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 ?
1251	2^560405-39943	168699	Enzo Doria	09/2015
1252	(23*10^168608-83)/3	168609	Robert Price	08/2019
1253	2^559686-350471	168483	Enzo Doria	06/2015
1254	2^559672-1855889	168479	Enzo Doria	09/2015
1255	(5*10^168379-473)/9	168379	Robert Price	01/2018
1256	2^559000-59939	168276	Enzo Doria	11/2015
1257	(16*10^168181+41)/3	168182	Robert Price	03/2019
1258	(19*10^168173+77)/3	168174	Robert Price	05/2019
1259	2^558640-114149	168168	Enzo Doria	12/2014
1260	2^558498-1849277	168125	Enzo Doria	08/2015
1261	2^558476-1850249	168119	Enzo Doria	08/2015
1262	(7*10^168067+71)/3	168068	Robert Price	05/2018
1263	2^558150-1852211	168020	Enzo Doria	08/2015
1264	2^558125-113661	168013	Enzo Doria	09/2014
1265	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
1266	(13*10^167911+179)/3	167912	Robert Price	11/2018
1267	39^105456+2	167788	Robert Price	04/2015
1268	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
1269	10^167639+121911	167640	Patrick De Geest	07/2018
1270	10^167639-8001	167639	Robert Price	03/2018
1271	2^556504-462059	167525	Enzo Doria	07/2015
1272	5*10^167510+9	167511	Robert Price	08/2015
1273	2^555343+1874333	167175	Enzo Doria	06/2016
1274	2^555210-461261	167135	Enzo Doria	07/2015
1275	2^554372+1880527	166883	Enzo Doria	11/2016
1276	2^554299+72173	166861	Enzo Doria	04/2016
1277	2^554037-2797063	166782	Enzo Doria	03/2016
1278	(49*10^166721-139)/9	166722	Robert Price	03/2019
1279	2^553484-29819	166616	Enzo Doria	08/2015
1280	2^553383-2784217	166585	Enzo Doria	10/2015
1281	2^553069+76427	166491	Enzo Doria	05/2016
1282	2*10^166458+51	166459	Robert Price	05/2018
1283	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
1284	11^159756-2424	166369	Mike Oakes	06/2010
1285	2^552649-361275	166364	Enzo Doria	05/2014
1286	2^552628-113669	166358	Enzo Doria	09/2014
1287	10^166324+550603	166325	Patrick De Geest	07/2018
1288	10^166324-801	166324	Robert Price	02/2018
1289	2^552137+1879397	166210	Enzo Doria	09/2016
1290	(23^121949-1)/22	166061	Paul Bourdelais	10/2017
1291	2^551542+19249	166031	Payam Samidoost	08/2002
1292	2^551535-23821	166029	Enzo Doria	08/2013
1293	2^551507-23557	166021	Enzo Doria	08/2013
1294	7*10^165916-3	165917	Robert Price	08/2015
1295	81^86837-80^86837	165728	Robert Price	01/2015
1296	(71*10^165663-539)/9	165664	Robert Price	07/2019
1297	2^550270-69551	165648	Enzo Doria	12/2015
1298	2^550000-23625	165567	Enzo Doria	08/2013
1299	2^549675-1852057	165469	Enzo Doria	08/2015
1300	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
1301	(28*10^165358-1)/9	165359	Serge Batalov	10/2014
1302	2^549278+1879669	165350	Enzo Doria	09/2016
1303	(7*10^165350-439)/9	165350	Robert Price	02/2018
1304	2^549252-351269	165342	Enzo Doria	06/2015
1305	(14*10^165282+73)/3	165283	Robert Price	12/2018
1306	2^549049+2797607	165281	Enzo Doria	04/2016
1307	(7*10^165239+107)/3	165240	Robert Price	02/2018
1308	(44^100511-1)/43	165184	Paul Bourdelais	11/2017
1309	(7*10^165134+107)/3	165135	Robert Price	02/2018
1310	(23*10^165060-83)/3	165061	Robert Price	08/2019
1311	2^547178-1856501	164717	Enzo Doria	10/2015
1312	11^158160-60	164707	Enzo Doria	07/2012
