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	2^1327766+48019	399698	Enzo Doria	06/2025
1002	2^1325567+248603	399036	Enzo Doria	05/2026
1003	2^1323373+27317	398375	Enzo Doria	01/2024
1004	Tau(863^24630)	397727	Nik Lygeros / Olivier Rozier	01/2016
1005	2^1320423+24293	397487	Enzo Doria	11/2023
1006	2^1320158+247939	397408	Enzo Doria	05/2026
1007	2^1320057+211517	397377	Enzo Doria	08/2023
1008	2^1319770+1884949	397291	Enzo Doria	06/2017
1009	2^1319616+30091	397244	Enzo Doria	04/2024
1010	2^1317657+31367	396655	Enzo Doria	04/2024
1011	2^1316848+43021	396411	Enzo Doria	02/2025
1012	2^1316687+45983	396363	Enzo Doria	05/2025
1013	2^1315753+226187	396082	Enzo Doria	09/2024
1014	2^1314741+219257	395777	Enzo Doria	03/2024
1015	2^1313062+1888849	395272	Enzo Doria	08/2017
1016	(1073516^81920+1)/(1073516^16384+1)	395236	Serge Batalov	01/2017
1017	2^1312349+221177	395057	Enzo Doria	04/2024
1018	(1059995^81920+1)/(1059995^16384+1)	394875	Serge Batalov	01/2017
1019	2^1311618+783529	394837	Enzo Doria	01/2017
1020	2^1310192+232531	394408	Enzo Doria	03/2025
1021	2^1308992+28111	394046	Enzo Doria	02/2024
1022	2^1308000+1883521	393748	Enzo Doria	02/2017
1023	2^1307563+232133	393616	Enzo Doria	03/2025
1024	2^1307324+224611	393544	Enzo Doria	07/2024
1025	2^1307262+28759	393526	Enzo Doria	02/2024
1026	(1009565^81920+1)/(1009565^16384+1)	393487	Serge Batalov	01/2017
1027	2^1306643+47333	393339	Enzo Doria	07/2025
1028	2^1305860+35461	393104	Enzo Doria	08/2024
1029	(995042^81920+1)/(995042^16384+1)	393075	Serge Batalov	01/2017
1030	2^1305333+47717	392945	Enzo Doria	06/2025
1031	2^1305200+54571	392905	Enzo Doria	01/2026
1032	(988945^81920+1)/(988945^16384+1)	392900	Serge Batalov	01/2017
1033	(988823^81920+1)/(988823^16384+1)	392897	Serge Batalov	01/2017
1034	(2^1304983-1)/52199321	392832	Tony Prest / Never Odd Or Even	03/2014
1035	2^1304675+243713	392747	Enzo Doria	01/2026
1036	(978970^81920+1)/(978970^16384+1)	392612	Serge Batalov	01/2017
1037	2^1303816+38251	392488	Enzo Doria	11/2024
1038	2^1303257+48527	392320	Enzo Doria	07/2025
1039	2^1303102+1866409	392273	Enzo Doria	09/2017
1040	2^1302818+283429	392188	Enzo Doria	01/2017
1041	2^1301430+22669	391770	Enzo Doria	10/2023
1042	2^1301229+222467	391709	Enzo Doria	04/2024
1043	2^1300835+232523	391591	Enzo Doria	03/2025
1044	(934422^81920+1)/(934422^16384+1)	391286	Serge Batalov	01/2017
1045	2^1299181+1886867	391093	Enzo Doria	04/2017
1046	(37^249341-1)/36	391016	Paul Bourdelais	08/2020
1047	2^1298304+1882891	390829	Enzo Doria	01/2017
1048	2^1297732+228721	390657	Enzo Doria	11/2024
1049	Phi(87181,13#)	390354	Henri Lifchitz	02/2026
1050	2^1295728+240751	390053	Enzo Doria	09/2025
1051	95196^12497+12497^95196	390000	Hans Havermann	12/2021
1052	2^1295539+35633	389997	Enzo Doria	08/2024
1053	86206^33381+33381^86206	389953	Hans Havermann	05/2023
1054	2^1294976+236731	389827	Enzo Doria	06/2025
1055	2^1294324+25171	389631	Enzo Doria	12/2023
1056	2^1294298+243649	389623	Enzo Doria	01/2026
1057	128^184830+127	389476	Alfred Reich	06/2026
1058	(874207^81920+1)/(874207^16384+1)	389390	Serge Batalov	01/2017
1059	2^1292338+229249	389033	Enzo Doria	11/2024
1060	2^1289624+32551	388216	Enzo Doria	05/2024
1061	2^1286857+37967	387383	Enzo Doria	10/2024
