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	2^699740+25	210643	Stefano Morozzi	05/2021
1002	2^698929-2788423	210399	Enzo Doria	11/2015
1003	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
1004	2^698316+1878601	210215	Enzo Doria	08/2016
1005	2^697036+1878751	209829	Enzo Doria	08/2016
1006	6^269407+5	209640	Paul Bourdelais	02/2021
1007	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
1008	2^696254-115151	209594	Enzo Doria	06/2015
1009	(35^135623+1)/36	209410	Paul Bourdelais	07/2018
1010	2^694633+1887257	209106	Enzo Doria	05/2017
1011	2^693959+180923	208903	Enzo Doria	07/2016
1012	2^693462-1847561	208753	Enzo Doria	07/2015
1013	2^690890-59981	207979	Enzo Doria	11/2015
1014	(38^131591+1)/39	207884	Paul Bourdelais	07/2018
1015	2^690163+1877063	207760	Enzo Doria	07/2016
1016	7^245608-2	207563	Paul Bourdelais	01/2021
1017	2^689286-29381	207496	Enzo Doria	08/2015
1018	2^689122-114521	207447	Enzo Doria	04/2015
1019	2^688373+6077	207221	Enzo Doria	02/2016
1020	2^688201+1875527	207170	Enzo Doria	07/2016
1021	(42^127609+1)/43	207140	Paul Bourdelais	07/2018
1022	2^687619+81563	206994	Enzo Doria	08/2016
1023	2^686572-1845299	206679	Enzo Doria	07/2015
1024	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
1025	(2^685739+1)/(3*87774593)	206420	Gord Palameta	08/2018
1026	2^685578+3	206380	Paul Bourdelais	04/2012
1027	2^684836-49349	206157	Enzo Doria	10/2015
1028	(73^110603-1)/72	206088	Paul Bourdelais	06/2018
1029	2^684163-2790967	205954	Enzo Doria	12/2015
1030	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
1031	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
1032	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
1033	2^681545+467	205166	Lelio R Paula	11/2013
1034	2^681306+81049	205094	Enzo Doria	07/2016
1035	2^680697+1877057	204911	Enzo Doria	07/2016
1036	2^680415+71783	204826	Enzo Doria	04/2016
1037	2^679860-459995	204659	Enzo Doria	06/2015
1038	2^679593+1879547	204578	Enzo Doria	09/2016
1039	2^678651+1875023	204295	Enzo Doria	07/2016
1040	2^678561+678561	204268	Henri Lifchitz	05/2006
1041	2^678101-114043	204129	Enzo Doria	11/2014
1042	2^678028+1875631	204107	Enzo Doria	06/2016
1043	2^676992-59783	203795	Enzo Doria	10/2015
1044	2^676972+1866871	203789	Enzo Doria	03/2016
1045	2^676761-9	203726	Robert Price	01/2017
1046	2^676563-2792407	203666	Enzo Doria	02/2016
1047	2^676306-114713	203589	Enzo Doria	04/2015
1048	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
1049	2^674627-25161	203083	Enzo Doria	09/2013
1050	2^674603-69337	203076	Enzo Doria	12/2015
1051	2^674459+74213	203033	Enzo Doria	04/2016
1052	2^674116-458879	202930	Enzo Doria	04/2015
1053	2^674076-114755	202918	Enzo Doria	04/2015
1054	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
1055	(467617#+14534)/(2^21343)	202603	Makoto Morimoto	06/2019
1056	2^672556-1835519	202460	Enzo Doria	04/2015
1057	2^671446-351401	202126	Enzo Doria	07/2015
1058	2^671373+77747	202104	Enzo Doria	05/2016
1059	2^670726-114845	201909	Enzo Doria	05/2015
1060	2^670539-25045	201853	Enzo Doria	09/2013
1061	43284^43519-43519^43284	201769	Norbert Schneider	08/2018
1062	2^670213+282317	201755	Enzo Doria	09/2016
1063	2^670133+89	201731	Stefano Morozzi	05/2021
