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 (> 30000)	Who ?	When ?
1001	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
1002	2^597424-1859729	179843	Enzo Doria	11/2015
1003	Phi(180683,10)	179760	Maksym Voznyy	09/2015
1004	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
1005	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
1006	(29*10^179697+223)/9	179698	Robert Price	09/2018
1007	2^596690-461261	179622	Enzo Doria	07/2015
1008	2^596684-113939	179620	Enzo Doria	10/2014
1009	2*10^179602+63	179603	Robert Price	05/2018
1010	3^375887-112696	179344	Enzo Doria	07/2014
1011	2^595144-1850429	179157	Enzo Doria	08/2015
1012	2^594531+82253	178972	Enzo Doria	09/2016
1013	2^594260-2787899	178891	Enzo Doria	11/2015
1014	2^593631+101381	178701	Jorge Menendez	04/2018
1015	10^178695+136719	178696	Patrick De Geest	05/2016
1016	10^178695-71	178695	Serge Batalov	12/2014
1017	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
1018	2^593222-14145	178578	Jorge Menendez	10/2017
1019	2^593178+1867219	178565	Enzo Doria	03/2016
1020	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
1021	(5*10^178206+91)/3	178207	Robert Price	04/2018
1022	2^591872-291929	178172	Enzo Doria	07/2015
1023	2^591682-286871	178115	Enzo Doria	07/2015
1024	4*10^178091+9	178092	Robert Price	05/2015
1025	410747#+478483	178007	Makoto Morimoto	02/2016
1026	3*10^177872+73	177873	Robert Price	08/2018
1027	2^590762-396765	177838	Enzo Doria	08/2013
1028	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
1029	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
1030	3*10^177373-97	177374	Robert Price	07/2018
1031	2^589204+1881151	177369	Enzo Doria	11/2016
1032	2^589132-69479	177347	Enzo Doria	01/2016
1033	2^588912-113519	177281	Enzo Doria	08/2014
1034	15^150706+2	177245	Robert Price	06/2015
1035	2^588194-1861001	177065	Enzo Doria	11/2015
1036	(19*10^176932+521)/9	176933	Robert Price	05/2018
1037	(8*10^176908+43)/3	176909	Robert Price	06/2018
1038	2^587560-113699	176874	Enzo Doria	09/2014
1039	5^252763-12862	176674	Enzo Doria	05/2014
1040	2^586804+81721	176646	Enzo Doria	08/2016
1041	(10^176584+77)/3	176584	Robert Price	01/2018
1042	2^586570+1874419	176576	Enzo Doria	06/2016
1043	2^585994-3311	176402	Yves Minet	12/2014
1044	2^585832-112799	176354	Enzo Doria	07/2014
1045	2^585336-461039	176204	Enzo Doria	06/2015
1046	2^585095-1848127	176132	Enzo Doria	08/2015
1047	2^584950-115451	176088	Enzo Doria	07/2015
1048	2^584671-3697	176004	Yves Minet	03/2017
1049	2*10^175860-87	175861	Robert Price	04/2018
1050	10^175608+2971	175609	Mike Oakes	05/2010
1051	10^175608-55829	175608	Patrick De Geest	09/2013
1052	2^583051+1879793	175516	Enzo Doria	09/2016
1053	2^582860-23829	175459	Enzo Doria	08/2013
1054	2^582670-23913	175402	Enzo Doria	08/2013
1055	2^582573-29563	175372	Enzo Doria	08/2015
1056	2^582435-1862767	175331	Enzo Doria	12/2015
1057	(11*10^175250-149)/3	175251	Robert Price	09/2018
1058	2^582072-1848599	175222	Enzo Doria	08/2015
1059	(220221^32768+1)/2	175075	Serge Batalov	03/2018
1060	2^581560+1874911	175068	Enzo Doria	06/2016
1061	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
1062	2^580528-114035	174757	Enzo Doria	11/2014