1062	2^1285458+46159	386962	Enzo Doria	06/2025
1063	2^1285456+230611	386961	Enzo Doria	01/2025
1064	(7^457871-5^457871)/2	386946	Jon Grantham	08/2023
1065	79455^73828+73828^79455	386805	Hans Havermann	03/2023
1066	81650^54369+54369^81650	386642	Yusuf AttarBashi	06/2021
1067	80565^62824+62824^80565	386561	Hans Havermann	08/2021
1068	83747^41272+41272^83747	386548	Hans Havermann	08/2021
1069	15^328574+328574^15	386434	Serge Batalov	05/2014
1070	2^1283304+53551	386313	Enzo Doria	01/2026
1071	2^1283177+57887	386275	Enzo Doria	06/2026
1072	2^1283147+54833	386266	Enzo Doria	02/2026
1073	2^1282676+30493	386124	Enzo Doria	12/2024
1074	2^1280078+1885099	385342	Enzo Doria	08/2017
1075	2^1279921+17	385295	Stefano Morozzi	10/2022
1076	2^1279245+224087	385092	Enzo Doria	07/2024
1077	2^1278091+47963	384744	Enzo Doria	07/2025
1078	2^1277980+231391	384711	Enzo Doria	01/2025
1079	2^1277688+231241	384623	Enzo Doria	01/2025
1080	2^1277142+234979	384459	Enzo Doria	04/2025
1081	2^1276977+71657	384409	Enzo Doria	08/2023
1082	(76803^78961-1)/(76803^281-1)	384382	Ryan Propper	11/2023
1083	2^1276571+26213	384287	Enzo Doria	12/2023
1084	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
1085	2^1274941+1880717	383796	Enzo Doria	10/2016
1086	15^325833+14	383210	Alfred Reich	06/2026
1087	2^1272632+383431	383101	Enzo Doria	01/2017
1088	2^1271346+1889839	382714	Enzo Doria	08/2017
1089	2^1271173+219587	382662	Enzo Doria	03/2024
1090	2^1266263+239783	381184	Enzo Doria	09/2025
1091	5*3^798534-2^798534	380999	Jon Grantham	08/2023
1092	(10^380976-7)/3	380976	Leonid Durman	01/2012
1093	2^1264748+23221	380728	Enzo Doria	11/2023
1094	2^1262877+56897	380164	Enzo Doria	04/2026
1095	(4*10^380056+11)/3	380057	Tyler Busby	03/2023
1096	2^1262504+242821	380052	Enzo Doria	12/2025
1097	2^1262431+228353	380030	Enzo Doria	11/2024
1098	2^1260859+222683	379557	Enzo Doria	06/2024
1099	2^1258313+43727	378790	Enzo Doria	03/2025
1100	2^1257787+1447761	378632	Makoto Morimoto	10/2013
1101	(2^1257787+32270)/(223328122073011)	378620	Makoto Morimoto	12/2016
1102	2^1257728+20851	378614	Enzo Doria	08/2023
1103	(77^200657-1)/76	378536	Paul Bourdelais	08/2020
1104	2^1257107+45413	378427	Enzo Doria	05/2025
1105	2^1254797+229487	377732	Enzo Doria	11/2024
1106	(98^189619+1)/99	377573	Paul Bourdelais	02/2021
1107	Phi(17#,12492)	377546	Henri Lifchitz	10/2025
1108	F(1803059)	376817	Henri Lifchitz	06/2009
1109	2^1250590+29389	376466	Enzo Doria	03/2024
1110	(10^376417-3^376417)/7	376417	Jon Grantham	08/2023
1111	2^1250116+34951	376323	Enzo Doria	08/2024
1112	2^1248318+51859	375782	Enzo Doria	11/2025
1113	2^1248184-57329	375741	Enzo Doria	05/2026
1114	2^1246724+213961	375302	Enzo Doria	10/2023
1115	2^1246340+54961	375186	Enzo Doria	02/2026
1116	2^1245610+237919	374966	Enzo Doria	06/2025
1117	2^1245230+19	374852	Stefano Morozzi	10/2022
1118	2^1244480+52021	374626	Enzo Doria	11/2025
1119	2^1244368+247771	374593	Enzo Doria	04/2026
1120	2^1244263+230033	374561	Enzo Doria	01/2025
1121	7^442674+4	374103	Paul Bourdelais	02/2021
1122	2^1242374+240919	373992	Enzo Doria	09/2025
1123	2^1242268+239641	373960	Enzo Doria	08/2025
1124	2^1239939+242513	373259	Enzo Doria	12/2025
1125	2^1239151+35633	373022	Enzo Doria	08/2024
1126	2^1238732+39181	372896	Enzo Doria	11/2024
