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	(7*10^187645+53)/3	187646	Robert Price	05/2018
1002	2^623146+1879609	187586	Enzo Doria	09/2016
1003	(5*10^187471+91)/3	187472	Robert Price	04/2018
1004	2^622500+81931	187392	Enzo Doria	08/2016
1005	2^622300-1861739	187331	Enzo Doria	12/2015
1006	(38*10^187281+349)/9	187282	Robert Price	10/2018
1007	2^622052+76771	187257	Enzo Doria	05/2016
1008	2^622005-24091	187243	Enzo Doria	08/2013
1009	2^621879-351787	187205	Enzo Doria	07/2015
1010	2^621700+79411	187151	Enzo Doria	06/2016
1011	(2*10^187062-71)/3	187062	Robert Price	12/2017
1012	2^620929-113203	186919	Enzo Doria	07/2014
1013	10^186842+168223	186843	Patrick De Geest	07/2018
1014	10^186842-8001	186842	Robert Price	03/2018
1015	2^620347-1777	186744	Lelio R Paula	07/2013
1016	11^179143-4170	186559	Enzo Doria	12/2012
1017	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
1018	2^619297-2792353	186427	Enzo Doria	02/2016
1019	(49*10^186409+383)/9	186410	Robert Price	04/2019
1020	2^618940-460139	186320	Enzo Doria	06/2015
1021	2^618046+74179	186051	Enzo Doria	04/2016
1022	3*10^186019+11	186020	Robert Price	07/2018
1023	(16*10^185978-19)/3	185979	Robert Price	02/2019
1024	2*10^185930-3	185931	Robert Price	07/2015
1025	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
1026	4*10^185905+91	185906	Robert Price	08/2018
1027	(37*10^185811+377)/9	185812	Robert Price	11/2018
1028	2^617250+9385	185811	Lelio R Paula	07/2013
1029	39^116749+2	185756	Robert Price	04/2015
1030	2^616924-39719	185713	Enzo Doria	09/2015
1031	2^616712+1867621	185649	Enzo Doria	04/2016
1032	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
1033	8*10^185529-67	185530	Robert Price	08/2019
1034	4*10^185355+9	185356	Robert Price	05/2015
1035	2^615622+76639	185321	Enzo Doria	05/2016
1036	2^615591+1879223	185312	Enzo Doria	08/2016
1037	2^615503+1876643	185285	Enzo Doria	07/2016
1038	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
1039	(4*10^185221-91)/3	185222	Robert Price	03/2018
1040	2^614783-2790097	185069	Enzo Doria	12/2015
1041	2^614745-29323	185057	Enzo Doria	07/2015
1042	(((((((((((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
1043	(49*10^184993-67)/9	184994	Robert Price	03/2019
1044	(14*10^184950+211)/9	184951	Robert Price	04/2018
1045	2^614315+81353	184928	Enzo Doria	08/2016
1046	2^614294-1849961	184921	Enzo Doria	08/2015
1047	2^614266+1877809	184913	Enzo Doria	08/2016
1048	2^613715-1860727	184747	Enzo Doria	11/2015
1049	2*10^184723+41	184724	Robert Price	05/2018
1050	2^613487-349987	184678	Enzo Doria	07/2015
1051	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
1052	14^161089-161089^14	184629	Serge Batalov	05/2016
1053	2^613033-114621	184542	Enzo Doria	05/2015
1054	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
1055	2^612341-1604809	184334	Enzo Doria	05/2015
1056	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
1057	(14*10^184150+37)/3	184151	Robert Price	12/2018
1058	2^611731-4837	184150	Yves Minet	08/2018
1059	3*10^184124-7	184125	Robert Price	08/2015
1060	2^611628-24537	184119	Enzo Doria	08/2013
1061	3*10^184110+13	184111	Robert Price	07/2018
1062	2^611460+71881	184068	Enzo Doria	04/2016
