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	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
1002	2^654400-39719	196995	Enzo Doria	09/2015
1003	(14*10^196965-221)/9	196966	Robert Price	04/2018
1004	2^654216-459995	196939	Enzo Doria	06/2015
1005	(17*10^196921+31)/3	196922	Robert Price	01/2019
1006	(14*10^196885-89)/3	196886	Robert Price	05/2020
1007	3*10^196881-59	196882	Robert Price	09/2018
1008	2^653851+82295	196829	Enzo Doria	09/2016
1009	(38*10^196792+691)/9	196793	Robert Price	10/2018
1010	2^653636-29429	196765	Enzo Doria	08/2015
1011	2^653601-69673	196754	Enzo Doria	02/2016
1012	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
1013	2^652786-1852571	196509	Enzo Doria	08/2015
1014	2^652752-1325	196498	Yves Minet	07/2015
1015	2^652470-1859141	196414	Enzo Doria	10/2015
1016	2^652307+1877483	196364	Enzo Doria	08/2016
1017	2^652293-115273	196360	Enzo Doria	06/2015
1018	(47*10^196281+403)/9	196282	Robert Price	03/2019
1019	6*10^196070+73	196071	Robert Price	04/2019
1020	2^651218-1868201	196037	Enzo Doria	04/2016
1021	2^651047-49687	195985	Enzo Doria	10/2015
1022	2^650285-2785333	195756	Enzo Doria	10/2015
1023	(69^106397-1)/68	195647	Paul Bourdelais	10/2017
1024	2^649811+1877573	195613	Enzo Doria	08/2016
1025	2^649662-170531	195568	Hans Havermann	10/2018
1026	2^649586+182839	195545	Enzo Doria	11/2016
1027	2^649537-1867363	195531	Enzo Doria	04/2016
1028	2^649536-1861499	195530	Enzo Doria	12/2015
1029	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
1030	2^649102-59351	195400	Enzo Doria	10/2015
1031	(2*10^195399+529)/9	195399	Robert Price	01/2018
1032	(202*10^195383-13)/9	195385	Robert Price	01/2020
1033	2^648988+1178971	195365	Enzo Doria	06/2016
1034	2^648975-114319	195361	Enzo Doria	02/2015
1035	(11*10^195350-137)/9	195351	Robert Price	01/2018
1036	2^648619-24835	195254	Enzo Doria	09/2013
1037	(14*10^195234-83)/3	195235	Robert Price	12/2018
1038	5*10^195221+81	195222	Robert Price	03/2019
1039	2^648190-24737	195125	Enzo Doria	09/2013
1040	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
1041	10^195060+89701	195061	Patrick De Geest	02/2021
1043	10^195060-40000000001	195060	Robert Price	09/2020
1042	10^195060-110337	195060	Patrick De Geest	02/2021
1044	56*10^195032-3	195034	Robert Price	03/2020
1045	11^187185-90	194934	Enzo Doria	09/2012
1046	(86*10^194818-437)/9	194819	Robert Price	03/2021
1047	2^647068+77281	194787	Enzo Doria	05/2016
1048	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
1049	F(931517)	194676	Henri Lifchitz	09/2008
1050	4*10^194668+49	194669	Robert Price	01/2019
1051	2^646589+1179407	194643	Enzo Doria	06/2016
1052	2^646289-114621	194553	Enzo Doria	05/2015
1053	2^646236-39659	194537	Enzo Doria	09/2015
1054	(16*10^194536+53)/3	194537	Robert Price	03/2019
1055	2^646161-59833	194514	Enzo Doria	11/2015
1056	(17*10^194502+31)/3	194503	Robert Price	01/2019
1057	2*10^194413+3	194414	Robert Price	07/2015
1058	2^645360-1848599	194273	Enzo Doria	08/2015
1059	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
1060	2*10^193981-43	193982	Robert Price	04/2018
1061	2^644382+75169	193979	Enzo Doria	04/2016
1062	2^644304-1861409	193955	Enzo Doria	11/2015
1063	5*10^193907-9	193908	Robert Price	05/2015
1064	2^644043+1876703	193877	Enzo Doria	07/2016
1065	2^643735+1879733	193784	Enzo Doria	09/2016
1066	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
1067	9*10^193712+71	193713	Robert Price	08/2020
1068	2^643216-286565	193628	Enzo Doria	07/2015
1069	2^642888-24965	193529	Enzo Doria	09/2013
1070	2^642448-114825	193397	Enzo Doria	05/2015
1071	2^642437-1856623	193393	Enzo Doria	10/2015
1072	2^642039-59797	193273	Enzo Doria	11/2015
1073	10^193230+513861	193231	Patrick De Geest	07/2018
1074	10^193230-8001	193230	Robert Price	03/2018
1075	2^641692-286349	193169	Enzo Doria	07/2015
1076	2^641690-24737	193168	Enzo Doria	09/2013
1077	2^641514+1876549	193115	Enzo Doria	07/2016
1078	2^640888-2785619	192927	Enzo Doria	10/2015
1079	2^640874-2783741	192923	Enzo Doria	09/2015
1080	34*10^192868-9	192870	Robert Price	06/2020
1081	(46*10^192841+683)/9	192842	Robert Price	03/2019
1082	2^640181+467	192714	Lelio R Paula	08/2013
1083	2^639536-1850249	192520	Enzo Doria	08/2015
1084	40714<>40712<>...<>1086421357911<>...<>40711<>40713	192464	Hans Havermann	12/2019
1085	5*10^192422-43	192423	Robert Price	01/2019