1313	2^546398-59201	164483	Enzo Doria	10/2015
1314	2^546332-114893	164463	Enzo Doria	05/2015
1315	2^545958+1876189	164350	Enzo Doria	07/2016
1316	2^545878-49841	164326	Enzo Doria	10/2015
1317	(10^164284+77)/3	164284	Robert Price	01/2018
1318	2^545668-4019	164263	Yves Minet	04/2017
1319	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
1320	(16*10^164122+197)/3	164123	Robert Price	04/2019
1321	2^545185+76757	164118	Enzo Doria	05/2016
1322	2^545076-114329	164085	Enzo Doria	01/2015
1323	(2*10^164043-143)/3	164043	Robert Price	03/2018
1324	(29^112153+1)/30	164011	Lelio R Paula	03/2017
1325	2^544757+1874777	163989	Enzo Doria	06/2016
1326	2^544444-457199	163894	Enzo Doria	01/2015
1327	2^544264-343529	163840	Enzo Doria	07/2015
1328	7*10^163780+9	163781	Robert Price	09/2015
1329	2^543989+2793047	163758	Enzo Doria	02/2016
1330	2^542870-69551	163421	Enzo Doria	12/2015
1331	2^542395+72533	163278	Enzo Doria	04/2016
1332	2^542072-3683	163180	Yves Minet	03/2017
1333	2^541779-1867357	163092	Enzo Doria	04/2016
1334	8*10^162924+9	162925	Robert Price	12/2015
1335	2^540905+81557	162829	Enzo Doria	08/2016
1336	2^540628-2939	162746	Yves Minet	09/2014
1337	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
1338	3*10^162620-59	162621	Robert Price	09/2018
1339	3^340694-112960	162553	Enzo Doria	07/2014
1340	2^539807-114081	162499	Enzo Doria	12/2014
1341	2^539654-114893	162453	Enzo Doria	05/2015
1342	2^539617-1851583	162441	Enzo Doria	08/2015
1343	2^539346+81049	162360	Enzo Doria	07/2016
1344	2^539220-115499	162322	Enzo Doria	07/2015
1345	2^539217-113713	162321	Enzo Doria	09/2014
1346	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
1347	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
1348	(10^162138+11)/3	162138	Serge Batalov	07/2015
1349	2^538473-112723	162097	Enzo Doria	06/2014
1350	2^538157+79337	162002	Enzo Doria	06/2016
1351	2^538136-114749	161996	Enzo Doria	05/2015
1352	2^538104+1531	161986	Lelio R Paula	01/2013
1353	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
1354	2^537815-22737	161899	Enzo Doria	07/2013
1355	2^537804-39839	161896	Enzo Doria	09/2015
1356	2^537458-59201	161791	Enzo Doria	10/2015
1357	2*10^161766+51	161767	Robert Price	05/2018
1358	2^537209-49849	161717	Enzo Doria	10/2015
1359	(58*10^161691+329)/9	161692	Robert Price	05/2019
1360	2^536937+1879397	161635	Enzo Doria	09/2016
1361	2^536569-22881	161524	Enzo Doria	07/2013
1362	10^161253+573493	161254	Patrick De Geest	07/2018
1363	10^161253-8001	161253	Robert Price	03/2018
1364	7*10^161192-9	161193	Robert Price	10/2015
1365	2^535269-113803	161133	Enzo Doria	09/2014
1366	2^535205-23295	161113	Enzo Doria	08/2013
1367	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
1368	2^534359-23229	160859	Enzo Doria	08/2013
1369	67^88037-66^88037	160763	Robert Price	10/2013
1370	2^533948-1852559	160735	Enzo Doria	08/2015
1371	2^533665-23335	160650	Enzo Doria	08/2013
1372	(19*10^160619+77)/3	160620	Robert Price	05/2019
1373	3^336353-2^336353	160482	Mike Oakes	10/2007
1374	2^532253+1868417	160225	Enzo Doria	04/2016
1375	2^532108-291989	160181	Enzo Doria	07/2015
1376	(17*10^160143+67)/3	160144	Robert Price	01/2019
