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	2^610982-1867301	183924	Enzo Doria	03/2016
1002	3*10^183872-49	183873	Robert Price	07/2018
1003	2^610597+1178897	183809	Enzo Doria	05/2016
1004	(17*10^183764+31)/3	183765	Robert Price	01/2019
1005	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
1006	2^610401+1277	183750	Lelio R Paula	07/2013
1007	2^610356-1849019	183736	Enzo Doria	08/2015
1008	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
1009	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
1010	(4*10^183659+149)/9	183659	Robert Price	04/2018
1011	2^609846-1834251	183582	Enzo Doria	07/2015
1012	11^176176-240	183469	Enzo Doria	11/2012
1013	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
1014	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
1015	2^608965-113989	183317	Enzo Doria	10/2014
1016	A005165(43592)	183312	Serge Batalov	07/2017
1017	2^608814-461261	183272	Enzo Doria	06/2015
1018	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
1019	2^608541-608541^2	183190	Henri Lifchitz	02/2018
1020	2^608293+143807	183115	Enzo Doria	10/2016
1021	2^608164-462419	183076	Enzo Doria	08/2015
1022	2^607950-1862303	183012	Enzo Doria	12/2015
1023	2^607101+1871987	182756	Enzo Doria	05/2016
1024	2^606869-69175	182686	Enzo Doria	11/2015
1025	3*10^182614-11	182615	Robert Price	07/2018
1026	2^606560-357	182593	Enzo Doria	05/2014
1027	2^605687+1866983	182330	Enzo Doria	03/2016
1028	2^605655-114445	182321	Enzo Doria	02/2015
1029	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
1030	(14*10^182177-221)/9	182178	Robert Price	04/2018
1031	2^605174-112751	182176	Enzo Doria	06/2014
1032	2^604761+1874507	182052	Enzo Doria	06/2016
1033	2^604705+1871957	182035	Enzo Doria	05/2016
1034	(14*10^182000+229)/9	182001	Robert Price	03/2018
1035	(10^181996+41)/3	181996	Robert Price	12/2017
1036	(5*10^181950-101)/3	181951	Robert Price	04/2018
1037	2^603915+75233	181797	Enzo Doria	04/2016
1038	11^174145-360	181354	Enzo Doria	10/2012
1039	2^602351-396765	181326	Enzo Doria	08/2013
1040	2^601957-113833	181208	Enzo Doria	09/2014
1041	66^99581-65^99581	181193	Robert Price	09/2013
1042	10^181182+383973	181183	Patrick De Geest	04/2016
1043	10^181182-21	181182	Serge Batalov	12/2014
1044	(5*10^181127-29)/3	181128	Robert Price	03/2018
1045	2^601521-29143	181076	Enzo Doria	07/2015
1046	2^601442-2797811	181053	Enzo Doria	04/2016
1047	5*10^180992-9	180993	Robert Price	05/2015
1048	10^180979+79477	180980	Patrick De Geest	04/2016
1049	10^180979+107739	180980	Patrick De Geest	04/2016
1050	10^180979-11	180979	Serge Batalov	12/2014
1051	2^601023-113851	180926	Enzo Doria	10/2014
1052	3*10^180852+29	180853	Robert Price	05/2018
1053	2^600300-1852559	180709	Enzo Doria	08/2015
1054	(10^180689+71)/9	180689	Serge Batalov	07/2015
1055	2^600209+76487	180681	Enzo Doria	05/2016
1056	2^599702-369885	180529	Enzo Doria	11/2013
1057	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
1058	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
1059	4*10^180360+93	180361	Robert Price	08/2018
1060	2^598942+80779	180300	Enzo Doria	07/2016
1061	(38*10^180296+403)/9	180297	Robert Price	10/2018
1062	2^598591-1844797	180194	Enzo Doria	06/2015