1063	4*10^184004-63	184005	Robert Price	10/2018
1064	2^610982-1867301	183924	Enzo Doria	03/2016
1065	3*10^183872-49	183873	Robert Price	07/2018
1066	2^610597+1178897	183809	Enzo Doria	05/2016
1067	(17*10^183764+31)/3	183765	Robert Price	01/2019
1068	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
1069	2^610401+1277	183750	Lelio R Paula	07/2013
1070	2^610356-1849019	183736	Enzo Doria	08/2015
1071	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
1072	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
1073	(4*10^183659+149)/9	183659	Robert Price	04/2018
1074	2^609846-1834251	183582	Enzo Doria	07/2015
1075	11^176176-240	183469	Enzo Doria	11/2012
1076	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
1077	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
1078	2^608965-113989	183317	Enzo Doria	10/2014
1079	A005165(43592)	183312	Serge Batalov	07/2017
1080	(61*10^183294+119)/9	183295	Robert Price	05/2019
1081	2^608814-461261	183272	Enzo Doria	06/2015
1082	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
1083	2^608541-608541^2	183190	Henri Lifchitz	02/2018
1084	2^608293+143807	183115	Enzo Doria	10/2016
1085	2^608164-462419	183076	Enzo Doria	08/2015
1086	2^607950-1862303	183012	Enzo Doria	12/2015
1087	(46*10^182896+683)/9	182897	Robert Price	03/2019
1088	2^607101+1871987	182756	Enzo Doria	05/2016
1089	2^606869-69175	182686	Enzo Doria	11/2015
1090	3*10^182614-11	182615	Robert Price	07/2018
1091	2^606560-357	182593	Enzo Doria	05/2014
1092	2^605687+1866983	182330	Enzo Doria	03/2016
1093	2^605655-114445	182321	Enzo Doria	02/2015
1094	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
1095	(14*10^182177-221)/9	182178	Robert Price	04/2018
1096	2^605174-112751	182176	Enzo Doria	06/2014
1097	2^604761+1874507	182052	Enzo Doria	06/2016
1098	2^604705+1871957	182035	Enzo Doria	05/2016
1099	(14*10^182000+229)/9	182001	Robert Price	03/2018
1100	(10^181996+41)/3	181996	Robert Price	12/2017
1101	(5*10^181950-101)/3	181951	Robert Price	04/2018
1102	2^603915+75233	181797	Enzo Doria	04/2016
1103	11^174145-360	181354	Enzo Doria	10/2012
1104	2^602351-396765	181326	Enzo Doria	08/2013
1105	6*10^181306+17	181307	Robert Price	04/2019
1106	2^601957-113833	181208	Enzo Doria	09/2014
1107	66^99581-65^99581	181193	Robert Price	09/2013
1108	10^181182+383973	181183	Patrick De Geest	04/2016
1109	10^181182-21	181182	Serge Batalov	12/2014
1110	(5*10^181127-29)/3	181128	Robert Price	03/2018
1111	2^601521-29143	181076	Enzo Doria	07/2015
1112	2^601442-2797811	181053	Enzo Doria	04/2016
1113	5*10^180992-9	180993	Robert Price	05/2015
1114	10^180979+79477	180980	Patrick De Geest	04/2016
1115	10^180979+107739	180980	Patrick De Geest	04/2016
1116	10^180979-11	180979	Serge Batalov	12/2014
1117	2^601023-113851	180926	Enzo Doria	10/2014
1118	3*10^180852+29	180853	Robert Price	05/2018
1119	2^600300-1852559	180709	Enzo Doria	08/2015
1120	(10^180689+71)/9	180689	Serge Batalov	07/2015
1121	2^600209+76487	180681	Enzo Doria	05/2016
1122	2^599702-369885	180529	Enzo Doria	11/2013
1123	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
1124	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
1125	(29*10^180432-17)/3	180433	Robert Price	09/2019