1377	(19*10^159921-49)/3	159922	Robert Price	05/2019
1378	2^531110-1853771	159881	Enzo Doria	09/2015
1379	2^530992-1845299	159845	Enzo Doria	07/2015
1380	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
1381	2^530417-113833	159672	Enzo Doria	09/2014
1382	2^530406-69701	159669	Enzo Doria	02/2016
1383	5*10^159656+41	159657	Robert Price	03/2019
1384	7^188858-188858^7	159604	Norbert Schneider	05/2018
1385	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
1386	(17*10^159438-377)/9	159439	Robert Price	03/2018
1387	2^528944-461315	159229	Enzo Doria	07/2015
1388	(13*10^159147+161)/3	159148	Robert Price	11/2018
1389	2^528620-113879	159131	Enzo Doria	10/2014
1390	2^528000-23307	158944	Enzo Doria	08/2013
1391	(29*10^158909+61)/9	158910	Robert Price	08/2018
1392	2^527817+1876817	158889	Enzo Doria	07/2016
1393	2^527774-49451	158876	Enzo Doria	10/2015
1394	2^527745-291553	158868	Enzo Doria	07/2015
1395	2^527644-1856999	158837	Enzo Doria	10/2015
1396	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
1397	2^527573-1863253	158816	Enzo Doria	12/2015
1398	2^527553-23401	158810	Enzo Doria	08/2013
1399	11^152420-210	158730	Enzo Doria	09/2012
1400	(13*10^158694+401)/9	158695	Robert Price	01/2018
1401	2^527052-69059	158659	Enzo Doria	11/2015
1402	2^526849-113233	158598	Enzo Doria	07/2014
1403	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016
1404	2^526658-3551	158540	Yves Minet	03/2017
1405	7*10^158465-11	158466	Robert Price	06/2019
1406	2^526375-23115	158455	Enzo Doria	08/2013
1407	2^526028-112793	158351	Enzo Doria	07/2014
1408	2^525690-9221	158249	Lelio R Paula	01/2013
1409	2*10^158242-7	158243	Robert Price	10/2015
1410	2^525667-525667^2	158242	Henri Lifchitz	12/2017
1411	2^525186-1857431	158097	Enzo Doria	10/2015
1412	2^524515-23245	157895	Enzo Doria	08/2013
1413	2^524499-109087	157890	Enzo Doria	04/2014
1414	2^18067*(2^506221+1)-1	157827	Makoto Morimoto	05/2014
1415	2^524288+189093	157827	Makoto Morimoto	01/2016
1416	(2^(2^19)-9333)/(1923463121331973)	157814	Makoto Morimoto	09/2017
1417	(10^157792+359)/9	157792	Serge Batalov	12/2014
1418	2^523924+1876591	157717	Enzo Doria	07/2016
1419	(17*10^157705+67)/3	157706	Robert Price	01/2019
1420	(46^94841+1)/47	157696	Robert Price	01/2014
1421	2^523774+77839	157672	Enzo Doria	05/2016
1422	2^523587+2799143	157616	Enzo Doria	04/2016
1423	2^523371+1872113	157551	Enzo Doria	05/2016
1424	2^522535-351457	157299	Enzo Doria	07/2015
1425	2^522226+2799079	157206	Enzo Doria	04/2016
1426	2^522134-1849451	157178	Enzo Doria	08/2015
1427	4*10^157150+93	157151	Robert Price	08/2018
1428	2^521401-29593	156958	Enzo Doria	08/2015
1429	7*10^156956+87	156957	Robert Price	07/2019
1430	2^521348-23397	156942	Enzo Doria	08/2013
1431	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
1432	65^86522+64	156857	Lelio R Paula	04/2016
1433	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
1434	2^520977-1858183	156830	Enzo Doria	10/2015
1435	(8*10^156718-101)/3	156719	Robert Price	08/2018
1436	2^520314-1849481	156631	Enzo Doria	08/2015
1437	(13*10^156522+89)/3	156523	Robert Price	09/2018
1438	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
1439	3*10^156435-97	156436	Robert Price	07/2018
