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	63722^51915+51915^63722	300468	Hans Havermann	06/2021
1002	2^998053+1879667	300444	Enzo Doria	09/2016
1003	77018^7959+7959^77018	300437	Hans Havermann	07/2021
1004	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
1005	2^997689+217787	300335	Enzo Doria	01/2024
1006	69478^20987+20987^69478	300281	Hans Havermann	07/2021
1007	64088^48393+48393^64088	300239	Hans Havermann	07/2021
1008	64605^44146+44146^64605	300084	Hans Havermann	08/2021
1009	2^996845+29027	300081	Enzo Doria	02/2024
1010	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
1011	67594^27465+27465^67594	300035	Hans Havermann	06/2021
1012	10^300000+287389	300001	Patrick De Geest	10/2019
1013	10^300000-83657	300000	Patrick De Geest	10/2019
1014	70599^17756+17756^70599	300000	Hans Havermann	06/2021
1015	numbpart(72526161452)	299999	Serge Batalov	04/2017
1016	2^996182-114431	299881	Enzo Doria	02/2015
1017	3*2^996126+5	299865	Jon Grantham	07/2023
1018	2^996034-17	299837	Stefano Morozzi	07/2022
1019	(19*10^299640+77)/3	299641	Robert Price	03/2023
1020	2^995214-2788361	299590	Enzo Doria	12/2015
1021	2^994791-114319	299462	Enzo Doria	01/2015
1022	2^994490-1863791	299372	Enzo Doria	01/2016
1023	2^993322+1885729	299020	Enzo Doria	03/2017
1024	(36395^65536+36393^65536)/2	298913	Kellen Shenton	04/2022
1025	2^992711-2788807	298836	Enzo Doria	12/2015
1026	2^992525-114199	298780	Enzo Doria	12/2014
1027	(7^353501-3^353501)/4	298743	Jon Grantham	08/2023
1028	2^992329+1884707	298721	Enzo Doria	02/2017
1029	2^992052+215491	298638	Enzo Doria	11/2023
1030	2^991968-23	298613	Stefano Morozzi	07/2022
1031	2^991715-19	298536	Stefano Morozzi	07/2022
1032	(10^298414+7)/191/823/56921/1334467	298398	Alfred Reich	10/2021
1033	2^989562+25	297888	Stefano Morozzi	05/2021
1034	2^988580+214051	297593	Enzo Doria	10/2023
1035	2^988537+218837	297580	Enzo Doria	03/2024
1036	(19*10^297497+77)/3	297498	Robert Price	03/2023
1037	(2*10^297488-23)/3	297488	Robert Price	10/2022
1038	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
1039	2^985217-114553	296580	Enzo Doria	03/2015
1040	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
1041	2^984650+21529	296410	Enzo Doria	08/2023
1042	2^984131-1828009	296253	Enzo Doria	01/2015
1043	2^983620+60451	296100	Phil Moore	03/2008
1044	2^982721-2683	295829	Yves Minet	02/2016
1045	(23*10^295581+7)/3	295582	Robert Price	05/2023
1046	2^981298-2788421	295401	Enzo Doria	12/2015
1047	2^981163-2790967	295360	Enzo Doria	12/2015
1048	2^981016-15	295316	Stefano Morozzi	07/2022
1049	8*10^295160-13	295161	Robert Price	08/2023
1050	2^979594+1865839	294888	Enzo Doria	02/2016
1051	2^979502+221029	294860	Enzo Doria	03/2024
1052	2*10^294527-91	294528	Robert Price	02/2023
1053	(49363^63001-1)/(49363^251-1)	294511	Ryan Propper	11/2023
1054	10^294475+49	294476	Robert Price	02/2023
1055	(11*10^294308+91)/3	294309	Robert Price	03/2023
1056	2^976760+1885021	294035	Enzo Doria	02/2017
1057	3*2^976518+5	293962	Jon Grantham	07/2023
1058	2^975798+218599	293745	Enzo Doria	01/2024
1059	2^974441+1878407	293336	Enzo Doria	08/2016
1060	2^974180+1876831	293258	Enzo Doria	07/2016
1061	2^974170+453319	293255	Enzo Doria	01/2017