1063	(19*10^174754+737)/9	174755	Robert Price	07/2018
1064	(35*10^174704-377)/9	174705	Robert Price	07/2018
1065	3*10^174665-97	174666	Robert Price	07/2018
1066	2^580046-459161	174612	Enzo Doria	05/2015
1067	2^579992-39779	174595	Enzo Doria	09/2015
1068	(2*10^174301-71)/3	174301	Robert Price	12/2017
1069	(2^578696+1)/257	174203	Lelio R Paula	09/2015
1070	2^578656-1851809	174193	Enzo Doria	08/2015
1071	2^578583-113917	174171	Enzo Doria	10/2014
1072	2^578434-83	174126	Yves Minet	07/2017
1073	15^148048-2	174118	Robert Price	06/2015
1074	2^578346+2794249	174100	Enzo Doria	03/2016
1075	2*10^173809-87	173810	Robert Price	04/2018
1076	(L!41532)/2	173772	Serge Batalov	07/2017
1077	2^577146-49877	173739	Enzo Doria	10/2015
1078	2^576889+49727	173661	Enzo Doria	09/2016
1079	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
1080	2^576016-113919	173399	Enzo Doria	11/2014
1081	2^575911-1849387	173367	Enzo Doria	08/2015
1082	2^575196-114053	173152	Enzo Doria	11/2014
1083	2^574591-115387	172970	Enzo Doria	07/2015
1084	2^574328+81121	172890	Enzo Doria	07/2016
1085	(115*10^172862-1)/3	172864	Serge Batalov	12/2014
1086	3*10^172812+13	172813	Robert Price	07/2018
1087	4*5^247217-9	172798	Lelio R Paula	10/2015
1088	69061#+(467617#)/(69061#)	172766	Makoto Morimoto	10/2017
1089	2^573668-2782319	172692	Enzo Doria	09/2015
1090	2^573444-1855109	172624	Enzo Doria	09/2015
1091	3^361608+2	172531	Robert Price	08/2014
1092	(54^99563+1)/55	172481	Paul Bourdelais	11/2017
1093	2^572592-114893	172368	Enzo Doria	05/2015
1094	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
1095	(38^109037-1)/37	172254	Paul Bourdelais	10/2017
1096	3*10^172219+73	172220	Robert Price	08/2018
1097	(36^110503+1)/37	171975	Lelio R Paula	04/2017
1098	2^570980-2782289	171883	Enzo Doria	09/2015
1099	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
1100	2^569563-1854607	171456	Enzo Doria	09/2015
1101	3*10^171391+59	171392	Robert Price	08/2018
1102	(55^98419-1)/54	171284	Paul Bourdelais	12/2017
1103	2^568642+1876129	171179	Enzo Doria	07/2016
1104	(58*10^170842+221)/9	170843	Robert Price	02/2017
1105	3*10^170800+73	170801	Robert Price	08/2018
1106	11^164009-270	170798	Enzo Doria	10/2012
1107	2*10^170767+41	170768	Robert Price	05/2018
1108	3^357706-112358	170670	Enzo Doria	07/2014
1109	TheodorusPrime(170657)	170657	Eric W. Weisstein	08/2013
1110	2^566871+1876163	170646	Enzo Doria	07/2016
1111	(10657#+(404267#)/(10657#))/(1675379)	170624	Makoto Morimoto	10/2017
1112	2^566496+7	170533	Donovan Johnson	07/2006
1113	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
1114	2^565183-352021	170138	Enzo Doria	07/2015
1115	2^565143-114457	170125	Enzo Doria	02/2015
1116	2^564976-49869	170075	Enzo Doria	10/2015
1117	2^564526-351401	169940	Enzo Doria	07/2015
1118	21^128327-20^128327	169677	Jean-Louis Charton	11/2014
1119	(4*10^169559+83)/3	169560	Robert Price	02/2018
1120	2^562749+2793047	169405	Enzo Doria	02/2016
1121	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
1122	2^562369-29503	169290	Enzo Doria	08/2015
1123	(22*10^169019+383)/9	169020	Robert Price	05/2018
1124	2^560405-39943	168699	Enzo Doria	09/2015
