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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
1002	2^612341-1604809	184334	Enzo Doria	05/2015
1003	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
1004	(14*10^184150+37)/3	184151	Robert Price	12/2018
1005	2^611731-4837	184150	Yves Minet	08/2018
1006	3*10^184124-7	184125	Robert Price	08/2015
1007	2^611628-24537	184119	Enzo Doria	08/2013
1008	3*10^184110+13	184111	Robert Price	07/2018
1009	2^611460+71881	184068	Enzo Doria	04/2016
1010	4*10^184004-63	184005	Robert Price	10/2018
1011	2^610982-1867301	183924	Enzo Doria	03/2016
1012	3*10^183872-49	183873	Robert Price	07/2018
1013	2^610597+1178897	183809	Enzo Doria	05/2016
1014	(17*10^183764+31)/3	183765	Robert Price	01/2019
1015	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
1016	2^610401+1277	183750	Lelio R Paula	07/2013
1017	2^610356-1849019	183736	Enzo Doria	08/2015
1018	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
1019	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
1020	(4*10^183659+149)/9	183659	Robert Price	04/2018
1021	2^609846-1834251	183582	Enzo Doria	07/2015
1022	11^176176-240	183469	Enzo Doria	11/2012
1023	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
1024	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
1025	2^608965-113989	183317	Enzo Doria	10/2014
1026	A005165(43592)	183312	Serge Batalov	07/2017
1027	2^608814-461261	183272	Enzo Doria	06/2015
1028	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
1029	2^608541-608541^2	183190	Henri Lifchitz	02/2018
1030	2^608293+143807	183115	Enzo Doria	10/2016
1031	2^608164-462419	183076	Enzo Doria	08/2015
1032	2^607950-1862303	183012	Enzo Doria	12/2015
1033	(46*10^182896+683)/9	182897	Robert Price	03/2019
1034	2^607101+1871987	182756	Enzo Doria	05/2016
1035	2^606869-69175	182686	Enzo Doria	11/2015
1036	3*10^182614-11	182615	Robert Price	07/2018
1037	2^606560-357	182593	Enzo Doria	05/2014
1038	2^605687+1866983	182330	Enzo Doria	03/2016
1039	2^605655-114445	182321	Enzo Doria	02/2015
1040	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
1041	(14*10^182177-221)/9	182178	Robert Price	04/2018
1042	2^605174-112751	182176	Enzo Doria	06/2014
1043	2^604761+1874507	182052	Enzo Doria	06/2016
1044	2^604705+1871957	182035	Enzo Doria	05/2016
1045	(14*10^182000+229)/9	182001	Robert Price	03/2018
1046	(10^181996+41)/3	181996	Robert Price	12/2017
1047	(5*10^181950-101)/3	181951	Robert Price	04/2018
1048	2^603915+75233	181797	Enzo Doria	04/2016
1049	11^174145-360	181354	Enzo Doria	10/2012
1050	2^602351-396765	181326	Enzo Doria	08/2013
1051	6*10^181306+17	181307	Robert Price	04/2019
1052	2^601957-113833	181208	Enzo Doria	09/2014
1053	66^99581-65^99581	181193	Robert Price	09/2013
1054	10^181182+383973	181183	Patrick De Geest	04/2016
1055	10^181182-21	181182	Serge Batalov	12/2014
1056	(5*10^181127-29)/3	181128	Robert Price	03/2018
1057	2^601521-29143	181076	Enzo Doria	07/2015
1058	2^601442-2797811	181053	Enzo Doria	04/2016
1059	5*10^180992-9	180993	Robert Price	05/2015
1060	10^180979+79477	180980	Patrick De Geest	04/2016
1061	10^180979+107739	180980	Patrick De Geest	04/2016
1062	10^180979-11	180979	Serge Batalov	12/2014