1126	4*10^180360+93	180361	Robert Price	08/2018
1127	2^598942+80779	180300	Enzo Doria	07/2016
1128	(38*10^180296+403)/9	180297	Robert Price	10/2018
1129	2^598591-1844797	180194	Enzo Doria	06/2015
1130	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
1131	6*10^179970+91	179971	Robert Price	05/2019
1132	(4*10^179963-79)/3	179964	Robert Price	02/2018
1133	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
1134	2^597424-1859729	179843	Enzo Doria	11/2015
1135	Phi(180683,10)	179760	Maksym Voznyy	09/2015
1136	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
1137	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
1138	(29*10^179697+223)/9	179698	Robert Price	09/2018
1139	2^596690-461261	179622	Enzo Doria	07/2015
1140	2^596684-113939	179620	Enzo Doria	10/2014
1141	2*10^179602+63	179603	Robert Price	05/2018
1142	3^375887-112696	179344	Enzo Doria	07/2014
1143	4*10^179265-71	179266	Robert Price	12/2018
1144	2^595144-1850429	179157	Enzo Doria	08/2015
1145	3*10^179138+89	179139	Robert Price	10/2018
1146	2^594531+82253	178972	Enzo Doria	09/2016
1147	2^594260-2787899	178891	Enzo Doria	11/2015
1148	2^593631+101381	178701	Jorge Menendez	04/2018
1149	10^178695+136719	178696	Patrick De Geest	05/2016
1150	10^178695-71	178695	Serge Batalov	12/2014
1151	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
1152	2^593222-14145	178578	Jorge Menendez	10/2017
1153	2^593178+1867219	178565	Enzo Doria	03/2016
1154	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
1155	(5*10^178206+91)/3	178207	Robert Price	04/2018
1156	2^591872-291929	178172	Enzo Doria	07/2015
1157	2^591682-286871	178115	Enzo Doria	07/2015
1158	4*10^178091+9	178092	Robert Price	05/2015
1159	410747#+478483	178007	Makoto Morimoto	02/2016
1160	3*10^177872+73	177873	Robert Price	08/2018
1161	2^590762-396765	177838	Enzo Doria	08/2013
1162	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
1163	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
1164	(11*10^177466-113)/3	177467	Robert Price	10/2018
1165	3*10^177373-97	177374	Robert Price	07/2018
1166	2^589204+1881151	177369	Enzo Doria	11/2016
1167	2^589132-69479	177347	Enzo Doria	01/2016
1168	2^588912-113519	177281	Enzo Doria	08/2014
1169	15^150706+2	177245	Robert Price	06/2015
1170	2^588194-1861001	177065	Enzo Doria	11/2015
1171	(19*10^176932+521)/9	176933	Robert Price	05/2018
1172	(8*10^176908+43)/3	176909	Robert Price	06/2018
1173	2^587560-113699	176874	Enzo Doria	09/2014
1174	5^252763-12862	176674	Enzo Doria	05/2014
1175	2^586804+81721	176646	Enzo Doria	08/2016
1176	(10^176584+77)/3	176584	Robert Price	01/2018
1177	2^586570+1874419	176576	Enzo Doria	06/2016
1178	2^585994-3311	176402	Yves Minet	12/2014
1179	2^585832-112799	176354	Enzo Doria	07/2014
1180	2^585336-461039	176204	Enzo Doria	06/2015
1181	2^585095-1848127	176132	Enzo Doria	08/2015
1182	2^584950-115451	176088	Enzo Doria	07/2015
1183	2^584671-3697	176004	Yves Minet	03/2017
1184	(13*10^175965-37)/3	175966	Robert Price	01/2019
1185	2*10^175860-87	175861	Robert Price	04/2018
1186	(86*10^175774-221)/9	175775	Robert Price	09/2019
1187	10^175608+2971	175609	Mike Oakes	05/2010
1188	10^175608-55829	175608	Patrick De Geest	09/2013
1189	2^583051+1879793	175516	Enzo Doria	09/2016