1063	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
1064	(4*10^179963-79)/3	179964	Robert Price	02/2018
1065	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
1066	2^597424-1859729	179843	Enzo Doria	11/2015
1067	Phi(180683,10)	179760	Maksym Voznyy	09/2015
1068	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
1069	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
1070	(29*10^179697+223)/9	179698	Robert Price	09/2018
1071	2^596690-461261	179622	Enzo Doria	07/2015
1072	2^596684-113939	179620	Enzo Doria	10/2014
1073	2*10^179602+63	179603	Robert Price	05/2018
1074	3^375887-112696	179344	Enzo Doria	07/2014
1075	4*10^179265-71	179266	Robert Price	12/2018
1076	2^595144-1850429	179157	Enzo Doria	08/2015
1077	3*10^179138+89	179139	Robert Price	10/2018
1078	2^594531+82253	178972	Enzo Doria	09/2016
1079	2^594260-2787899	178891	Enzo Doria	11/2015
1080	2^593631+101381	178701	Jorge Menendez	04/2018
1081	10^178695+136719	178696	Patrick De Geest	05/2016
1082	10^178695-71	178695	Serge Batalov	12/2014
1083	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
1084	2^593222-14145	178578	Jorge Menendez	10/2017
1085	2^593178+1867219	178565	Enzo Doria	03/2016
1086	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
1087	(5*10^178206+91)/3	178207	Robert Price	04/2018
1088	2^591872-291929	178172	Enzo Doria	07/2015
1089	2^591682-286871	178115	Enzo Doria	07/2015
1090	4*10^178091+9	178092	Robert Price	05/2015
1091	410747#+478483	178007	Makoto Morimoto	02/2016
1092	3*10^177872+73	177873	Robert Price	08/2018
1093	2^590762-396765	177838	Enzo Doria	08/2013
1094	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
1095	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
1096	(11*10^177466-113)/3	177467	Robert Price	10/2018
1097	3*10^177373-97	177374	Robert Price	07/2018
1098	2^589204+1881151	177369	Enzo Doria	11/2016
1099	2^589132-69479	177347	Enzo Doria	01/2016
1100	2^588912-113519	177281	Enzo Doria	08/2014
1101	15^150706+2	177245	Robert Price	06/2015
1102	2^588194-1861001	177065	Enzo Doria	11/2015
1103	(19*10^176932+521)/9	176933	Robert Price	05/2018
1104	(8*10^176908+43)/3	176909	Robert Price	06/2018
1105	2^587560-113699	176874	Enzo Doria	09/2014
1106	5^252763-12862	176674	Enzo Doria	05/2014
1107	2^586804+81721	176646	Enzo Doria	08/2016
1108	(10^176584+77)/3	176584	Robert Price	01/2018
1109	2^586570+1874419	176576	Enzo Doria	06/2016
1110	2^585994-3311	176402	Yves Minet	12/2014
1111	2^585832-112799	176354	Enzo Doria	07/2014
1112	2^585336-461039	176204	Enzo Doria	06/2015
1113	2^585095-1848127	176132	Enzo Doria	08/2015
1114	2^584950-115451	176088	Enzo Doria	07/2015
1115	2^584671-3697	176004	Yves Minet	03/2017
1116	(13*10^175965-37)/3	175966	Robert Price	01/2019
1117	2*10^175860-87	175861	Robert Price	04/2018
1118	10^175608+2971	175609	Mike Oakes	05/2010
1119	10^175608-55829	175608	Patrick De Geest	09/2013
1120	2^583051+1879793	175516	Enzo Doria	09/2016
1121	2^582860-23829	175459	Enzo Doria	08/2013
1122	2^582670-23913	175402	Enzo Doria	08/2013
1123	2^582573-29563	175372	Enzo Doria	08/2015
1124	2^582435-1862767	175331	Enzo Doria	12/2015
1125	(11*10^175250-149)/3	175251	Robert Price	09/2018
1126	2^582072-1848599	175222	Enzo Doria	08/2015