1063	2^601023-113851	180926	Enzo Doria	10/2014
1064	3*10^180852+29	180853	Robert Price	05/2018
1065	2^600300-1852559	180709	Enzo Doria	08/2015
1066	(10^180689+71)/9	180689	Serge Batalov	07/2015
1067	2^600209+76487	180681	Enzo Doria	05/2016
1068	2^599702-369885	180529	Enzo Doria	11/2013
1069	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
1070	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
1071	4*10^180360+93	180361	Robert Price	08/2018
1072	2^598942+80779	180300	Enzo Doria	07/2016
1073	(38*10^180296+403)/9	180297	Robert Price	10/2018
1074	2^598591-1844797	180194	Enzo Doria	06/2015
1075	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
1076	(4*10^179963-79)/3	179964	Robert Price	02/2018
1077	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
1078	2^597424-1859729	179843	Enzo Doria	11/2015
1079	Phi(180683,10)	179760	Maksym Voznyy	09/2015
1080	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
1081	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
1082	(29*10^179697+223)/9	179698	Robert Price	09/2018
1083	2^596690-461261	179622	Enzo Doria	07/2015
1084	2^596684-113939	179620	Enzo Doria	10/2014
1085	2*10^179602+63	179603	Robert Price	05/2018
1086	3^375887-112696	179344	Enzo Doria	07/2014
1087	4*10^179265-71	179266	Robert Price	12/2018
1088	2^595144-1850429	179157	Enzo Doria	08/2015
1089	3*10^179138+89	179139	Robert Price	10/2018
1090	2^594531+82253	178972	Enzo Doria	09/2016
1091	2^594260-2787899	178891	Enzo Doria	11/2015
1092	2^593631+101381	178701	Jorge Menendez	04/2018
1093	10^178695+136719	178696	Patrick De Geest	05/2016
1094	10^178695-71	178695	Serge Batalov	12/2014
1095	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
1096	2^593222-14145	178578	Jorge Menendez	10/2017
1097	2^593178+1867219	178565	Enzo Doria	03/2016
1098	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
1099	(5*10^178206+91)/3	178207	Robert Price	04/2018
1100	2^591872-291929	178172	Enzo Doria	07/2015
1101	2^591682-286871	178115	Enzo Doria	07/2015
1102	4*10^178091+9	178092	Robert Price	05/2015
1103	410747#+478483	178007	Makoto Morimoto	02/2016
1104	3*10^177872+73	177873	Robert Price	08/2018
1105	2^590762-396765	177838	Enzo Doria	08/2013
1106	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
1107	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
1108	(11*10^177466-113)/3	177467	Robert Price	10/2018
1109	3*10^177373-97	177374	Robert Price	07/2018
1110	2^589204+1881151	177369	Enzo Doria	11/2016
1111	2^589132-69479	177347	Enzo Doria	01/2016
1112	2^588912-113519	177281	Enzo Doria	08/2014
1113	15^150706+2	177245	Robert Price	06/2015
1114	2^588194-1861001	177065	Enzo Doria	11/2015
1115	(19*10^176932+521)/9	176933	Robert Price	05/2018
1116	(8*10^176908+43)/3	176909	Robert Price	06/2018
1117	2^587560-113699	176874	Enzo Doria	09/2014
1118	5^252763-12862	176674	Enzo Doria	05/2014
1119	2^586804+81721	176646	Enzo Doria	08/2016
1120	(10^176584+77)/3	176584	Robert Price	01/2018
1121	2^586570+1874419	176576	Enzo Doria	06/2016
1122	2^585994-3311	176402	Yves Minet	12/2014
1123	2^585832-112799	176354	Enzo Doria	07/2014
1124	2^585336-461039	176204	Enzo Doria	06/2015
1125	2^585095-1848127	176132	Enzo Doria	08/2015
