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	2^641514+1876549	193115	Enzo Doria	07/2016
1002	2^640888-2785619	192927	Enzo Doria	10/2015
1003	2^640874-2783741	192923	Enzo Doria	09/2015
1004	34*10^192868-9	192870	Robert Price	06/2020
1005	(46*10^192841+683)/9	192842	Robert Price	03/2019
1006	2^640181+467	192714	Lelio R Paula	08/2013
1007	2^639536-1850249	192520	Enzo Doria	08/2015
1008	40714<>40712<>...<>1086421357911<>...<>40711<>40713	192464	Hans Havermann	12/2019
1009	5*10^192422-43	192423	Robert Price	01/2019
1010	2^639110-2792441	192392	Enzo Doria	02/2016
1011	2^638955-29827	192345	Enzo Doria	08/2015
1012	2^638713-2784223	192272	Enzo Doria	10/2015
1013	2^638490-113507	192205	Enzo Doria	08/2014
1014	2^638189-39943	192115	Enzo Doria	09/2015
1015	2^638110+1877119	192091	Enzo Doria	07/2016
1016	2^638066-2785211	192078	Enzo Doria	10/2015
1017	(112*10^191900+17)/3	191902	Robert Price	03/2020
1018	2^637475-115309	191900	Enzo Doria	07/2015
1019	2^636661+1876577	191655	Enzo Doria	07/2016
1020	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
1021	2^636177-1855123	191509	Enzo Doria	09/2015
1022	2^636158-113627	191503	Enzo Doria	08/2014
1023	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
1024	2^636035+79823	191466	Enzo Doria	06/2016
1025	2^636011-1860847	191459	Enzo Doria	11/2015
1026	2^635926-1860611	191433	Enzo Doria	11/2015
1027	3*10^191152-7	191153	Robert Price	08/2015
1028	2^634883-1865677	191119	Enzo Doria	02/2016
1029	2^634801+1871957	191095	Enzo Doria	05/2016
1030	(35*10^191073+1)/9	191074	Serge Batalov	07/2010
1031	9*10^191018-41	191019	Robert Price	08/2020
1032	2^634470-59861	190995	Enzo Doria	11/2015
1033	2^634368-29519	190964	Enzo Doria	08/2015
1034	2^634188-350609	190910	Enzo Doria	06/2015
1035	(26*10^190789-131)/3	190790	Robert Price	10/2019
1036	(13*10^190732-61)/3	190733	Robert Price	11/2018
1037	(7*10^190683+143)/3	190684	Robert Price	03/2018
1038	2^633088-113879	190579	Enzo Doria	10/2014
1039	2^633064+1874911	190572	Enzo Doria	06/2016
1040	(43*10^190547+83)/9	190548	Robert Price	11/2018
1041	(299*10^190533+1)/3	190535	Robert Price	04/2020
1042	2^632795-351205	190491	Enzo Doria	06/2015
1043	(16*10^190420-19)/3	190421	Robert Price	02/2019
1044	(43*10^190351+101)/9	190352	Robert Price	11/2018
1045	2^632156+78391	190298	Enzo Doria	06/2016
1046	97*10^190295-3	190297	Robert Price	05/2020
1047	2^632082-1851971	190276	Enzo Doria	08/2015
1048	2^632020+1880311	190257	Enzo Doria	09/2016
1049	2^631637-462373	190142	Enzo Doria	08/2015
1050	2*10^190126-21	190127	Robert Price	09/2020
1051	(28*10^190105+191)/3	190106	Robert Price	02/2020
1052	2^631122-39251	189987	Enzo Doria	08/2015
1053	(26*10^189928-89)/9	189929	Robert Price	06/2018
1054	2^630839-97	189902	Yves Minet	07/2017
1055	99*10^189876-7	189878	Robert Price	07/2020
1056	2^630359+1788953	189757	Enzo Doria	05/2016
1057	2^630228+1871971	189718	Enzo Doria	05/2016
1058	2^630108+781	189682	Lelio R Paula	08/2013
1059	2^629870-1867811	189610	Enzo Doria	04/2016
1060	(359^74189-1)/358	189558	Alexander Zhirkov	11/2017
1061	2^629326+2792929	189447	Enzo Doria	02/2016
1062	(10^189385-61)/3	189385	Serge Batalov	12/2014
1063	2^629036+1874011	189359	Enzo Doria	06/2016