1062	(211^126023-1)/210	292911	Anonymous	05/2024
1063	2^972744-114419	292826	Enzo Doria	03/2015
1064	11^281143+6	292781	Paul Bourdelais	03/2021
1065	(4*10^292619-91)/3	292620	Robert Price	12/2022
1066	E(69468)/13247122135	292549	Sergey Batalov	10/2023
1067	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
1068	3*10^292344-97	292345	Robert Price	01/2023
1069	2^970911+1873373	292274	Enzo Doria	07/2016
1070	2^970670+383059	292201	Enzo Doria	12/2016
1071	2^970141-100363	292042	Enzo Doria	02/2014
1072	2^969945+1874717	291983	Enzo Doria	06/2016
1073	2^969384+1880701	291814	Enzo Doria	10/2016
1074	(13*10^291721-43)/3	291722	Robert Price	08/2023
1075	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
1076	3*2^963892+5	290161	Jon Grantham	07/2023
1077	(151*10^289877-1)/3	289879	Robert Price	07/2023
1078	2^962194+60139	289650	Enzo Doria	02/2016
1079	2^959307-1861507	288781	Enzo Doria	11/2015
1080	(17*10^288692+31)/3	288693	Robert Price	04/2023
1081	14^251797-3	288592	Paul Bourdelais	12/2020
1082	(8745^73441-1)/(8745^271-1)	288419	Ryan Propper	11/2023
1083	(2*10^288371-23)/3	288371	Robert Price	10/2022
1084	(31*10^288238-1)/3	288240	Robert Price	02/2023
1085	(7^341063-2^341063)/5	288231	Jon Grantham	08/2023
1086	2^957372+283531	288198	Enzo Doria	02/2017
1087	2^957192-1864049	288144	Enzo Doria	01/2016
1088	(95774^58081-1)/(95774^241-1)	288116	Ryan Propper	11/2023
1089	2^956446+1875199	287919	Enzo Doria	06/2016
1090	2^956283+219143	287870	Enzo Doria	02/2024
1091	7*10^287854+39	287855	Robert Price	01/2023
1092	2^956082+28309	287810	Enzo Doria	02/2024
1093	(17^233689+1)/18	287542	Paul Bourdelais	09/2013
1094	2^955178+1883587	287538	Enzo Doria	12/2016
1095	2^954127-954127^2	287221	Henri Lifchitz	01/2021
1096	2^954001+1875257	287183	Enzo Doria	07/2016
1097	2*10^287175-49	287176	Robert Price	05/2023
1098	(22*10^287085-19)/3	287086	Robert Price	07/2023
1099	2^953488+22411	287029	Enzo Doria	09/2023
1100	(23891^65536+1)/2	286932	Serge Batalov	03/2018
1101	5*3^601336-2^601336	286911	Jon Grantham	08/2023
1102	2^952268+1878601	286662	Enzo Doria	09/2016
1103	2^950801+81557	286220	Enzo Doria	08/2016
1104	2^949403+217523	285799	Enzo Doria	01/2024
1105	22845^65536+22844^65536	285658	Kellen Shenton	03/2021
1106	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
1107	(54^164839+1)/55	285565	Paul Bourdelais	07/2019
1108	2^948510+782569	285530	Enzo Doria	10/2016
1109	2^948374-114137	285490	Enzo Doria	01/2015
1110	2^947739+1872923	285298	Enzo Doria	06/2016
1111	2^946274+218407	284857	Enzo Doria	03/2024
1112	7*10^284751+9	284752	Robert Price	04/2023
1113	2^944561-21	284342	Stefano Morozzi	07/2022
1114	(4*10^284330-31)/9	284330	Serge Batalov	11/2022
1115	(32*10^283826-23)/9	283827	Serge Batalov	01/2023
1116	2^942533+82067	283731	Enzo Doria	09/2016
1117	2^941469+39	283411	Jon Grantham	08/2023
1118	(10^283342-31)/3	283342	Robert Price	03/2023
1119	2^940950+1874989	283255	Enzo Doria	06/2016
1120	2^940426-2786141	283097	Enzo Doria	11/2015
1121	(2*10^282948-11)/9	282948	Serge Batalov	11/2022
1122	2^939881-114115	282933	Enzo Doria	12/2014
1123	(14*10^282673-143)/3	282674	Robert Price	05/2023
1124	10^282493+632551	282494	Patrick De Geest	02/2017