1125	2^559686-350471	168483	Enzo Doria	06/2015
1126	2^559672-1855889	168479	Enzo Doria	09/2015
1127	(5*10^168379-473)/9	168379	Robert Price	01/2018
1128	2^559000-59939	168276	Enzo Doria	11/2015
1129	2^558640-114149	168168	Enzo Doria	12/2014
1130	2^558498-1849277	168125	Enzo Doria	08/2015
1131	2^558476-1850249	168119	Enzo Doria	08/2015
1132	(7*10^168067+71)/3	168068	Robert Price	05/2018
1133	2^558150-1852211	168020	Enzo Doria	08/2015
1134	2^558125-113661	168013	Enzo Doria	09/2014
1135	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
1136	39^105456+2	167788	Robert Price	04/2015
1137	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
1138	10^167639+121911	167640	Patrick De Geest	07/2018
1139	10^167639-8001	167639	Robert Price	03/2018
1140	2^556504-462059	167525	Enzo Doria	07/2015
1141	5*10^167510+9	167511	Robert Price	08/2015
1142	2^555343+1874333	167175	Enzo Doria	06/2016
1143	2^555210-461261	167135	Enzo Doria	07/2015
1144	2^554372+1880527	166883	Enzo Doria	11/2016
1145	2^554299+72173	166861	Enzo Doria	04/2016
1146	2^554037-2797063	166782	Enzo Doria	03/2016
1147	2^553484-29819	166616	Enzo Doria	08/2015
1148	2^553383-2784217	166585	Enzo Doria	10/2015
1149	2^553069+76427	166491	Enzo Doria	05/2016
1150	2*10^166458+51	166459	Robert Price	05/2018
1151	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
1152	11^159756-2424	166369	Mike Oakes	06/2010
1153	2^552649-361275	166364	Enzo Doria	05/2014
1154	2^552628-113669	166358	Enzo Doria	09/2014
1155	10^166324+550603	166325	Patrick De Geest	07/2018
1156	10^166324-801	166324	Robert Price	02/2018
1157	2^552137+1879397	166210	Enzo Doria	09/2016
1158	(23^121949-1)/22	166061	Paul Bourdelais	10/2017
1159	2^551542+19249	166031	Payam Samidoost	08/2002
1160	2^551535-23821	166029	Enzo Doria	08/2013
1161	2^551507-23557	166021	Enzo Doria	08/2013
1162	7*10^165916-3	165917	Robert Price	08/2015
1163	81^86837-80^86837	165728	Robert Price	01/2015
1164	2^550270-69551	165648	Enzo Doria	12/2015
1165	2^550000-23625	165567	Enzo Doria	08/2013
1166	2^549675-1852057	165469	Enzo Doria	08/2015
1167	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
1168	(28*10^165358-1)/9	165359	Serge Batalov	10/2014
1170	2^549278+1879669	165350	Enzo Doria	09/2016
1169	(7*10^165350-439)/9	165350	Robert Price	02/2018
1171	2^549252-351269	165342	Enzo Doria	06/2015
1172	2^549049+2797607	165281	Enzo Doria	04/2016
1173	(7*10^165239+107)/3	165240	Robert Price	02/2018
1174	(44^100511-1)/43	165184	Paul Bourdelais	11/2017
1175	(7*10^165134+107)/3	165135	Robert Price	02/2018
1176	2^547178-1856501	164717	Enzo Doria	10/2015
1177	11^158160-60	164707	Enzo Doria	07/2012
1178	2^546398-59201	164483	Enzo Doria	10/2015
1179	2^546332-114893	164463	Enzo Doria	05/2015
1180	2^545958+1876189	164350	Enzo Doria	07/2016
1181	2^545878-49841	164326	Enzo Doria	10/2015
1182	(10^164284+77)/3	164284	Robert Price	01/2018
1183	2^545668-4019	164263	Yves Minet	04/2017
1184	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
1185	2^545185+76757	164118	Enzo Doria	05/2016
1186	2^545076-114329	164085	Enzo Doria	01/2015
1187	(2*10^164043-143)/3	164043	Robert Price	03/2018
1188	(29^112153+1)/30	164011	Lelio R Paula	03/2017