1127	2^1237699+34703	372585	Enzo Doria	07/2024
1128	(97^187393-1)/96	372306	Paul Bourdelais	09/2020
1129	2^1235070+46219	371794	Enzo Doria	05/2025
1130	10^371696+7	371697	Alfred Reich	05/2021
1131	2^1234709+883127	371685	Enzo Doria	12/2016
1132	2^1234688+237151	371679	Enzo Doria	08/2025
1133	2^1234119+21803	371507	Enzo Doria	09/2023
1134	(67^203431+1)/68	371479	Paul Bourdelais	09/2021
1135	2^1233971+216593	371463	Enzo Doria	12/2023
1136	2^1233212+27301	371234	Enzo Doria	12/2023
1137	2^1231847+244103	370823	Enzo Doria	01/2026
1138	2^1231529+237557	370728	Enzo Doria	06/2025
1139	2^1231466+283819	370709	Enzo Doria	07/2017
1140	2^1229766+26659	370197	Enzo Doria	12/2023
1141	2^1228899+30713	369936	Enzo Doria	03/2024
1142	2^1228892+223831	369934	Enzo Doria	06/2024
1143	2^1227635+45413	369555	Enzo Doria	05/2025
1144	(49627^78961-1)/(49627^281-1)	369460	Ryan Propper	11/2023
1145	2^1227060+226663	369382	Enzo Doria	09/2024
1146	2^1226987+28163	369360	Enzo Doria	02/2024
1147	2^1226725+234887	369282	Enzo Doria	04/2025
1148	2^1226569+30857	369235	Enzo Doria	03/2024
1149	2^1225268+46591	368843	Enzo Doria	05/2025
1150	73^197880+197880	368715	Kellen Shenton	06/2023
1151	2^1223601+242357	368341	Enzo Doria	11/2025
1152	5*3^771723-2^771723	368207	Jon Grantham	08/2023
1153	2^1222741+231707	368082	Enzo Doria	02/2025
1154	2^1222473+221597	368002	Enzo Doria	04/2024
1155	2^1222211+22703	367923	Enzo Doria	11/2023
1156	(2^1222097+19)/3	367888	Stefano Morozzi	09/2022
1157	2^1220335+1881263	367358	Enzo Doria	11/2016
1158	2^1219565+49967	367126	Enzo Doria	03/2026
1159	2^1219561+47897	367125	Enzo Doria	09/2025
1160	2^1219351+240773	367062	Enzo Doria	09/2025
1161	2^1219016+53041	366961	Enzo Doria	12/2025
1162	2^1218344+215641	366759	Enzo Doria	12/2023
1163	2^1217510+220039	366508	Enzo Doria	03/2024
1164	2^1217500+226321	366505	Enzo Doria	09/2024
1165	(233^154787-1)/232	366434	Anonymous	05/2024
1166	2^1216694+1884769	366262	Enzo Doria	02/2017
1167	2^1216267+45143	366133	Enzo Doria	05/2025
1168	2^1215889-3	366020	Paul Bourdelais	06/2019
1169	2^1215296+1885441	365841	Enzo Doria	03/2017
1170	(80^192133+1)/81	365645	Paul Bourdelais	01/2021
1171	2^1214307+1888115	365543	Enzo Doria	05/2017
1172	2^1213815+3	365395	Paul Bourdelais	06/2019
1173	(80^191953+1)/81	365302	Paul Bourdelais	01/2021
1174	2^1213313+215837	365244	Enzo Doria	11/2023
1175	2^1208816+55081	363890	Enzo Doria	02/2026
1176	2^1208276+22201	363728	Enzo Doria	09/2023
1177	2^1207345+1882577	363448	Enzo Doria	12/2016
1178	2^1207336+217801	363445	Enzo Doria	03/2024
1179	2^1207073+883727	363366	Enzo Doria	03/2017
1180	3^761457-2	363308	Ryan Propper	07/2015
1181	(10^363030+7)/337/443	363025	Alfred Reich	12/2021
1182	2^1204869+224885	362702	Enzo Doria	07/2024
1183	2^1204540+237541	362603	Enzo Doria	07/2025
1184	2^1203721+44117	362357	Enzo Doria	04/2025
1185	2^1203309+54857	362233	Enzo Doria	02/2026
1186	2^1200972+141811	361529	Stefano Morozzi	10/2022
1187	(2^1200924+324730)/2	361514	Stefano Morozzi	06/2021
1188	(2^1200912+274110)/2	361511	Stefano Morozzi	01/2021
1189	2^1200906+165249	361509	Stefano Morozzi	07/2022
1190	2^1200890+166339	361504	Stefano Morozzi	01/2023
1191	(2^1200887+344126)/2	361503	Stefano Morozzi	10/2020
1192	2^1200877+186755	361500	Stefano Morozzi	09/2022
