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	82358^82358+2025^2025	404848	Henri Lifchitz	01/2025
1002	9*10^404644-11	404645	Mischa Rodermond	04/2023
1003	2^1343509+237947	404437	Enzo Doria	07/2025
1004	1215^131072+242^131072	404302	Kellen Shenton	08/2022
1005	2^1341908+212911	403955	Enzo Doria	09/2023
1006	2^1341625+226187	403870	Enzo Doria	09/2024
1007	2^1340881+53255	403646	Enzo Doria	01/2026
1008	2^1340284+43801	403466	Enzo Doria	04/2025
1009	2^1340172+240991	403432	Enzo Doria	10/2025
1010	1196^131072+595^131072	403405	Kellen Shenton	08/2022
1011	2^1339302+29389	403171	Enzo Doria	04/2024
1012	2^1335130+31669	401915	Enzo Doria	07/2024
1013	2^1333062+236449	401292	Enzo Doria	07/2025
1014	2^1330791+46763	400609	Enzo Doria	06/2025
1015	2^1330712+45631	400585	Enzo Doria	05/2025
1016	2^1330388+38527	400487	Enzo Doria	11/2024
1017	2^1330371+28313	400482	Enzo Doria	03/2024
1018	2^1330120+247831	400407	Enzo Doria	05/2026
1019	10^400310+9	400311	Boyan Hu	06/2025
1020	10^400000+1415223	400001	Patrick De Geest	10/2020
1021	10^400000-339233	400000	Patrick De Geest	10/2020
1022	2^1327766+48019	399698	Enzo Doria	06/2025
1023	2^1325567+248603	399036	Enzo Doria	05/2026
1024	2^1323373+27317	398375	Enzo Doria	01/2024
1025	Tau(863^24630)	397727	Nik Lygeros / Olivier Rozier	01/2016
1026	2^1320423+24293	397487	Enzo Doria	11/2023
1027	2^1320158+247939	397408	Enzo Doria	05/2026
1028	2^1320057+211517	397377	Enzo Doria	08/2023
1029	2^1319770+1884949	397291	Enzo Doria	06/2017
1030	2^1319616+30091	397244	Enzo Doria	04/2024
1031	2^1317657+31367	396655	Enzo Doria	04/2024
1032	2^1316848+43021	396411	Enzo Doria	02/2025
1033	2^1316687+45983	396363	Enzo Doria	05/2025
1034	2^1315753+226187	396082	Enzo Doria	09/2024
1035	2^1314741+219257	395777	Enzo Doria	03/2024
1036	2^1313062+1888849	395272	Enzo Doria	08/2017
1037	(1073516^81920+1)/(1073516^16384+1)	395236	Serge Batalov	01/2017
1038	2^1312349+221177	395057	Enzo Doria	04/2024
1039	(1059995^81920+1)/(1059995^16384+1)	394875	Serge Batalov	01/2017
1040	2^1311618+783529	394837	Enzo Doria	01/2017
1041	2^1310192+232531	394408	Enzo Doria	03/2025
1042	2^1308992+28111	394046	Enzo Doria	02/2024
1043	2^1308000+1883521	393748	Enzo Doria	02/2017
1044	2^1307563+232133	393616	Enzo Doria	03/2025
1045	2^1307324+224611	393544	Enzo Doria	07/2024
1046	2^1307262+28759	393526	Enzo Doria	02/2024
1047	(1009565^81920+1)/(1009565^16384+1)	393487	Serge Batalov	01/2017
1048	2^1306643+47333	393339	Enzo Doria	07/2025
1049	2^1305860+35461	393104	Enzo Doria	08/2024
1050	(995042^81920+1)/(995042^16384+1)	393075	Serge Batalov	01/2017
1051	2^1305333+47717	392945	Enzo Doria	06/2025
1052	2^1305200+54571	392905	Enzo Doria	01/2026
1053	(988945^81920+1)/(988945^16384+1)	392900	Serge Batalov	01/2017
1054	(988823^81920+1)/(988823^16384+1)	392897	Serge Batalov	01/2017
1055	(2^1304983-1)/52199321	392832	Tony Prest / Never Odd Or Even	03/2014
1056	2^1304675+243713	392747	Enzo Doria	01/2026
1057	(978970^81920+1)/(978970^16384+1)	392612	Serge Batalov	01/2017
1058	2^1303816+38251	392488	Enzo Doria	11/2024
1059	2^1303257+48527	392320	Enzo Doria	07/2025
1060	2^1303102+1866409	392273	Enzo Doria	09/2017
1061	2^1302818+283429	392188	Enzo Doria	01/2017
1062	2^1301430+22669	391770	Enzo Doria	10/2023