1086	2^639110-2792441	192392	Enzo Doria	02/2016
1087	2^638955-29827	192345	Enzo Doria	08/2015
1088	2^638713-2784223	192272	Enzo Doria	10/2015
1089	2^638490-113507	192205	Enzo Doria	08/2014
1090	2^638189-39943	192115	Enzo Doria	09/2015
1091	2^638110+1877119	192091	Enzo Doria	07/2016
1092	2^638066-2785211	192078	Enzo Doria	10/2015
1093	(112*10^191900+17)/3	191902	Robert Price	03/2020
1094	2^637475-115309	191900	Enzo Doria	07/2015
1095	(68*10^191754-113)/9	191755	Robert Price	03/2021
1096	2^636661+1876577	191655	Enzo Doria	07/2016
1097	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
1098	2^636177-1855123	191509	Enzo Doria	09/2015
1099	2^636158-113627	191503	Enzo Doria	08/2014
1100	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
1101	2^636035+79823	191466	Enzo Doria	06/2016
1102	2^636011-1860847	191459	Enzo Doria	11/2015
1103	2^635926-1860611	191433	Enzo Doria	11/2015
1104	3*10^191152-7	191153	Robert Price	08/2015
1105	2^634883-1865677	191119	Enzo Doria	02/2016
1106	2^634801+1871957	191095	Enzo Doria	05/2016
1107	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
1108	9*10^191018-41	191019	Robert Price	08/2020
1109	2^634470-59861	190995	Enzo Doria	11/2015
1110	2^634368-29519	190964	Enzo Doria	08/2015
1111	2^634188-350609	190910	Enzo Doria	06/2015
1112	(26*10^190789-131)/3	190790	Robert Price	10/2019
1113	(13*10^190732-61)/3	190733	Robert Price	11/2018
1114	(7*10^190683+143)/3	190684	Robert Price	03/2018
1115	2^633088-113879	190579	Enzo Doria	10/2014
1116	2^633064+1874911	190572	Enzo Doria	06/2016
1117	(43*10^190547+83)/9	190548	Robert Price	11/2018
1118	(299*10^190533+1)/3	190535	Robert Price	04/2020
1119	(1744*10^190519-1747)/3	190522	Robert Price	12/2020
1120	2^632795-351205	190491	Enzo Doria	06/2015
1121	(16*10^190420-19)/3	190421	Robert Price	02/2019
1122	(43*10^190351+101)/9	190352	Robert Price	11/2018
1123	2^632156+78391	190298	Enzo Doria	06/2016
1124	97*10^190295-3	190297	Robert Price	05/2020
1125	2^632082-1851971	190276	Enzo Doria	08/2015
1126	2^632020+1880311	190257	Enzo Doria	09/2016
1127	7*10^190210+13	190211	Robert Price	03/2021
1128	2^631637-462373	190142	Enzo Doria	08/2015
1129	2*10^190126-21	190127	Robert Price	09/2020
1130	(28*10^190105+191)/3	190106	Robert Price	02/2020
1131	(68*10^190053-113)/9	190054	Robert Price	03/2021
1132	2^631122-39251	189987	Enzo Doria	08/2015
1133	(26*10^189928-89)/9	189929	Robert Price	06/2018
1134	2^630839-97	189902	Yves Minet	07/2017
1135	99*10^189876-7	189878	Robert Price	07/2020
1136	2^630359+1788953	189757	Enzo Doria	05/2016
1137	2^630228+1871971	189718	Enzo Doria	05/2016
1138	2^630108+781	189682	Lelio R Paula	08/2013
1139	2^629870-1867811	189610	Enzo Doria	04/2016
1140	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
1141	2^629326+2792929	189447	Enzo Doria	02/2016
1142	4*10^189401+13	189402	Robert Price	02/2021
1143	(10^189385-61)/3	189385	Serge Batalov	12/2014
1144	2^629036+1874011	189359	Enzo Doria	06/2016
1145	2^628930+80779	189327	Enzo Doria	07/2016
1146	2^628582+1179439	189223	Enzo Doria	06/2016
1147	(44*10^188999-503)/9	189000	Robert Price	12/2018
1148	(16*10^188823+167)/3	188824	Robert Price	06/2019
1149	2^627037-2785843	188757	Enzo Doria	10/2015
1150	(16*10^188457+161)/3	188458	Robert Price	02/2019
1151	L(901657)	188436	Renaud Lifchitz	11/2008
1152	2^625651+74213	188340	Enzo Doria	04/2016
1153	2^625584-460919	188320	Enzo Doria	06/2015
1154	(10^188164+359)/9	188164	Serge Batalov	12/2014
1155	2^624481-113611	187988	Enzo Doria	08/2014
1156	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
1157	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
1158	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
1159	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
1160	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
1161	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
1163	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
1162	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
1164	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
1165	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
1166	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
1167	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
1168	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
1170	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
