo Doria	10/2012
1125	2^602351-396765	181326	Enzo Doria	08/2013
1126	6*10^181306+17	181307	Robert Price	04/2019
1127	2^601957-113833	181208	Enzo Doria	09/2014
1128	66^99581-65^99581	181193	Robert Price	09/2013
1129	10^181182+383973	181183	Patrick De Geest	04/2016
1130	10^181182-21	181182	Serge Batalov	12/2014
1131	(5*10^181127-29)/3	181128	Robert Price	03/2018
1132	2^601521-29143	181076	Enzo Doria	07/2015
1133	2^601442-2797811	181053	Enzo Doria	04/2016
1134	5*10^180992-9	180993	Robert Price	05/2015
1135	10^180979+79477	180980	Patrick De Geest	04/2016
1136	10^180979+107739	180980	Patrick De Geest	04/2016
1137	10^180979-11	180979	Serge Batalov	12/2014
1138	2^601023-113851	180926	Enzo Doria	10/2014
1139	(23*10^180862-143)/3	180863	Robert Price	12/2019
1140	3*10^180852+29	180853	Robert Price	05/2018
1141	2^600300-1852559	180709	Enzo Doria	08/2015
1142	(10^180689+71)/9	180689	Serge Batalov	07/2015
1143	2^600209+76487	180681	Enzo Doria	05/2016
1144	2^599702-369885	180529	Enzo Doria	11/2013
1145	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
1146	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
1147	(29*10^180432-17)/3	180433	Robert Price	09/2019
1148	4*10^180360+93	180361	Robert Price	08/2018
1149	2^598942+80779	180300	Enzo Doria	07/2016
1150	(38*10^180296+403)/9	180297	Robert Price	10/2018
1151	2^598591-1844797	180194	Enzo Doria	06/2015
1152	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
1153	6*10^179970+91	179971	Robert Price	05/2019
1154	(4*10^179963-79)/3	179964	Robert Price	02/2018
1155	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
1156	2^597424-1859729	179843	Enzo Doria	11/2015
1157	Phi(180683,10)	179760	Maksym Voznyy	09/2015
1158	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
1159	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
1160	(29*10^179697+223)/9	179698	Robert Price	09/2018
1161	(68*10^179656+7)/3	179658	Robert Price	01/2020
1162	2^596690-461261	179622	Enzo Doria	07/2015
1163	2^596684-113939	179620	Enzo Doria	10/2014
1164	2*10^179602+63	179603	Robert Price	05/2018
1165	3^375887-112696	179344	Enzo Doria	07/2014
1166	4*10^179265-71	179266	Robert Price	12/2018
1167	2^595144-1850429	179157	Enzo Doria	08/2015
1168	3*10^179138+89	179139	Robert Price	10/2018
1169	2^594531+82253	178972	Enzo Doria	09/2016
1170	2^594260-2787899	178891	Enzo Doria	11/2015
1171	2^593631+101381	178701	Jorge Menendez	04/2018
1172	10^178695+136719	178696	Patrick De Geest	05/2016
1173	10^178695-71	178695	Serge Batalov	12/2014
1174	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
1175	2^593222-14145	178578	Jorge Menendez	10/2017
1176	2^593178+1867219	178565	Enzo Doria	03/2016
1177	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
1178	(5*10^178206+91)/3	178207	Robert Price	04/2018
1179	2^591872-291929	178172	Enzo Doria	07/2015
1180	2^591682-286871	178115	Enzo Doria	07/2015
1181	4*10^178091+9	178092	Robert Price	05/2015
1182	410747#+478483	178007	Makoto Morimoto	02/2016
1183	3*10^177872+73	177873	Robert Price	08/2018
1184	2^590762-396765	177838	Enzo Doria	08/2013
1185	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
1186	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
1187	(11*10^177466-113)/3	177467	Robert Price	10/2018