1064	2^628930+80779	189327	Enzo Doria	07/2016
1065	2^628582+1179439	189223	Enzo Doria	06/2016
1066	(44*10^188999-503)/9	189000	Robert Price	12/2018
1067	(16*10^188823+167)/3	188824	Robert Price	06/2019
1068	2^627037-2785843	188757	Enzo Doria	10/2015
1069	(16*10^188457+161)/3	188458	Robert Price	02/2019
1070	L(901657)	188436	Renaud Lifchitz	11/2008
1071	2^625651+74213	188340	Enzo Doria	04/2016
1072	2^625584-460919	188320	Enzo Doria	06/2015
1073	(10^188164+359)/9	188164	Serge Batalov	12/2014
1074	2^624481-113611	187988	Enzo Doria	08/2014
1075	(2^624389+125582)/2	187960	Stefano Morozzi	09/2019
1076	(2^624389+166982)/2	187960	Stefano Morozzi	09/2019
1077	(2^624389+179886)/2	187960	Stefano Morozzi	09/2019
1078	(2^624387+64466)/2	187959	Stefano Morozzi	09/2019
1079	(2^624378+112990)/2	187957	Stefano Morozzi	09/2019
1080	(2^624380+161986)/2	187957	Stefano Morozzi	09/2019
1082	(2^624376+55762)/2	187956	Stefano Morozzi	09/2019
1081	(2^624377+169506)/2	187956	Stefano Morozzi	09/2019
1083	(2^624355+80178)/2	187950	Stefano Morozzi	09/2019
1084	(2^624351+61350)/2	187949	Stefano Morozzi	09/2019
1085	(2^624341+63462)/2	187946	Stefano Morozzi	09/2019
1086	(2^624344+135990)/2	187946	Stefano Morozzi	09/2019
1087	(2^624344+183898)/2	187946	Stefano Morozzi	09/2019
1089	(2^624340+126982)/2	187945	Stefano Morozzi	09/2019
1088	(2^624338+196110)/2	187945	Stefano Morozzi	09/2019
1090	(2^624337+105162)/2	187944	Stefano Morozzi	09/2019
1091	(2^624333+44594)/2	187943	Stefano Morozzi	09/2019
1092	(2^624321+88742)/2	187940	Stefano Morozzi	09/2019
1093	(2^624324+135178)/2	187940	Stefano Morozzi	09/2019
1094	(2^624317+14186)/2	187938	Stefano Morozzi	09/2019
1095	(2^624313+24450)/2	187937	Stefano Morozzi	09/2019
1096	(2^624309+184590)/2	187936	Stefano Morozzi	09/2019
1098	(2^624307+152658)/2	187935	Stefano Morozzi	09/2019
1097	(2^624307+185978)/2	187935	Stefano Morozzi	09/2019
1099	(2^624303+40814)/2	187934	Stefano Morozzi	09/2019
1100	(2^624304+99238)/2	187934	Stefano Morozzi	09/2019
1101	2^624077-112723	187866	Enzo Doria	07/2014
1102	2^624008+1874941	187846	Enzo Doria	06/2016
1103	2^623870+78679	187804	Enzo Doria	05/2016
1104	2^623714-114035	187757	Enzo Doria	11/2014
1105	2^623651-1834251	187738	Enzo Doria	07/2015
1106	(7*10^187645+53)/3	187646	Robert Price	05/2018
1107	2^623146+1879609	187586	Enzo Doria	09/2016
1108	(5*10^187471+91)/3	187472	Robert Price	04/2018
1109	2^622500+81931	187392	Enzo Doria	08/2016
1110	2^622300-1861739	187331	Enzo Doria	12/2015
1111	(38*10^187281+349)/9	187282	Robert Price	10/2018
1112	2^622052+76771	187257	Enzo Doria	05/2016
1113	2^622005-24091	187243	Enzo Doria	08/2013
1114	7*10^187205-57	187206	Robert Price	06/2020
1115	2^621879-351787	187205	Enzo Doria	07/2015
1116	(5*10^187168-53)/3	187169	Robert Price	09/2020
1117	(23*10^187164-143)/3	187165	Robert Price	12/2019
1118	2^621700+79411	187151	Enzo Doria	06/2016
1119	(7*10^187101+131)/3	187102	Robert Price	06/2020
1120	(2*10^187062-71)/3	187062	Robert Price	12/2017
1121	2^620929-113203	186919	Enzo Doria	07/2014
1122	10^186842+168223	186843	Patrick De Geest	07/2018
1123	10^186842-8001	186842	Robert Price	03/2018
1124	2^620347-1777	186744	Lelio R Paula	07/2013
1125	11^179143-4170	186559	Enzo Doria	12/2012