1169	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
1171	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
1172	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
1173	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
1174	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
1175	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
1176	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
1177	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
1179	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
1178	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
1180	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
1181	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
1182	2^624077-112723	187866	Enzo Doria	07/2014
1183	2^624008+1874941	187846	Enzo Doria	06/2016
1184	2^623870+78679	187804	Enzo Doria	05/2016
1185	2^623714-114035	187757	Enzo Doria	11/2014
1186	2^623651-1834251	187738	Enzo Doria	07/2015
1187	(7*10^187645+53)/3	187646	Robert Price	05/2018
1188	2^623146+1879609	187586	Enzo Doria	09/2016
1189	(5*10^187471+91)/3	187472	Robert Price	04/2018
1190	2^622500+81931	187392	Enzo Doria	08/2016
1191	2^622300-1861739	187331	Enzo Doria	12/2015
1192	(38*10^187281+349)/9	187282	Robert Price	10/2018
1193	2^622052+76771	187257	Enzo Doria	05/2016
1194	2^622005-24091	187243	Enzo Doria	08/2013
1195	7*10^187205-57	187206	Robert Price	06/2020
1196	2^621879-351787	187205	Enzo Doria	07/2015
1197	(5*10^187168-53)/3	187169	Robert Price	09/2020
1198	(23*10^187164-143)/3	187165	Robert Price	12/2019
1199	2^621700+79411	187151	Enzo Doria	06/2016
1200	(7*10^187101+131)/3	187102	Robert Price	06/2020
1201	(2*10^187062-71)/3	187062	Robert Price	12/2017
1202	2^620929-113203	186919	Enzo Doria	07/2014
1203	10^186842+168223	186843	Patrick De Geest	07/2018
1204	10^186842-8001	186842	Robert Price	03/2018
1205	2^620347-1777	186744	Lelio R Paula	07/2013
1206	11^179143-4170	186559	Enzo Doria	12/2012
1207	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
1208	2^619297-2792353	186427	Enzo Doria	02/2016
1209	(49*10^186409+383)/9	186410	Robert Price	04/2019
1210	2^618940-460139	186320	Enzo Doria	06/2015
1211	2^618046+74179	186051	Enzo Doria	04/2016
1212	3*10^186019+11	186020	Robert Price	07/2018
1213	(16*10^185978-19)/3	185979	Robert Price	02/2019
1214	2*10^185930-3	185931	Robert Price	07/2015
1215	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
1216	4*10^185905+91	185906	Robert Price	08/2018
1217	(19*10^185873+131)/3	185874	Robert Price	06/2020
1218	(37*10^185811+377)/9	185812	Robert Price	11/2018
1219	2^617250+9385	185811	Lelio R Paula	07/2013
1220	39^116749+2	185756	Robert Price	04/2015
1221	2^616924-39719	185713	Enzo Doria	09/2015
1222	2^616712+1867621	185649	Enzo Doria	04/2016
1223	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
1224	8*10^185529-67	185530	Robert Price	08/2019
1225	4*10^185355+9	185356	Robert Price	05/2015
1226	(16*10^185347+89)/3	185348	Robert Price	03/2021
1227	2^615622+76639	185321	Enzo Doria	05/2016
1228	2^615591+1879223	185312	Enzo Doria	08/2016
1229	2^615503+1876643	185285	Enzo Doria	07/2016
1230	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
1232	(4*10^185221-91)/3	185222	Robert Price	03/2018
1231	(7*10^185221+131)/3	185222	Robert Price	06/2020
1233	(232*10^185180+17)/3	185182	Robert Price	04/2021
1234	56*10^185139-3	185141	Robert Price	03/2020
1235	(28*10^185105+47)/3	185106	Robert Price	02/2021
1236	2^614783-2790097	185069	Enzo Doria	12/2015
1237	2^614745-29323	185057	Enzo Doria	07/2015
1238	(((((((((((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
1239	(49*10^184993-67)/9	184994	Robert Price	03/2019
1240	(14*10^184950+211)/9	184951	Robert Price	04/2018
1241	2^614315+81353	184928	Enzo Doria	08/2016
1242	2^614294-1849961	184921	Enzo Doria	08/2015
1243	2^614266+1877809	184913	Enzo Doria	08/2016
1244	(185*10^184878-11)/3	184880	Robert Price	10/2020
1245	2^613715-1860727	184747	Enzo Doria	11/2015
1246	2*10^184723+41	184724	Robert Price	05/2018
1247	(49*10^184703+293)/9	184704	Robert Price	03/2021
1248	2^613487-349987	184678	Enzo Doria	07/2015
1249	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
1250	14^161089-161089^14	184629	Serge Batalov	05/2016

Find by discoverer :

PRP Records

Probable Primes Top 10000

(280932 PRPs in the top)