1440	(8*10^156371-77)/3	156372	Robert Price	07/2018
1441	53^90679-52^90679	156356	Robert Price	01/2013
1442	2^519106-59141	156267	Enzo Doria	10/2015
1443	2^519053+6077	156251	Enzo Doria	02/2016
1444	2^518968-1860989	156225	Enzo Doria	11/2015
1445	(25*10^156221-7)/9	156222	Robert Price	05/2018
1446	2^518931-2782297	156214	Enzo Doria	09/2015
1447	2^518608-2939	156117	Yves Minet	09/2014
1448	10*27^109005+697	156027	Curtis Bright	05/2015
1449	2^517967-113485	155924	Enzo Doria	08/2014
1450	2^517698+4429	155843	Lelio R Paula	01/2013
1451	2^517543-113257	155796	Enzo Doria	07/2014
1452	(14*10^155740-143)/3	155741	Robert Price	11/2018
1453	31^104309-30^104309	155563	Henri Lifchitz	08/2013
1454	2^516742-39851	155555	Enzo Doria	09/2015
1455	2^516440+1878421	155464	Enzo Doria	08/2016
1456	2^515863-1867237	155291	Enzo Doria	03/2016
1457	2^515786-461861	155268	Enzo Doria	07/2015
1458	2^515644-113247	155225	Enzo Doria	07/2014
1459	(7*10^155203+107)/3	155204	Robert Price	02/2018
1460	(17*10^155133-89)/9	155134	Robert Price	07/2018
1461	2^515227-114997	155099	Enzo Doria	06/2015
1462	EPrime(155025)	155025	Eric W. Weisstein	10/2010
1463	(14*10^155024-221)/9	155025	Robert Price	04/2018
1464	(4*10^155022+173)/3	155023	Robert Price	02/2018
1465	(115*10^154869-1)/3	154871	Serge Batalov	12/2014
1466	2^514361+78167	154839	Enzo Doria	05/2016
1467	2^514281-115033	154815	Enzo Doria	06/2015
1468	2^514194-3311	154788	Yves Minet	12/2014
1469	(14*10^154773+37)/3	154774	Robert Price	12/2018
1470	2^513437+1879337	154560	Enzo Doria	09/2016
1471	2^513306-113201	154521	Enzo Doria	07/2014
1472	(10^154494-13)/3	154494	Robert Price	12/2017
1473	2^513042-113787	154442	Enzo Doria	09/2014
1474	2^512628-114053	154317	Enzo Doria	11/2014
1475	2^512529-49783	154287	Enzo Doria	10/2015
1476	(355573#+6991)/(6991*2031599)	154285	Makoto Morimoto	06/2019
1477	2^512315-115297	154223	Enzo Doria	06/2015
1478	2^512168+79561	154178	Enzo Doria	06/2016
1479	4*10^154078-57	154079	Robert Price	10/2018
1480	(355049#+1859)/(111310148891*62587751)	154051	Makoto Morimoto	06/2019
1481	2^511658-114371	154025	Enzo Doria	02/2015
1482	(57^87719+1)/58	154022	Paul Bourdelais	11/2017
1483	2^511580-1846679	154001	Enzo Doria	07/2015
1484	2^511541-113713	153990	Enzo Doria	09/2014
1485	2^511077-112723	153850	Enzo Doria	06/2014
1486	69^83653-68^83653	153826	Robert Price	12/2013
1487	2^510963-113707	153816	Enzo Doria	09/2014
1488	(154*10^153810-1)/9	153812	Serge Batalov	12/2014
1489	(181*25^109991-75077)/8	153763	Curtis Bright	05/2015
1490	2*10^153746-3	153747	Robert Price	07/2015
1491	2^510626+1179379	153714	Enzo Doria	05/2016
1492	(7*10^153664+113)/3	153665	Robert Price	02/2018
1493	2^510420+81121	153652	Enzo Doria	07/2016
1494	(197*7^181761-1)/2	153608	Karsten Bonath	05/2017
1495	2^509894-459161	153494	Enzo Doria	05/2015
1496	2^509841+71657	153478	Enzo Doria	04/2016
1497	2^509533-1846723	153385	Enzo Doria	07/2015
1498	2^509468-39989	153366	Enzo Doria	09/2015
1499	70^83117-69^83117	153360	Robert Price	01/2014
1500	(112*10^153025-1)/3	153027	Serge Batalov	12/2014

Find by discoverer :

PRP Records

Probable Primes Top 10000

(253466 PRPs in the top)