1126	(5^266863+1)/6	186529	Paul Bourdelais	07/2010
1127	2^619297-2792353	186427	Enzo Doria	02/2016
1128	(49*10^186409+383)/9	186410	Robert Price	04/2019
1129	2^618940-460139	186320	Enzo Doria	06/2015
1130	2^618046+74179	186051	Enzo Doria	04/2016
1131	3*10^186019+11	186020	Robert Price	07/2018
1132	(16*10^185978-19)/3	185979	Robert Price	02/2019
1133	2*10^185930-3	185931	Robert Price	07/2015
1134	(82^97151+1)/83	185928	Paul Bourdelais	10/2017
1135	4*10^185905+91	185906	Robert Price	08/2018
1136	(19*10^185873+131)/3	185874	Robert Price	06/2020
1137	(37*10^185811+377)/9	185812	Robert Price	11/2018
1138	2^617250+9385	185811	Lelio R Paula	07/2013
1139	39^116749+2	185756	Robert Price	04/2015
1140	2^616924-39719	185713	Enzo Doria	09/2015
1141	2^616712+1867621	185649	Enzo Doria	04/2016
1142	(3^388897+2^388897)/5	185551	Jean-Louis Charton	09/2011
1143	8*10^185529-67	185530	Robert Price	08/2019
1144	4*10^185355+9	185356	Robert Price	05/2015
1145	2^615622+76639	185321	Enzo Doria	05/2016
1146	2^615591+1879223	185312	Enzo Doria	08/2016
1147	2^615503+1876643	185285	Enzo Doria	07/2016
1148	5^265007-4^265007	185232	Jean-Louis Charton	02/2013
1149	(4*10^185221-91)/3	185222	Robert Price	03/2018
1150	(7*10^185221+131)/3	185222	Robert Price	06/2020
1151	56*10^185139-3	185141	Robert Price	03/2020
1152	2^614783-2790097	185069	Enzo Doria	12/2015
1153	2^614745-29323	185057	Enzo Doria	07/2015
1154	(((((((((((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
1155	(49*10^184993-67)/9	184994	Robert Price	03/2019
1156	(14*10^184950+211)/9	184951	Robert Price	04/2018
1157	2^614315+81353	184928	Enzo Doria	08/2016
1158	2^614294-1849961	184921	Enzo Doria	08/2015
1159	2^614266+1877809	184913	Enzo Doria	08/2016
1160	2^613715-1860727	184747	Enzo Doria	11/2015
1161	2*10^184723+41	184724	Robert Price	05/2018
1162	2^613487-349987	184678	Enzo Doria	07/2015
1163	(95^93377+1)/96	184672	Paul Bourdelais	11/2017
1164	14^161089-161089^14	184629	Serge Batalov	05/2016
1165	2^613033-114621	184542	Enzo Doria	05/2015
1166	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
1167	2^612341-1604809	184334	Enzo Doria	05/2015
1168	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
1169	(14*10^184150+37)/3	184151	Robert Price	12/2018
1170	2^611731-4837	184150	Yves Minet	08/2018
1171	3*10^184124-7	184125	Robert Price	08/2015
1172	2^611628-24537	184119	Enzo Doria	08/2013
1173	3*10^184110+13	184111	Robert Price	07/2018
1174	2^611460+71881	184068	Enzo Doria	04/2016
1175	4*10^184004-63	184005	Robert Price	10/2018
1176	2^610982-1867301	183924	Enzo Doria	03/2016
1177	3*10^183872-49	183873	Robert Price	07/2018
1178	2^610597+1178897	183809	Enzo Doria	05/2016
1179	(17*10^183764+31)/3	183765	Robert Price	01/2019
1180	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
1181	2^610401+1277	183750	Lelio R Paula	07/2013
1182	2^610356-1849019	183736	Enzo Doria	08/2015
1183	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
1184	23*10^183710-7	183712	Robert Price	02/2020
1185	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
1186	(4*10^183659+149)/9	183659	Robert Price	04/2018
1187	2^609846-1834251	183582	Enzo Doria	07/2015
1188	10^183546-800000001	183546	Robert Price	09/2020