1126	2^584950-115451	176088	Enzo Doria	07/2015
1127	2^584671-3697	176004	Yves Minet	03/2017
1128	(13*10^175965-37)/3	175966	Robert Price	01/2019
1129	2*10^175860-87	175861	Robert Price	04/2018
1130	10^175608+2971	175609	Mike Oakes	05/2010
1131	10^175608-55829	175608	Patrick De Geest	09/2013
1132	2^583051+1879793	175516	Enzo Doria	09/2016
1133	2^582860-23829	175459	Enzo Doria	08/2013
1134	2^582670-23913	175402	Enzo Doria	08/2013
1135	2^582573-29563	175372	Enzo Doria	08/2015
1136	2^582435-1862767	175331	Enzo Doria	12/2015
1137	(11*10^175250-149)/3	175251	Robert Price	09/2018
1138	2^582072-1848599	175222	Enzo Doria	08/2015
1139	(220221^32768+1)/2	175075	Serge Batalov	03/2018
1140	2^581560+1874911	175068	Enzo Doria	06/2016
1141	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
1142	(47*10^174790+493)/9	174791	Robert Price	03/2019
1143	2^580528-114035	174757	Enzo Doria	11/2014
1144	(19*10^174754+737)/9	174755	Robert Price	07/2018
1145	(35*10^174704-377)/9	174705	Robert Price	07/2018
1146	3*10^174665-97	174666	Robert Price	07/2018
1147	2^580046-459161	174612	Enzo Doria	05/2015
1148	2^579992-39779	174595	Enzo Doria	09/2015
1149	(2*10^174301-71)/3	174301	Robert Price	12/2017
1150	(2^578696+1)/257	174203	Lelio R Paula	09/2015
1151	2^578656-1851809	174193	Enzo Doria	08/2015
1152	2^578583-113917	174171	Enzo Doria	10/2014
1153	2^578434-83	174126	Yves Minet	07/2017
1154	15^148048-2	174118	Robert Price	06/2015
1155	5*10^174101+81	174102	Robert Price	03/2019
1156	2^578346+2794249	174100	Enzo Doria	03/2016
1157	5*10^173904-13	173905	Robert Price	01/2019
1158	(43*10^173826+101)/9	173827	Robert Price	11/2018
1159	2*10^173809-87	173810	Robert Price	04/2018
1160	(L!41532)/2	173772	Serge Batalov	07/2017
1161	2^577146-49877	173739	Enzo Doria	10/2015
1162	2^576889+49727	173661	Enzo Doria	09/2016
1163	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
1164	(13*10^173467-37)/3	173468	Robert Price	01/2019
1165	2^576016-113919	173399	Enzo Doria	11/2014
1166	2^575911-1849387	173367	Enzo Doria	08/2015
1167	(16*10^173251+107)/3	173252	Robert Price	03/2019
1168	2^575196-114053	173152	Enzo Doria	11/2014
1169	2^574591-115387	172970	Enzo Doria	07/2015
1170	2^574328+81121	172890	Enzo Doria	07/2016
1171	(115*10^172862-1)/3	172864	Serge Batalov	12/2014
1172	3*10^172812+13	172813	Robert Price	07/2018
1173	4*5^247217-9	172798	Lelio R Paula	10/2015
1174	69061#+(467617#)/(69061#)	172766	Makoto Morimoto	10/2017
1175	5*10^172692+57	172693	Robert Price	12/2018
1176	2^573668-2782319	172692	Enzo Doria	09/2015
1177	2^573444-1855109	172624	Enzo Doria	09/2015
1178	3^361608+2	172531	Robert Price	08/2014
1179	(54^99563+1)/55	172481	Paul Bourdelais	11/2017
1180	2^572592-114893	172368	Enzo Doria	05/2015
1181	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
1182	(38^109037-1)/37	172254	Paul Bourdelais	10/2017
1183	3*10^172219+73	172220	Robert Price	08/2018
1184	(36^110503+1)/37	171975	Lelio R Paula	04/2017
1185	(22*10^171929-73)/3	171930	Robert Price	04/2019
1186	4*10^171891-63	171892	Robert Price	10/2018
1187	2^570980-2782289	171883	Enzo Doria	09/2015
1188	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
1189	2^569563-1854607	171456	Enzo Doria	09/2015