1126	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
1125	10^282493-132327	282493	Patrick De Geest	02/2017
1127	3^591827-2^591827	282374	Mike Oakes	08/2009
1128	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
1129	2^936716-1835519	281980	Enzo Doria	04/2015
1130	2^936588+79411	281942	Enzo Doria	06/2016
1131	2^936047+1877423	281779	Enzo Doria	08/2016
1132	2^935713+1869377	281678	Enzo Doria	05/2016
1133	2^933082+1877059	280886	Enzo Doria	08/2016
1134	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
1135	2^932064+26521	280580	Enzo Doria	12/2023
1136	2^931976+25	280553	Stefano Morozzi	05/2021
1137	(42^172663+1)/43	280274	Paul Bourdelais	07/2019
1138	(10^279978+11)/3	279978	Serge Batalov	07/2015
1139	2^929524-1864829	279815	Enzo Doria	01/2016
1140	2^929329+22697	279756	Enzo Doria	09/2023
1141	2^929152+60181	279703	Enzo Doria	02/2016
1142	2^928621-2787883	279543	Enzo Doria	11/2015
1143	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
1144	3*10^279271+77	279272	Robert Price	06/2024
1145	2^927429+1882277	279184	Enzo Doria	12/2016
1146	2^926766-11	278985	Stefano Morozzi	07/2022
1147	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
1148	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
1149	(166*10^278633-7)/3	278635	Robert Price	02/2023
1150	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
1151	2^925330-1301	278553	Yves Minet	06/2015
1152	(299*10^278546+1)/3	278548	Robert Price	01/2023
1153	2^925299+216053	278543	Enzo Doria	11/2023
1154	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
1155	(266*10^278325+1)/3	278327	Robert Price	01/2023
1156	2^923261-69175	277930	Enzo Doria	11/2015
1157	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
1158	2^922301+57	277641	Stefano Morozzi	05/2021
1159	7*10^277478-39	277479	Robert Price	07/2023
1160	((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	277369	Serge Batalov	07/2016
1161	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
1162	2^920318+2792299	277044	Enzo Doria	02/2016
1163	(16*10^276537-31)/3	276538	Robert Price	03/2023
1164	2^918596-2786939	276525	Enzo Doria	11/2015
1165	2^917910+28369	276319	Enzo Doria	01/2024
1166	(6737^72361-1)/(6737^269-1)	276002	Ryan Propper	11/2023
1167	2^916639+60563	275936	Enzo Doria	04/2016
1168	(2*10^275922+1)/3	275922	Serge Batalov	11/2022
1169	2^916385-2786383	275860	Enzo Doria	11/2015
1170	2^915928+82081	275722	Enzo Doria	09/2016
1171	(4*10^275671+11)/3	275672	Tyler Busby	02/2023
1172	2^915576-114137	275616	Enzo Doria	01/2015
1173	2^914828+1876741	275391	Enzo Doria	07/2016
1174	2^914757-2203	275370	Yves Minet	12/2015
1175	7*10^275157-27	275158	Robert Price	11/2022
1176	2^912744+20011	274764	Enzo Doria	06/2023
1177	2^911900+1871245	274510	Enzo Doria	05/2016
1178	(16*10^274251-91)/3	274252	Robert Price	11/2022
1179	2^910999+9	274239	Stefano Morozzi	05/2021
1180	(2^910869-7)/5	274199	Stefano Morozzi	08/2022
1181	2^910490+283429	274085	Enzo Doria	01/2017
1182	7*10^273983+39	273984	Robert Price	01/2023
1183	2^909988-1862249	273934	Enzo Doria	12/2015
1184	2^909297+1879157	273726	Enzo Doria	08/2016
1185	2^909257-1864423	273714	Enzo Doria	01/2016
1186	2^909254+31309	273713	Enzo Doria	03/2024
1187	2^908739-7	273558	Stefano Morozzi	07/2022