1193	2^1200861+198521	361496	Stefano Morozzi	11/2021
1194	(2^1200856+305790)/2	361494	Stefano Morozzi	10/2020
1195	(2^1200853+372822)/2	361493	Stefano Morozzi	06/2021
1196	2^1200812+324178)/2	361481	Stefano Morozzi	06/2021
1197	(2^1200768+380458)/2	361467	Stefano Morozzi	01/2021
1198	2^1200756+140917	361464	Stefano Morozzi	05/2022
1199	2^1200741+184781	361460	Stefano Morozzi	09/2022
1200	(2^1200741+293402)/2	361459	Stefano Morozzi	07/2021
1201	2^1200734+142653	361457	Stefano Morozzi	02/2023
1203	2^1200672+1880881	361439	Enzo Doria	10/2016
1202	2^1200672+141535	361439	Stefano Morozzi	09/2022
1204	2^1200669+178805	361438	Stefano Morozzi	11/2022
1205	2^1200660+198555	361435	Stefano Morozzi	12/2021
1206	2^1200657+164837	361434	Stefano Morozzi	05/2022
1207	2^1200631+166431	361426	Stefano Morozzi	02/2023
1208	2^1200627+150669	361425	Stefano Morozzi	02/2023
1209	(2^1200603+356030)/2	361418	Stefano Morozzi	10/2020
1210	(2^1200590+275854)/2	361414	Stefano Morozzi	03/2021
1211	2^1200550+139297	361402	Stefano Morozzi	10/2021
1212	2^1200486+172855	361383	Stefano Morozzi	01/2023
1213	(2^1200456+320526)/2	361373	Stefano Morozzi	10/2020
1214	2^1200443+142121	361370	Stefano Morozzi	01/2023
1215	2^1200416+164065	361362	Stefano Morozzi	01/2022
1216	2^1200331+155429	361336	Stefano Morozzi	10/2021
1218	(2^1200289+348366)/2	361323	Stefano Morozzi	10/2020
1217	2^1200289+141885	361323	Stefano Morozzi	11/2022
1219	(2^1200284+273162)/2	361322	Stefano Morozzi	10/2020
1220	2^1200252+194535	361312	Stefano Morozzi	11/2021
1221	(2^1200250+364230)/2	361311	Stefano Morozzi	10/2020
1222	2^1200227+156881	361305	Stefano Morozzi	05/2022
1223	(2^1200209+305990)/2	361299	Stefano Morozzi	10/2020
1224	(2^1200210+376278)/2	361299	Stefano Morozzi	10/2020
1225	2^1200202+216499	361297	Enzo Doria	12/2023
1226	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021
1227	2^1200178+149193	361290	Stefano Morozzi	07/2022
1228	2^1200168+140403	361287	Stefano Morozzi	03/2022
1229	(2^1200162+275910)/2	361285	Stefano Morozzi	03/2021
1230	2^1200157+168927	361284	Stefano Morozzi	02/2023
1231	2^1200134+141385	361277	Stefano Morozzi	08/2022
1232	(2^1200131+360150)/2	361276	Stefano Morozzi	10/2020
1233	(2^1200118+290718)/2	361272	Stefano Morozzi	01/2021
1234	2^1200022+192777	361243	Stefano Morozzi	09/2022
1235	2^1200021+149777	361243	Stefano Morozzi	10/2022
1236	Phi(451125,2^5)	361236	Henri Lifchitz	12/2025
1237	(64*10^360173-1)/243	360173	Serge Batalov	09/2014
1238	(59^203309+1)/60	360029	Paul Bourdelais	09/2021
1239	(2*10^359860-11)/9	359860	Rytis Slatkevicius	01/2023
1240	2^1195093+1882577	359759	Enzo Doria	12/2016
1241	3^753451+5*2^753451	359488	Jon Grantham	08/2023
1242	2^1193505+238397	359281	Enzo Doria	07/2025
1243	2^1192258+36739	358906	Enzo Doria	09/2024
1244	2^1192251+47183	358904	Enzo Doria	06/2025
1245	(6^461108-11)/5	358812	Paul Bourdelais	04/2019
1246	2^1191375+8543	358640	Phil Moore	06/2008
1247	2^1191335+50783	358628	Enzo Doria	10/2025
1248	2^1190972+1880191	358519	Enzo Doria	11/2016
1249	2^1190752+245041	358453	Enzo Doria	02/2026
1250	2^1189930+28549	358205	Enzo Doria	03/2024

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Probable Primes Top 10000

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