1064	2^669854-113501	201647	Enzo Doria	08/2014
1065	2^669718+81619	201606	Enzo Doria	08/2016
1066	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
1067	2^668938-1839821	201371	Enzo Doria	06/2015
1068	2^668492+1879303	201237	Enzo Doria	08/2016
1069	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
1070	10194^50161-50161^10194	201063	Norbert Schneider	09/2020
1071	2^667894+1875589	201057	Enzo Doria	06/2016
1072	2^667569-1836559	200959	Enzo Doria	05/2015
1073	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
1074	2^666430+782569	200616	Enzo Doria	10/2016
1075	(86^103471+1)/87	200163	Paul Bourdelais	05/2018
1076	103(10^100000+20110)^2-4707(10^100000+20110)+50383	200003	Robert Price	05/2017
1077	103(10^100000+33798)^2-4707(10^100000+33798)+50383	200003	Robert Price	01/2018
1078	numbpart(32235776596)	200002	Serge Batalov	04/2017
1079	(10^200001+149)/3	200001	Serge Batalov	12/2014
1080	10^200000+571791	200001	Patrick De Geest	08/2019
1081	(3^419180-621444)/3	200000	Stefano Morozzi	06/2019
1082	(3^419180-1941384)/3	200000	Stefano Morozzi	08/2019
1083	10^200000-45557	200000	Patrick De Geest	08/2019
1084	(10^200000-1)/9-10^58838	200000	Akihiko Yoshida	04/2020
1085	92*10^199980-9	199982	Robert Price	12/2021
1086	(85*10^199951-139)/9	199952	Robert Price	08/2021
1087	(10^199926+7)/29/373/2339	199919	Alfred Reich	08/2021
1088	23*10^199833-9	199835	Robert Price	10/2021
1089	(299*10^199801-17)/3	199803	Robert Price	04/2020
1090	6*10^199788+77	199789	Robert Price	06/2020
1091	2^663020-933075	199589	Paul Bourdelais	06/2021
1092	(14*10^199447+73)/3	199448	Robert Price	12/2018
1093	2^662103-29287	199313	Enzo Doria	08/2015
1094	(2*10^199283+457)/9	199283	Robert Price	01/2018
1095	(10^199248-19)/9	199248	Robert Price	01/2018
1096	(83*10^199213+529)/9	199214	Robert Price	12/2021
1097	(194*10^199146-17)/3	199148	Robert Price	09/2020
1098	(151*10^199003-1)/3	199005	Robert Price	03/2020
1099	9*10^198946-73	198947	Robert Price	01/2021
1100	45*10^198931-7	198933	Robert Price	07/2020
1101	2^660482-2891	198825	Yves Minet	05/2016
1102	2^659583+1879223	198555	Enzo Doria	08/2016
1103	(53*10^198529+1)/9	198530	Serge Batalov	07/2010
1104	(49*10^198403+311)/9	198404	Robert Price	06/2019
1105	96*10^198376-7	198378	Robert Price	03/2021
1106	(10^198375+7)/59/1201/87589	198366	Alfred Reich	08/2021
1107	2^658828-29819	198327	Enzo Doria	08/2015
1108	2^658776-2791229	198312	Enzo Doria	01/2016
1109	(35*10^198294-377)/9	198295	Robert Price	07/2018
1110	(4*10^198268+137)/3	198269	Robert Price	03/2018
1111	2^658544-1854029	198242	Enzo Doria	09/2015
1112	(157^90239-1)/156	198154	Alexander Zhirkov	06/2016
1113	2*10^197959-37	197960	Robert Price	11/2021
1114	(232*10^197897+17)/3	197899	Robert Price	04/2021
1115	(4*10^197778+173)/3	197779	Robert Price	02/2018
1116	78*10^197702-7	197704	Robert Price	10/2020
1117	(17*10^197640-23)/3	197641	Robert Price	03/2021
1118	(29*10^197629-77)/3	197630	Robert Price	02/2020
1119	2^656462+1874419	197615	Enzo Doria	06/2016
1120	(89^101363+1)/90	197595	Paul Bourdelais	11/2017
1121	2^655893-344563	197444	Enzo Doria	07/2015
1122	2^655875+71333	197439	Enzo Doria	04/2016
1123	2^655845-9	197430	Robert Price	01/2017
1124	(299*10^197426+1)/3	197428	Robert Price	04/2020