1188	2^908579-1861747	273510	Enzo Doria	12/2015
1189	3*2^908005-5	273338	Jon Grantham	07/2023
1190	2^907635-2791597	273226	Enzo Doria	01/2016
1191	2^907059+211193	273052	Enzo Doria	08/2023
1192	(53^158341+1)/54	273022	Paul Bourdelais	07/2019
1193	2^906594-113201	272912	Enzo Doria	08/2014
1194	9*10^272800+91	272801	Robert Price	05/2023
1195	2*10^272710-49	272711	Robert Price	05/2023
1196	2*10^272403-91	272404	Robert Price	02/2023
1197	2^904773+1872167	272364	Enzo Doria	06/2016
1198	6^349903+5	272278	Paul Bourdelais	02/2021
1199	2^904149-1862473	272176	Enzo Doria	12/2015
1200	(7*10^271757-61)/9	271757	Erik Branger	03/2012
1201	2^902497+1880117	271679	Enzo Doria	09/2016
1202	2^901858+77689	271487	Enzo Doria	06/2016
1203	2^901372+1875301	271341	Enzo Doria	06/2016
1204	2^901146+219049	271272	Enzo Doria	02/2024
1205	(8*10^271039-77)/3	271040	Robert Price	04/2023
1206	2^899999+1144031	270927	Norman Luhn	09/2023
1207	2*10^270802-91	270803	Robert Price	02/2023
1208	23*10^270799-7	270801	Robert Price	10/2022
1209	2^899121-115033	270663	Enzo Doria	07/2015
1210	2^898900+883021	270596	Enzo Doria	12/2016
1211	2^898762-251511	270555	Enzo Doria	12/2013
1212	2^898589+47	270503	Lelio R Paula	03/2016
1213	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
1214	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
1215	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
1216	2^897867-3217	270285	Yves Minet	12/2016
1217	2^897849-115273	270280	Enzo Doria	07/2015
1218	2^897367+26289	270135	Enzo Doria	03/2024
1219	2^896616-114179	269909	Enzo Doria	12/2014
1220	(12648^66049-1)/(12648^257-1)	269881	Ryan Propper	11/2023
1221	(22*10^269517-19)/3	269518	Robert Price	07/2023
1222	10^(2134739+1)-710^134739-1	269479	Robert Price	07/2023
1223	2^894928+583561	269401	Enzo Doria	04/2017
1224	2^894673-39343	269324	Enzo Doria	08/2015
1225	2^893836+23221	269072	Enzo Doria	10/2023
1226	2^892718+29539	268735	Enzo Doria	03/2024
1227	2^892660+213901	268718	Enzo Doria	10/2023
1228	F(1285607)	268676	Henri Lifchitz	11/2008
1229	2^892234+22189	268590	Enzo Doria	09/2023
1230	2^892151+24863	268565	Enzo Doria	11/2023
1231	2^892112+187663	268553	Enzo Doria	08/2016
1232	(266*10^268407-17)/3	268409	Robert Price	02/2023
1233	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
1234	2^890957-69583	268205	Enzo Doria	12/2015
1235	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
1236	2^890122-351401	267954	Enzo Doria	07/2015
1237	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
1238	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
1239	(1005^89087-1)/1004	267451	Jinyuan Wang	01/2024
1240	(485^99523-1)/484	267291	Michael Stocker	05/2020
1241	2^886324+77791	266811	Enzo Doria	06/2016
1242	7*10^266731+87	266732	Robert Price	11/2022
1243	2^886040+213901	266725	Enzo Doria	10/2023
1244	2^885242+217909	266485	Enzo Doria	01/2024
1245	2^884738+26809	266333	Enzo Doria	12/2023
1246	2^884714+1880527	266326	Enzo Doria	10/2016
1247	7*10^266024-47	266025	Robert Price	08/2023
1248	11^255426+255426^11	265999	Serge Batalov	05/2014
1249	2^883462-343421	265949	Enzo Doria	07/2015
1250	2^883442+1875019	265943	Enzo Doria	06/2016

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