1190	3*10^171391+59	171392	Robert Price	08/2018
1191	(13*10^171306-37)/3	171307	Robert Price	01/2019
1192	(55^98419-1)/54	171284	Paul Bourdelais	12/2017
1193	2^568642+1876129	171179	Enzo Doria	07/2016
1194	(46*10^170932+143)/9	170933	Robert Price	01/2019
1195	(58*10^170842+221)/9	170843	Robert Price	02/2017
1196	3*10^170800+73	170801	Robert Price	08/2018
1197	11^164009-270	170798	Enzo Doria	10/2012
1198	2*10^170767+41	170768	Robert Price	05/2018
1199	3^357706-112358	170670	Enzo Doria	07/2014
1200	TheodorusPrime(170657)	170657	Eric W. Weisstein	08/2013
1201	2^566871+1876163	170646	Enzo Doria	07/2016
1202	(10657#+(404267#)/(10657#))/(1675379)	170624	Makoto Morimoto	10/2017
1203	2^566496+7	170533	Donovan Johnson	07/2006
1204	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
1205	2^565183-352021	170138	Enzo Doria	07/2015
1206	2^565143-114457	170125	Enzo Doria	02/2015
1207	2^564976-49869	170075	Enzo Doria	10/2015
1208	2^564526-351401	169940	Enzo Doria	07/2015
1209	4*10^169759+19	169760	Robert Price	10/2018
1210	21^128327-20^128327	169677	Jean-Louis Charton	11/2014
1211	(4*10^169559+83)/3	169560	Robert Price	02/2018
1212	2^562749+2793047	169405	Enzo Doria	02/2016
1213	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
1214	(56*10^169311+691)/9	169312	Robert Price	05/2019
1215	2^562369-29503	169290	Enzo Doria	08/2015
1216	(22*10^169019+383)/9	169020	Robert Price	05/2018
1217	5*10^168807+87	168808	Robert Price	02/2019
1218	2^560405-39943	168699	Enzo Doria	09/2015
1219	2^559686-350471	168483	Enzo Doria	06/2015
1220	2^559672-1855889	168479	Enzo Doria	09/2015
1221	(5*10^168379-473)/9	168379	Robert Price	01/2018
1222	2^559000-59939	168276	Enzo Doria	11/2015
1223	(16*10^168181+41)/3	168182	Robert Price	03/2019
1224	2^558640-114149	168168	Enzo Doria	12/2014
1225	2^558498-1849277	168125	Enzo Doria	08/2015
1226	2^558476-1850249	168119	Enzo Doria	08/2015
1227	(7*10^168067+71)/3	168068	Robert Price	05/2018
1228	2^558150-1852211	168020	Enzo Doria	08/2015
1229	2^558125-113661	168013	Enzo Doria	09/2014
1230	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
1231	(13*10^167911+179)/3	167912	Robert Price	11/2018
1232	39^105456+2	167788	Robert Price	04/2015
1233	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
1234	10^167639+121911	167640	Patrick De Geest	07/2018
1235	10^167639-8001	167639	Robert Price	03/2018
1236	2^556504-462059	167525	Enzo Doria	07/2015
1237	5*10^167510+9	167511	Robert Price	08/2015
1238	2^555343+1874333	167175	Enzo Doria	06/2016
1239	2^555210-461261	167135	Enzo Doria	07/2015
1240	2^554372+1880527	166883	Enzo Doria	11/2016
1241	2^554299+72173	166861	Enzo Doria	04/2016
1242	2^554037-2797063	166782	Enzo Doria	03/2016
1243	(49*10^166721-139)/9	166722	Robert Price	03/2019
1244	2^553484-29819	166616	Enzo Doria	08/2015
1245	2^553383-2784217	166585	Enzo Doria	10/2015
1246	2^553069+76427	166491	Enzo Doria	05/2016
1247	2*10^166458+51	166459	Robert Price	05/2018
1248	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
1249	11^159756-2424	166369	Mike Oakes	06/2010
1250	2^552649-361275	166364	Enzo Doria	05/2014

Find by discoverer :

PRP Records

Probable Primes Top 10000

(252812 PRPs in the top)