1125	2^655682-1849121	197380	Enzo Doria	08/2015
1126	4*10^197268-89	197269	Robert Price	11/2018
1127	(11*10^197198-89)/3	197199	Robert Price	05/2021
1128	2^655045-49603	197189	Enzo Doria	10/2015
1129	2^655000-2784089	197175	Enzo Doria	10/2015
1130	(18^157051-1)/17	197141	Paul Bourdelais	03/2010
1131	2^654400-39719	196995	Enzo Doria	09/2015
1132	(14*10^196965-221)/9	196966	Robert Price	04/2018
1133	2^654216-459995	196939	Enzo Doria	06/2015
1134	(17*10^196921+31)/3	196922	Robert Price	01/2019
1135	(14*10^196885-89)/3	196886	Robert Price	05/2020
1136	3*10^196881-59	196882	Robert Price	09/2018
1137	2^653851+82295	196829	Enzo Doria	09/2016
1138	(38*10^196792+691)/9	196793	Robert Price	10/2018
1139	(65*10^196768+493)/9	196769	Robert Price	08/2021
1140	2^653636-29429	196765	Enzo Doria	08/2015
1141	2^653601-69673	196754	Enzo Doria	02/2016
1142	(44*10^196684+1)/9	196685	Serge Batalov	07/2010
1143	2^652786-1852571	196509	Enzo Doria	08/2015
1144	2^652752-1325	196498	Yves Minet	07/2015
1145	2^652470-1859141	196414	Enzo Doria	10/2015
1146	2^652307+1877483	196364	Enzo Doria	08/2016
1147	2^652293-115273	196360	Enzo Doria	06/2015
1148	(47*10^196281+403)/9	196282	Robert Price	03/2019
1149	(7*10^196125-31)/3	196126	Robert Price	12/2021
1150	6*10^196070+73	196071	Robert Price	04/2019
1151	2^651218-1868201	196037	Enzo Doria	04/2016
1152	2^651047-49687	195985	Enzo Doria	10/2015
1153	10^195968-700001	195968	Robert Price	08/2021
1154	(29*10^195875-197)/3	195876	Robert Price	08/2021
1155	(25*10^195808-97)/9	195809	Robert Price	01/2022
1156	2^650285-2785333	195756	Enzo Doria	10/2015
1157	(10^195732+7)/18089/49605893	195721	Alfred Reich	08/2021
1158	(69^106397-1)/68	195647	Paul Bourdelais	10/2017
1159	2^649811+1877573	195613	Enzo Doria	08/2016
1160	2^649662-170531	195568	Hans Havermann	10/2018
1161	2^649586+182839	195545	Enzo Doria	11/2016
1162	2^649537-1867363	195531	Enzo Doria	04/2016
1163	2^649536-1861499	195530	Enzo Doria	12/2015
1164	(103*10^195478-1)/3	195480	Serge Batalov	12/2014
1165	2^649102-59351	195400	Enzo Doria	10/2015
1166	(2*10^195399+529)/9	195399	Robert Price	01/2018
1167	(202*10^195383-13)/9	195385	Robert Price	01/2020
1168	2^648988+1178971	195365	Enzo Doria	06/2016
1169	2^648975-114319	195361	Enzo Doria	02/2015
1170	(11*10^195350-137)/9	195351	Robert Price	01/2018
1171	2^648619-24835	195254	Enzo Doria	09/2013
1172	5*10^195250-21	195251	Robert Price	12/2021
1173	(14*10^195234-83)/3	195235	Robert Price	12/2018
1174	5*10^195221+81	195222	Robert Price	03/2019
1175	10^195143-5001	195143	Robert Price	12/2021
1176	2^648190-24737	195125	Enzo Doria	09/2013
1177	(57^111119+1)/58	195110	Paul Bourdelais	10/2017
1178	(29*10^195098-197)/3	195099	Robert Price	08/2021
1179	10^195060+89701	195061	Patrick De Geest	02/2021
1181	10^195060-40000000001	195060	Robert Price	09/2020
1180	10^195060-110337	195060	Patrick De Geest	02/2021
1182	56*10^195032-3	195034	Robert Price	03/2020
1183	11^187185-90	194934	Enzo Doria	09/2012
1184	(86*10^194818-437)/9	194819	Robert Price	03/2021
1185	2^647068+77281	194787	Enzo Doria	05/2016
1186	2*10^194716-93	194717	Robert Price	12/2021
1187	15^165559-14^165559	194713	Jean-Louis Charton	03/2011
1188	F(931517)	194676	Henri Lifchitz	09/2008