1127	(220221^32768+1)/2	175075	Serge Batalov	03/2018
1128	2^581560+1874911	175068	Enzo Doria	06/2016
1129	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
1130	2^580528-114035	174757	Enzo Doria	11/2014
1131	(19*10^174754+737)/9	174755	Robert Price	07/2018
1132	(35*10^174704-377)/9	174705	Robert Price	07/2018
1133	3*10^174665-97	174666	Robert Price	07/2018
1134	2^580046-459161	174612	Enzo Doria	05/2015
1135	2^579992-39779	174595	Enzo Doria	09/2015
1136	(2*10^174301-71)/3	174301	Robert Price	12/2017
1137	(2^578696+1)/257	174203	Lelio R Paula	09/2015
1138	2^578656-1851809	174193	Enzo Doria	08/2015
1139	2^578583-113917	174171	Enzo Doria	10/2014
1140	2^578434-83	174126	Yves Minet	07/2017
1141	15^148048-2	174118	Robert Price	06/2015
1142	5*10^174101+81	174102	Robert Price	03/2019
1143	2^578346+2794249	174100	Enzo Doria	03/2016
1144	5*10^173904-13	173905	Robert Price	01/2019
1145	(43*10^173826+101)/9	173827	Robert Price	11/2018
1146	2*10^173809-87	173810	Robert Price	04/2018
1147	(L!41532)/2	173772	Serge Batalov	07/2017
1148	2^577146-49877	173739	Enzo Doria	10/2015
1149	2^576889+49727	173661	Enzo Doria	09/2016
1150	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
1151	(13*10^173467-37)/3	173468	Robert Price	01/2019
1152	2^576016-113919	173399	Enzo Doria	11/2014
1153	2^575911-1849387	173367	Enzo Doria	08/2015
1154	(16*10^173251+107)/3	173252	Robert Price	03/2019
1155	2^575196-114053	173152	Enzo Doria	11/2014
1156	2^574591-115387	172970	Enzo Doria	07/2015
1157	2^574328+81121	172890	Enzo Doria	07/2016
1158	(115*10^172862-1)/3	172864	Serge Batalov	12/2014
1159	3*10^172812+13	172813	Robert Price	07/2018
1160	4*5^247217-9	172798	Lelio R Paula	10/2015
1161	69061#+(467617#)/(69061#)	172766	Makoto Morimoto	10/2017
1162	5*10^172692+57	172693	Robert Price	12/2018
1163	2^573668-2782319	172692	Enzo Doria	09/2015
1164	2^573444-1855109	172624	Enzo Doria	09/2015
1165	3^361608+2	172531	Robert Price	08/2014
1166	(54^99563+1)/55	172481	Paul Bourdelais	11/2017
1167	2^572592-114893	172368	Enzo Doria	05/2015
1168	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
1169	(38^109037-1)/37	172254	Paul Bourdelais	10/2017
1170	3*10^172219+73	172220	Robert Price	08/2018
1171	(36^110503+1)/37	171975	Lelio R Paula	04/2017
1172	4*10^171891-63	171892	Robert Price	10/2018
1173	2^570980-2782289	171883	Enzo Doria	09/2015
1174	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
1175	2^569563-1854607	171456	Enzo Doria	09/2015
1176	3*10^171391+59	171392	Robert Price	08/2018
1177	(13*10^171306-37)/3	171307	Robert Price	01/2019
1178	(55^98419-1)/54	171284	Paul Bourdelais	12/2017
1179	2^568642+1876129	171179	Enzo Doria	07/2016
1180	(46*10^170932+143)/9	170933	Robert Price	01/2019
1181	(58*10^170842+221)/9	170843	Robert Price	02/2017
1182	3*10^170800+73	170801	Robert Price	08/2018
1183	11^164009-270	170798	Enzo Doria	10/2012
1184	2*10^170767+41	170768	Robert Price	05/2018
1185	3^357706-112358	170670	Enzo Doria	07/2014
1186	TheodorusPrime(170657)	170657	Eric W. Weisstein	08/2013
1187	2^566871+1876163	170646	Enzo Doria	07/2016
1188	(10657#+(404267#)/(10657#))/(1675379)	170624	Makoto Morimoto	10/2017
1189	2^566496+7	170533	Donovan Johnson	07/2006