1063	2^1301229+222467	391709	Enzo Doria	04/2024
1064	2^1300835+232523	391591	Enzo Doria	03/2025
1065	(934422^81920+1)/(934422^16384+1)	391286	Serge Batalov	01/2017
1066	2^1299181+1886867	391093	Enzo Doria	04/2017
1067	(37^249341-1)/36	391016	Paul Bourdelais	08/2020
1068	2^1298304+1882891	390829	Enzo Doria	01/2017
1069	2^1297732+228721	390657	Enzo Doria	11/2024
1070	Phi(87181,13#)	390354	Henri Lifchitz	02/2026
1071	2^1295728+240751	390053	Enzo Doria	09/2025
1072	95196^12497+12497^95196	390000	Hans Havermann	12/2021
1073	2^1295539+35633	389997	Enzo Doria	08/2024
1074	86206^33381+33381^86206	389953	Hans Havermann	05/2023
1075	2^1294976+236731	389827	Enzo Doria	06/2025
1076	2^1294324+25171	389631	Enzo Doria	12/2023
1077	2^1294298+243649	389623	Enzo Doria	01/2026
1078	128^184830+127	389476	Alfred Reich	06/2026
1079	(874207^81920+1)/(874207^16384+1)	389390	Serge Batalov	01/2017
1080	2^1292338+229249	389033	Enzo Doria	11/2024
1081	2^1289624+32551	388216	Enzo Doria	05/2024
1082	2^1286857+37967	387383	Enzo Doria	10/2024
1083	2^1285458+46159	386962	Enzo Doria	06/2025
1084	2^1285456+230611	386961	Enzo Doria	01/2025
1085	(7^457871-5^457871)/2	386946	Jon Grantham	08/2023
1086	79455^73828+73828^79455	386805	Hans Havermann	03/2023
1087	81650^54369+54369^81650	386642	Yusuf AttarBashi	06/2021
1088	80565^62824+62824^80565	386561	Hans Havermann	08/2021
1089	83747^41272+41272^83747	386548	Hans Havermann	08/2021
1090	15^328574+328574^15	386434	Serge Batalov	05/2014
1091	2^1283304+53551	386313	Enzo Doria	01/2026
1092	2^1283177+57887	386275	Enzo Doria	06/2026
1093	2^1283147+54833	386266	Enzo Doria	02/2026
1094	2^1282676+30493	386124	Enzo Doria	12/2024
1095	2^1280078+1885099	385342	Enzo Doria	08/2017
1096	2^1279921+17	385295	Stefano Morozzi	10/2022
1097	2^1279245+224087	385092	Enzo Doria	07/2024
1098	2^1278091+47963	384744	Enzo Doria	07/2025
1099	2^1277980+231391	384711	Enzo Doria	01/2025
1100	2^1277688+231241	384623	Enzo Doria	01/2025
1101	2^1277142+234979	384459	Enzo Doria	04/2025
1102	2^1276977+71657	384409	Enzo Doria	08/2023
1103	(76803^78961-1)/(76803^281-1)	384382	Ryan Propper	11/2023
1104	2^1276571+26213	384287	Enzo Doria	12/2023
1105	MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832,26908)	384166	Sergey Batalov	05/2024
1106	2^1274941+1880717	383796	Enzo Doria	10/2016
1107	15^325833+14	383210	Alfred Reich	06/2026
1108	2^1272632+383431	383101	Enzo Doria	01/2017
1109	2^1271346+1889839	382714	Enzo Doria	08/2017
1110	2^1271173+219587	382662	Enzo Doria	03/2024
1111	2^1266263+239783	381184	Enzo Doria	09/2025
1112	5*3^798534-2^798534	380999	Jon Grantham	08/2023
1113	(10^380976-7)/3	380976	Leonid Durman	01/2012
1114	2^1264748+23221	380728	Enzo Doria	11/2023
1115	2^1262877+56897	380164	Enzo Doria	04/2026
1116	(4*10^380056+11)/3	380057	Tyler Busby	03/2023
1117	2^1262504+242821	380052	Enzo Doria	12/2025
1118	2^1262431+228353	380030	Enzo Doria	11/2024
1119	2^1260859+222683	379557	Enzo Doria	06/2024
1120	2^1258313+43727	378790	Enzo Doria	03/2025
1121	2^1257787+1447761	378632	Makoto Morimoto	10/2013
1122	(2^1257787+32270)/(223328122073011)	378620	Makoto Morimoto	12/2016
1123	2^1257728+20851	378614	Enzo Doria	08/2023
1124	(77^200657-1)/76	378536	Paul Bourdelais	08/2020
1125	2^1257107+45413	378427	Enzo Doria	05/2025