1189	2^544757+1874777	163989	Enzo Doria	06/2016
1190	2^544444-457199	163894	Enzo Doria	01/2015
1191	2^544264-343529	163840	Enzo Doria	07/2015
1192	7*10^163780+9	163781	Robert Price	09/2015
1193	2^543989+2793047	163758	Enzo Doria	02/2016
1194	2^542870-69551	163421	Enzo Doria	12/2015
1195	2^542395+72533	163278	Enzo Doria	04/2016
1196	2^542072-3683	163180	Yves Minet	03/2017
1197	2^541779-1867357	163092	Enzo Doria	04/2016
1198	8*10^162924+9	162925	Robert Price	12/2015
1199	2^540905+81557	162829	Enzo Doria	08/2016
1200	2^540628-2939	162746	Yves Minet	09/2014
1201	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
1202	3*10^162620-59	162621	Robert Price	09/2018
1203	3^340694-112960	162553	Enzo Doria	07/2014
1204	2^539807-114081	162499	Enzo Doria	12/2014
1205	2^539654-114893	162453	Enzo Doria	05/2015
1206	2^539617-1851583	162441	Enzo Doria	08/2015
1207	2^539346+81049	162360	Enzo Doria	07/2016
1208	2^539220-115499	162322	Enzo Doria	07/2015
1209	2^539217-113713	162321	Enzo Doria	09/2014
1210	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
1211	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
1212	(10^162138+11)/3	162138	Serge Batalov	07/2015
1213	2^538473-112723	162097	Enzo Doria	06/2014
1214	2^538157+79337	162002	Enzo Doria	06/2016
1215	2^538136-114749	161996	Enzo Doria	05/2015
1216	2^538104+1531	161986	Lelio R Paula	01/2013
1217	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
1218	2^537815-22737	161899	Enzo Doria	07/2013
1219	2^537804-39839	161896	Enzo Doria	09/2015
1220	2^537458-59201	161791	Enzo Doria	10/2015
1221	2*10^161766+51	161767	Robert Price	05/2018
1222	2^537209-49849	161717	Enzo Doria	10/2015
1223	2^536937+1879397	161635	Enzo Doria	09/2016
1224	2^536569-22881	161524	Enzo Doria	07/2013
1225	10^161253+573493	161254	Patrick De Geest	07/2018
1226	10^161253-8001	161253	Robert Price	03/2018
1227	7*10^161192-9	161193	Robert Price	10/2015
1228	2^535269-113803	161133	Enzo Doria	09/2014
1229	2^535205-23295	161113	Enzo Doria	08/2013
1230	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
1231	2^534359-23229	160859	Enzo Doria	08/2013
1232	67^88037-66^88037	160763	Robert Price	10/2013
1233	2^533948-1852559	160735	Enzo Doria	08/2015
1234	2^533665-23335	160650	Enzo Doria	08/2013
1235	3^336353-2^336353	160482	Mike Oakes	10/2007
1236	2^532253+1868417	160225	Enzo Doria	04/2016
1237	2^532108-291989	160181	Enzo Doria	07/2015
1238	2^531110-1853771	159881	Enzo Doria	09/2015
1239	2^530992-1845299	159845	Enzo Doria	07/2015
1240	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
1241	2^530417-113833	159672	Enzo Doria	09/2014
1242	2^530406-69701	159669	Enzo Doria	02/2016
1243	7^188858-188858^7	159604	Norbert Schneider	05/2018
1244	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
1245	(17*10^159438-377)/9	159439	Robert Price	03/2018
1246	2^528944-461315	159229	Enzo Doria	07/2015
1247	2^528620-113879	159131	Enzo Doria	10/2014
1248	2^528000-23307	158944	Enzo Doria	08/2013
1249	(29*10^158909+61)/9	158910	Robert Price	08/2018
1250	2^527817+1876817	158889	Enzo Doria	07/2016

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PRP Records

Probable Primes Top 10000

(221609 PRPs in the top)