1190	2^582860-23829	175459	Enzo Doria	08/2013
1191	2^582670-23913	175402	Enzo Doria	08/2013
1192	2^582573-29563	175372	Enzo Doria	08/2015
1193	2^582435-1862767	175331	Enzo Doria	12/2015
1194	(11*10^175250-149)/3	175251	Robert Price	09/2018
1195	2^582072-1848599	175222	Enzo Doria	08/2015
1196	(404267#+465)/(3^45^231)	175208	Makoto Morimoto	06/2019
1197	(220221^32768+1)/2	175075	Serge Batalov	03/2018
1198	2^581560+1874911	175068	Enzo Doria	06/2016
1199	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
1200	(47*10^174790+493)/9	174791	Robert Price	03/2019
1201	2^580528-114035	174757	Enzo Doria	11/2014
1202	(19*10^174754+737)/9	174755	Robert Price	07/2018
1203	(35*10^174704-377)/9	174705	Robert Price	07/2018
1204	3*10^174665-97	174666	Robert Price	07/2018
1205	2^580046-459161	174612	Enzo Doria	05/2015
1206	2^579992-39779	174595	Enzo Doria	09/2015
1207	(2*10^174301-71)/3	174301	Robert Price	12/2017
1208	(2^578696+1)/257	174203	Lelio R Paula	09/2015
1209	2^578656-1851809	174193	Enzo Doria	08/2015
1210	2^578583-113917	174171	Enzo Doria	10/2014
1211	2^578434-83	174126	Yves Minet	07/2017
1212	15^148048-2	174118	Robert Price	06/2015
1213	5*10^174101+81	174102	Robert Price	03/2019
1214	2^578346+2794249	174100	Enzo Doria	03/2016
1215	5*10^173904-13	173905	Robert Price	01/2019
1216	(71*10^173854-287)/9	173855	Robert Price	09/2019
1217	(43*10^173826+101)/9	173827	Robert Price	11/2018
1218	2*10^173809-87	173810	Robert Price	04/2018
1219	(L!41532)/2	173772	Serge Batalov	07/2017
1220	2^577146-49877	173739	Enzo Doria	10/2015
1221	2^576889+49727	173661	Enzo Doria	09/2016
1222	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
1223	(13*10^173467-37)/3	173468	Robert Price	01/2019
1224	2^576016-113919	173399	Enzo Doria	11/2014
1225	2^575911-1849387	173367	Enzo Doria	08/2015
1226	(16*10^173251+107)/3	173252	Robert Price	03/2019
1227	2^575196-114053	173152	Enzo Doria	11/2014
1228	2^574591-115387	172970	Enzo Doria	07/2015
1229	2^574328+81121	172890	Enzo Doria	07/2016
1230	(115*10^172862-1)/3	172864	Serge Batalov	12/2014
1231	3*10^172812+13	172813	Robert Price	07/2018
1232	4*5^247217-9	172798	Lelio R Paula	10/2015
1233	69061#+(467617#)/(69061#)	172766	Makoto Morimoto	10/2017
1234	5*10^172692+57	172693	Robert Price	12/2018
1235	2^573668-2782319	172692	Enzo Doria	09/2015
1236	2^573444-1855109	172624	Enzo Doria	09/2015
1237	3^361608+2	172531	Robert Price	08/2014
1238	(54^99563+1)/55	172481	Paul Bourdelais	11/2017
1239	2^572592-114893	172368	Enzo Doria	05/2015
1240	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
1241	(38^109037-1)/37	172254	Paul Bourdelais	10/2017
1242	3*10^172219+73	172220	Robert Price	08/2018
1243	(36^110503+1)/37	171975	Lelio R Paula	04/2017
1244	(22*10^171929-73)/3	171930	Robert Price	04/2019
1245	4*10^171891-63	171892	Robert Price	10/2018
1246	2^570980-2782289	171883	Enzo Doria	09/2015
1247	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
1248	7*10^171535-99	171536	Robert Price	06/2019
1249	2^569563-1854607	171456	Enzo Doria	09/2015
1250	3*10^171391+59	171392	Robert Price	08/2018

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Probable Primes Top 10000

(253538 PRPs in the top)