1126	2^1254797+229487	377732	Enzo Doria	11/2024
1127	(98^189619+1)/99	377573	Paul Bourdelais	02/2021
1128	Phi(17#,12492)	377546	Henri Lifchitz	10/2025
1129	F(1803059)	376817	Henri Lifchitz	06/2009
1130	2^1250590+29389	376466	Enzo Doria	03/2024
1131	(10^376417-3^376417)/7	376417	Jon Grantham	08/2023
1132	2^1250116+34951	376323	Enzo Doria	08/2024
1133	2^1248318+51859	375782	Enzo Doria	11/2025
1134	2^1248184-57329	375741	Enzo Doria	05/2026
1135	2^1246724+213961	375302	Enzo Doria	10/2023
1136	2^1246340+54961	375186	Enzo Doria	02/2026
1137	2^1245610+237919	374966	Enzo Doria	06/2025
1138	2^1245230+19	374852	Stefano Morozzi	10/2022
1139	2^1244480+52021	374626	Enzo Doria	11/2025
1140	2^1244368+247771	374593	Enzo Doria	04/2026
1141	2^1244263+230033	374561	Enzo Doria	01/2025
1142	7^442674+4	374103	Paul Bourdelais	02/2021
1143	2^1242374+240919	373992	Enzo Doria	09/2025
1144	2^1242268+239641	373960	Enzo Doria	08/2025
1145	2^1239939+242513	373259	Enzo Doria	12/2025
1146	2^1239151+35633	373022	Enzo Doria	08/2024
1147	2^1238732+39181	372896	Enzo Doria	11/2024
1148	2^1237699+34703	372585	Enzo Doria	07/2024
1149	(97^187393-1)/96	372306	Paul Bourdelais	09/2020
1150	2^1235070+46219	371794	Enzo Doria	05/2025
1151	10^371696+7	371697	Alfred Reich	05/2021
1152	2^1234709+883127	371685	Enzo Doria	12/2016
1153	2^1234688+237151	371679	Enzo Doria	08/2025
1154	2^1234119+21803	371507	Enzo Doria	09/2023
1155	(67^203431+1)/68	371479	Paul Bourdelais	09/2021
1156	2^1233971+216593	371463	Enzo Doria	12/2023
1157	2^1233212+27301	371234	Enzo Doria	12/2023
1158	2^1231847+244103	370823	Enzo Doria	01/2026
1159	2^1231529+237557	370728	Enzo Doria	06/2025
1160	2^1231466+283819	370709	Enzo Doria	07/2017
1161	2^1229766+26659	370197	Enzo Doria	12/2023
1162	2^1228899+30713	369936	Enzo Doria	03/2024
1163	2^1228892+223831	369934	Enzo Doria	06/2024
1164	2^1227635+45413	369555	Enzo Doria	05/2025
1165	(49627^78961-1)/(49627^281-1)	369460	Ryan Propper	11/2023
1166	2^1227060+226663	369382	Enzo Doria	09/2024
1167	2^1226987+28163	369360	Enzo Doria	02/2024
1168	2^1226725+234887	369282	Enzo Doria	04/2025
1169	2^1226569+30857	369235	Enzo Doria	03/2024
1170	2^1225268+46591	368843	Enzo Doria	05/2025
1171	73^197880+197880	368715	Kellen Shenton	06/2023
1172	2^1223601+242357	368341	Enzo Doria	11/2025
1173	5*3^771723-2^771723	368207	Jon Grantham	08/2023
1174	2^1222741+231707	368082	Enzo Doria	02/2025
1175	2^1222473+221597	368002	Enzo Doria	04/2024
1176	2^1222211+22703	367923	Enzo Doria	11/2023
1177	(2^1222097+19)/3	367888	Stefano Morozzi	09/2022
1178	2^1220335+1881263	367358	Enzo Doria	11/2016
1179	2^1219565+49967	367126	Enzo Doria	03/2026
1180	2^1219561+47897	367125	Enzo Doria	09/2025
1181	2^1219351+240773	367062	Enzo Doria	09/2025
1182	2^1219016+53041	366961	Enzo Doria	12/2025
1183	2^1218344+215641	366759	Enzo Doria	12/2023
1184	2^1217510+220039	366508	Enzo Doria	03/2024
1185	2^1217500+226321	366505	Enzo Doria	09/2024
1186	(233^154787-1)/232	366434	Anonymous	05/2024
1187	2^1216694+1884769	366262	Enzo Doria	02/2017
1188	2^1216267+45143	366133	Enzo Doria	05/2025
1189	2^1215889-3	366020	Paul Bourdelais	06/2019
1190	2^1215296+1885441	365841	Enzo Doria	03/2017
1191	(80^192133+1)/81	365645	Paul Bourdelais	01/2021