1189	4*10^194668+49	194669	Robert Price	01/2019
1190	2^646589+1179407	194643	Enzo Doria	06/2016
1191	2^646289-114621	194553	Enzo Doria	05/2015
1192	2^646236-39659	194537	Enzo Doria	09/2015
1193	(16*10^194536+53)/3	194537	Robert Price	03/2019
1194	2^646161-59833	194514	Enzo Doria	11/2015
1195	(17*10^194502+31)/3	194503	Robert Price	01/2019
1196	(19*10^194428+287)/9	194429	Robert Price	10/2021
1197	2*10^194413+3	194414	Robert Price	07/2015
1198	2^645360-1848599	194273	Enzo Doria	08/2015
1199	(112*10^194150-1)/3	194152	Serge Batalov	12/2014
1200	2*10^193981-43	193982	Robert Price	04/2018
1201	2^644382+75169	193979	Enzo Doria	04/2016
1202	2^644304-1861409	193955	Enzo Doria	11/2015
1203	5*10^193907-9	193908	Robert Price	05/2015
1204	2^644043+1876703	193877	Enzo Doria	07/2016
1205	2*10^193841-63	193842	Robert Price	01/2022
1206	2^643735+1879733	193784	Enzo Doria	09/2016
1207	(5^277183+1)/6	193742	Paul Bourdelais	07/2010
1208	9*10^193712+71	193713	Robert Price	08/2020
1209	2^643216-286565	193628	Enzo Doria	07/2015
1210	10^193566-10000000001	193566	Robert Price	04/2021
1211	10^193566-454041	193566	Patrick De Geest	08/2021
1212	2^642888-24965	193529	Enzo Doria	09/2013
1213	2^642448-114825	193397	Enzo Doria	05/2015
1214	2^642437-1856623	193393	Enzo Doria	10/2015
1215	2^642039-59797	193273	Enzo Doria	11/2015
1216	10^193230+513861	193231	Patrick De Geest	07/2018
1217	10^193230-8001	193230	Robert Price	03/2018
1218	2^641692-286349	193169	Enzo Doria	07/2015
1219	2^641690-24737	193168	Enzo Doria	09/2013
1220	2^641514+1876549	193115	Enzo Doria	07/2016
1221	2^640888-2785619	192927	Enzo Doria	10/2015
1222	2^640874-2783741	192923	Enzo Doria	09/2015
1223	10^192922+192207	192923	Patrick De Geest	08/2021
1224	10^192922-7001	192922	Robert Price	04/2021
1225	2^640854+25	192917	Stefano Morozzi	05/2021
1226	34*10^192868-9	192870	Robert Price	06/2020
1227	(46*10^192841+683)/9	192842	Robert Price	03/2019
1228	2^640181+467	192714	Lelio R Paula	08/2013
1229	2^639536-1850249	192520	Enzo Doria	08/2015
1230	40714<>40712<>...<>1086421357911<>...<>40711<>40713	192464	Hans Havermann	12/2019
1231	5*10^192422-43	192423	Robert Price	01/2019
1232	2^639110-2792441	192392	Enzo Doria	02/2016
1233	2^638955-29827	192345	Enzo Doria	08/2015
1234	2^638713-2784223	192272	Enzo Doria	10/2015
1235	(10^192216+7)/149	192214	Alfred Reich	07/2021
1236	2^638490-113507	192205	Enzo Doria	08/2014
1237	2^638189-39943	192115	Enzo Doria	09/2015
1238	2^638110+1877119	192091	Enzo Doria	07/2016
1239	2^638066-2785211	192078	Enzo Doria	10/2015
1240	(35*10^191973-341)/9	191974	Robert Price	08/2021
1241	(112*10^191900+17)/3	191902	Robert Price	03/2020
1242	2^637475-115309	191900	Enzo Doria	07/2015
1243	(68*10^191754-113)/9	191755	Robert Price	03/2021
1244	2^636661+1876577	191655	Enzo Doria	07/2016
1245	(34^125101-1)/33	191589	Paul Bourdelais	11/2017
1246	2^636177-1855123	191509	Enzo Doria	09/2015
1247	2^636158-113627	191503	Enzo Doria	08/2014
1248	(37*25^136966+63)/4	191472	Curtis Bright	05/2015
1249	2^636035+79823	191466	Enzo Doria	06/2016
1250	2^636011-1860847	191459	Enzo Doria	11/2015

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PRP Records

Probable Primes Top 10000

(288949 PRPs in the top)