1190	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
1191	2^565183-352021	170138	Enzo Doria	07/2015
1192	2^565143-114457	170125	Enzo Doria	02/2015
1193	2^564976-49869	170075	Enzo Doria	10/2015
1194	2^564526-351401	169940	Enzo Doria	07/2015
1195	4*10^169759+19	169760	Robert Price	10/2018
1196	21^128327-20^128327	169677	Jean-Louis Charton	11/2014
1197	(4*10^169559+83)/3	169560	Robert Price	02/2018
1198	2^562749+2793047	169405	Enzo Doria	02/2016
1199	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
1200	2^562369-29503	169290	Enzo Doria	08/2015
1201	(22*10^169019+383)/9	169020	Robert Price	05/2018
1202	5*10^168807+87	168808	Robert Price	02/2019
1203	2^560405-39943	168699	Enzo Doria	09/2015
1204	2^559686-350471	168483	Enzo Doria	06/2015
1205	2^559672-1855889	168479	Enzo Doria	09/2015
1206	(5*10^168379-473)/9	168379	Robert Price	01/2018
1207	2^559000-59939	168276	Enzo Doria	11/2015
1208	(16*10^168181+41)/3	168182	Robert Price	03/2019
1209	2^558640-114149	168168	Enzo Doria	12/2014
1210	2^558498-1849277	168125	Enzo Doria	08/2015
1211	2^558476-1850249	168119	Enzo Doria	08/2015
1212	(7*10^168067+71)/3	168068	Robert Price	05/2018
1213	2^558150-1852211	168020	Enzo Doria	08/2015
1214	2^558125-113661	168013	Enzo Doria	09/2014
1215	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
1216	(13*10^167911+179)/3	167912	Robert Price	11/2018
1217	39^105456+2	167788	Robert Price	04/2015
1218	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
1219	10^167639+121911	167640	Patrick De Geest	07/2018
1220	10^167639-8001	167639	Robert Price	03/2018
1221	2^556504-462059	167525	Enzo Doria	07/2015
1222	5*10^167510+9	167511	Robert Price	08/2015
1223	2^555343+1874333	167175	Enzo Doria	06/2016
1224	2^555210-461261	167135	Enzo Doria	07/2015
1225	2^554372+1880527	166883	Enzo Doria	11/2016
1226	2^554299+72173	166861	Enzo Doria	04/2016
1227	2^554037-2797063	166782	Enzo Doria	03/2016
1228	(49*10^166721-139)/9	166722	Robert Price	03/2019
1229	2^553484-29819	166616	Enzo Doria	08/2015
1230	2^553383-2784217	166585	Enzo Doria	10/2015
1231	2^553069+76427	166491	Enzo Doria	05/2016
1232	2*10^166458+51	166459	Robert Price	05/2018
1233	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
1234	11^159756-2424	166369	Mike Oakes	06/2010
1235	2^552649-361275	166364	Enzo Doria	05/2014
1236	2^552628-113669	166358	Enzo Doria	09/2014
1237	10^166324+550603	166325	Patrick De Geest	07/2018
1238	10^166324-801	166324	Robert Price	02/2018
1239	2^552137+1879397	166210	Enzo Doria	09/2016
1240	(23^121949-1)/22	166061	Paul Bourdelais	10/2017
1241	2^551542+19249	166031	Payam Samidoost	08/2002
1242	2^551535-23821	166029	Enzo Doria	08/2013
1243	2^551507-23557	166021	Enzo Doria	08/2013
1244	7*10^165916-3	165917	Robert Price	08/2015
1245	81^86837-80^86837	165728	Robert Price	01/2015
1246	2^550270-69551	165648	Enzo Doria	12/2015
1247	2^550000-23625	165567	Enzo Doria	08/2013
1248	2^549675-1852057	165469	Enzo Doria	08/2015
1249	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
1250	(28*10^165358-1)/9	165359	Serge Batalov	10/2014

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PRP Records

Probable Primes Top 10000

(252602 PRPs in the top)