1188	3*10^177373-97	177374	Robert Price	07/2018
1189	2^589204+1881151	177369	Enzo Doria	11/2016
1190	2^589132-69479	177347	Enzo Doria	01/2016
1191	2^588912-113519	177281	Enzo Doria	08/2014
1192	15^150706+2	177245	Robert Price	06/2015
1193	2^588194-1861001	177065	Enzo Doria	11/2015
1194	(23*10^176964-47)/3	176965	Robert Price	09/2019
1195	(19*10^176932+521)/9	176933	Robert Price	05/2018
1196	(8*10^176908+43)/3	176909	Robert Price	06/2018
1197	2^587560-113699	176874	Enzo Doria	09/2014
1198	(25*10^176715-37)/3	176716	Robert Price	10/2019
1199	5^252763-12862	176674	Enzo Doria	05/2014
1200	2^586804+81721	176646	Enzo Doria	08/2016
1201	(10^176584+77)/3	176584	Robert Price	01/2018
1202	2^586570+1874419	176576	Enzo Doria	06/2016
1203	2^585994-3311	176402	Yves Minet	12/2014
1204	2^585832-112799	176354	Enzo Doria	07/2014
1205	2^585336-461039	176204	Enzo Doria	06/2015
1206	2^585095-1848127	176132	Enzo Doria	08/2015
1207	2^584950-115451	176088	Enzo Doria	07/2015
1208	2^584671-3697	176004	Yves Minet	03/2017
1209	(13*10^175965-37)/3	175966	Robert Price	01/2019
1210	2*10^175860-87	175861	Robert Price	04/2018
1211	(86*10^175774-221)/9	175775	Robert Price	09/2019
1212	10^175608+2971	175609	Mike Oakes	05/2010
1213	10^175608-55829	175608	Patrick De Geest	09/2013
1214	2^583051+1879793	175516	Enzo Doria	09/2016
1215	2^582860-23829	175459	Enzo Doria	08/2013
1216	2^582670-23913	175402	Enzo Doria	08/2013
1217	2^582573-29563	175372	Enzo Doria	08/2015
1218	2^582435-1862767	175331	Enzo Doria	12/2015
1219	(11*10^175250-149)/3	175251	Robert Price	09/2018
1220	2^582072-1848599	175222	Enzo Doria	08/2015
1221	(404267#+465)/(3^45^231)	175208	Makoto Morimoto	06/2019
1222	(220221^32768+1)/2	175075	Serge Batalov	03/2018
1223	2^581560+1874911	175068	Enzo Doria	06/2016
1224	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
1225	(47*10^174790+493)/9	174791	Robert Price	03/2019
1226	2^580528-114035	174757	Enzo Doria	11/2014
1227	(19*10^174754+737)/9	174755	Robert Price	07/2018
1228	(35*10^174704-377)/9	174705	Robert Price	07/2018
1229	3*10^174665-97	174666	Robert Price	07/2018
1230	2^580046-459161	174612	Enzo Doria	05/2015
1231	2^579992-39779	174595	Enzo Doria	09/2015
1232	(2*10^174301-71)/3	174301	Robert Price	12/2017
1233	(2^578696+1)/257	174203	Lelio R Paula	09/2015
1234	2^578656-1851809	174193	Enzo Doria	08/2015
1235	2^578583-113917	174171	Enzo Doria	10/2014
1236	2^578434-83	174126	Yves Minet	07/2017
1237	15^148048-2	174118	Robert Price	06/2015
1238	5*10^174101+81	174102	Robert Price	03/2019
1239	2^578346+2794249	174100	Enzo Doria	03/2016
1240	5*10^173904-13	173905	Robert Price	01/2019
1241	(71*10^173854-287)/9	173855	Robert Price	09/2019
1242	(43*10^173826+101)/9	173827	Robert Price	11/2018
1243	2*10^173809-87	173810	Robert Price	04/2018
1244	(L!41532)/2	173772	Serge Batalov	07/2017
1245	2^577146-49877	173739	Enzo Doria	10/2015
1246	2^576889+49727	173661	Enzo Doria	09/2016
1247	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
1248	(13*10^173467-37)/3	173468	Robert Price	01/2019
1249	2^576016-113919	173399	Enzo Doria	11/2014
1250	2^575911-1849387	173367	Enzo Doria	08/2015

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Probable Primes Top 10000

(258084 PRPs in the top)