1192	2^1214307+1888115	365543	Enzo Doria	05/2017
1193	2^1213815+3	365395	Paul Bourdelais	06/2019
1194	(80^191953+1)/81	365302	Paul Bourdelais	01/2021
1195	2^1213313+215837	365244	Enzo Doria	11/2023
1196	2^1208816+55081	363890	Enzo Doria	02/2026
1197	2^1208276+22201	363728	Enzo Doria	09/2023
1198	2^1207345+1882577	363448	Enzo Doria	12/2016
1199	2^1207336+217801	363445	Enzo Doria	03/2024
1200	2^1207073+883727	363366	Enzo Doria	03/2017
1201	3^761457-2	363308	Ryan Propper	07/2015
1202	(10^363030+7)/337/443	363025	Alfred Reich	12/2021
1203	2^1204869+224885	362702	Enzo Doria	07/2024
1204	2^1204540+237541	362603	Enzo Doria	07/2025
1205	2^1203721+44117	362357	Enzo Doria	04/2025
1206	2^1203309+54857	362233	Enzo Doria	02/2026
1207	2^1200972+141811	361529	Stefano Morozzi	10/2022
1208	(2^1200924+324730)/2	361514	Stefano Morozzi	06/2021
1209	(2^1200912+274110)/2	361511	Stefano Morozzi	01/2021
1210	2^1200906+165249	361509	Stefano Morozzi	07/2022
1211	2^1200890+166339	361504	Stefano Morozzi	01/2023
1212	(2^1200887+344126)/2	361503	Stefano Morozzi	10/2020
1213	2^1200877+186755	361500	Stefano Morozzi	09/2022
1214	2^1200861+198521	361496	Stefano Morozzi	11/2021
1215	(2^1200856+305790)/2	361494	Stefano Morozzi	10/2020
1216	(2^1200853+372822)/2	361493	Stefano Morozzi	06/2021
1217	2^1200812+324178)/2	361481	Stefano Morozzi	06/2021
1218	(2^1200768+380458)/2	361467	Stefano Morozzi	01/2021
1219	2^1200756+140917	361464	Stefano Morozzi	05/2022
1220	2^1200741+184781	361460	Stefano Morozzi	09/2022
1221	(2^1200741+293402)/2	361459	Stefano Morozzi	07/2021
1222	2^1200734+142653	361457	Stefano Morozzi	02/2023
1224	2^1200672+1880881	361439	Enzo Doria	10/2016
1223	2^1200672+141535	361439	Stefano Morozzi	09/2022
1225	2^1200669+178805	361438	Stefano Morozzi	11/2022
1226	2^1200660+198555	361435	Stefano Morozzi	12/2021
1227	2^1200657+164837	361434	Stefano Morozzi	05/2022
1228	2^1200631+166431	361426	Stefano Morozzi	02/2023
1229	2^1200627+150669	361425	Stefano Morozzi	02/2023
1230	(2^1200603+356030)/2	361418	Stefano Morozzi	10/2020
1231	(2^1200590+275854)/2	361414	Stefano Morozzi	03/2021
1232	2^1200550+139297	361402	Stefano Morozzi	10/2021
1233	2^1200486+172855	361383	Stefano Morozzi	01/2023
1234	(2^1200456+320526)/2	361373	Stefano Morozzi	10/2020
1235	2^1200443+142121	361370	Stefano Morozzi	01/2023
1236	2^1200416+164065	361362	Stefano Morozzi	01/2022
1237	2^1200331+155429	361336	Stefano Morozzi	10/2021
1239	(2^1200289+348366)/2	361323	Stefano Morozzi	10/2020
1238	2^1200289+141885	361323	Stefano Morozzi	11/2022
1240	(2^1200284+273162)/2	361322	Stefano Morozzi	10/2020
1241	2^1200252+194535	361312	Stefano Morozzi	11/2021
1242	(2^1200250+364230)/2	361311	Stefano Morozzi	10/2020
1243	2^1200227+156881	361305	Stefano Morozzi	05/2022
1244	(2^1200209+305990)/2	361299	Stefano Morozzi	10/2020
1245	(2^1200210+376278)/2	361299	Stefano Morozzi	10/2020
1246	2^1200202+216499	361297	Enzo Doria	12/2023
1247	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021
1248	2^1200178+149193	361290	Stefano Morozzi	07/2022
1249	2^1200168+140403	361287	Stefano Morozzi	03/2022
1250	(2^1200162+275910)/2	361285	Stefano Morozzi	03/2021

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Probable Primes Top 10000

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