1189	(23*10^183477-71)/3	183478	Robert Price	07/2020
1190	11^176176-240	183469	Enzo Doria	11/2012
1191	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
1192	6*10^183429+53	183430	Robert Price	05/2020
1193	(28*10^183403+191)/3	183404	Robert Price	02/2020
1194	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
1195	2^608965-113989	183317	Enzo Doria	10/2014
1196	A005165(43592)	183312	Serge Batalov	07/2017
1197	(61*10^183294+119)/9	183295	Robert Price	05/2019
1198	2^608814-461261	183272	Enzo Doria	06/2015
1199	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
1200	2^608541-608541^2	183190	Henri Lifchitz	02/2018
1201	2^608293+143807	183115	Enzo Doria	10/2016
1202	2^608164-462419	183076	Enzo Doria	08/2015
1203	2^607950-1862303	183012	Enzo Doria	12/2015
1204	(46*10^182896+683)/9	182897	Robert Price	03/2019
1205	(2*10^182787+73)/3	182787	Robert Price	09/2020
1206	2^607101+1871987	182756	Enzo Doria	05/2016
1207	2^606869-69175	182686	Enzo Doria	11/2015
1208	(23*10^182666-71)/3	182667	Robert Price	07/2020
1209	3*10^182614-11	182615	Robert Price	07/2018
1210	2^606560-357	182593	Enzo Doria	05/2014
1211	66*10^182420+7	182422	Robert Price	07/2020
1212	2^605687+1866983	182330	Enzo Doria	03/2016
1213	2^605655-114445	182321	Enzo Doria	02/2015
1214	94*10^182291-3	182293	Robert Price	05/2020
1215	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
1216	(14*10^182177-221)/9	182178	Robert Price	04/2018
1217	2^605174-112751	182176	Enzo Doria	06/2014
1218	2^604761+1874507	182052	Enzo Doria	06/2016
1219	2^604705+1871957	182035	Enzo Doria	05/2016
1220	(14*10^182000+229)/9	182001	Robert Price	03/2018
1221	(10^181996+41)/3	181996	Robert Price	12/2017
1222	(5*10^181950-101)/3	181951	Robert Price	04/2018
1223	2^603915+75233	181797	Enzo Doria	04/2016
1224	7*10^181594-57	181595	Robert Price	06/2020
1225	(194*10^181369-11)/3	181371	Robert Price	09/2020
1226	11^174145-360	181354	Enzo Doria	10/2012
1227	2^602351-396765	181326	Enzo Doria	08/2013
1228	6*10^181306+17	181307	Robert Price	04/2019
1229	2^601957-113833	181208	Enzo Doria	09/2014
1230	66^99581-65^99581	181193	Robert Price	09/2013
1231	10^181182+383973	181183	Patrick De Geest	04/2016
1232	10^181182-21	181182	Serge Batalov	12/2014
1233	(5*10^181127-29)/3	181128	Robert Price	03/2018
1234	2^601521-29143	181076	Enzo Doria	07/2015
1235	2^601442-2797811	181053	Enzo Doria	04/2016
1236	44*10^181029+3	181031	Robert Price	04/2020
1237	5*10^180992-9	180993	Robert Price	05/2015
1238	10^180979+79477	180980	Patrick De Geest	04/2016
1239	10^180979+107739	180980	Patrick De Geest	04/2016
1240	10^180979-11	180979	Serge Batalov	12/2014
1241	2^601023-113851	180926	Enzo Doria	10/2014
1242	(23*10^180862-143)/3	180863	Robert Price	12/2019
1243	3*10^180852+29	180853	Robert Price	05/2018
1244	(79*10^180710-1)/3	180712	Robert Price	02/2020
1245	2^600300-1852559	180709	Enzo Doria	08/2015
1246	(10^180689+71)/9	180689	Serge Batalov	07/2015
1247	2^600209+76487	180681	Enzo Doria	05/2016
1248	2^599702-369885	180529	Enzo Doria	11/2013
1249	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
1250	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015

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Probable Primes Top 10000

(271023 PRPs in the top)