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	2^579992-39779	174595	Enzo Doria	09/2015
1252	(2*10^174301-71)/3	174301	Robert Price	12/2017
1253	(2^578696+1)/257	174203	Lelio R Paula	09/2015
1254	2^578656-1851809	174193	Enzo Doria	08/2015
1255	2^578583-113917	174171	Enzo Doria	10/2014
1256	2^578434-83	174126	Yves Minet	07/2017
1257	15^148048-2	174118	Robert Price	06/2015
1258	5*10^174101+81	174102	Robert Price	03/2019
1259	2^578346+2794249	174100	Enzo Doria	03/2016
1260	5*10^173904-13	173905	Robert Price	01/2019
1261	(71*10^173854-287)/9	173855	Robert Price	09/2019
1262	(43*10^173826+101)/9	173827	Robert Price	11/2018
1263	2*10^173809-87	173810	Robert Price	04/2018
1264	(L!41532)/2	173772	Serge Batalov	07/2017
1265	2^577146-49877	173739	Enzo Doria	10/2015
1266	2^576889+49727	173661	Enzo Doria	09/2016
1267	(167*10^173571-17)/3	173573	Robert Price	03/2020
1268	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
1269	(13*10^173467-37)/3	173468	Robert Price	01/2019
1270	2^576016-113919	173399	Enzo Doria	11/2014
1271	2^575911-1849387	173367	Enzo Doria	08/2015
1272	(16*10^173251+107)/3	173252	Robert Price	03/2019
1273	2^575196-114053	173152	Enzo Doria	11/2014
1274	2^574591-115387	172970	Enzo Doria	07/2015
1275	(202*10^172940-13)/9	172942	Robert Price	01/2020
1276	2^574328+81121	172890	Enzo Doria	07/2016
1277	(115*10^172862-1)/3	172864	Serge Batalov	12/2014
1278	3*10^172812+13	172813	Robert Price	07/2018
1279	4*5^247217-9	172798	Lelio R Paula	10/2015
1280	69061#+(467617#)/(69061#)	172766	Makoto Morimoto	10/2017
1281	5*10^172692+57	172693	Robert Price	12/2018
1282	2^573668-2782319	172692	Enzo Doria	09/2015
1283	2^573444-1855109	172624	Enzo Doria	09/2015
1284	3^361608+2	172531	Robert Price	08/2014
1285	(54^99563+1)/55	172481	Paul Bourdelais	11/2017
1286	2^572592-114893	172368	Enzo Doria	05/2015
1287	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
1288	(38^109037-1)/37	172254	Paul Bourdelais	10/2017
1289	3*10^172219+73	172220	Robert Price	08/2018
1290	(36^110503+1)/37	171975	Lelio R Paula	04/2017
1291	(22*10^171929-73)/3	171930	Robert Price	04/2019
1292	4*10^171891-63	171892	Robert Price	10/2018
1293	2^570980-2782289	171883	Enzo Doria	09/2015
1294	(25*10^171849-37)/3	171850	Robert Price	10/2019
1295	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
1296	(536*10^171601-23)/9	171603	Robert Price	02/2020
1297	7*10^171535-99	171536	Robert Price	06/2019
1298	2^569563-1854607	171456	Enzo Doria	09/2015
1299	3*10^171391+59	171392	Robert Price	08/2018
1300	(13*10^171306-37)/3	171307	Robert Price	01/2019
1301	8*10^171296+87	171297	Robert Price	10/2019
1302	(55^98419-1)/54	171284	Paul Bourdelais	12/2017
1303	(29*10^171275+67)/3	171276	Robert Price	12/2019
1304	2^568642+1876129	171179	Enzo Doria	07/2016
1305	(46*10^170932+143)/9	170933	Robert Price	01/2019
1306	(79*10^170901-1)/3	170903	Robert Price	02/2020
1307	(58*10^170842+221)/9	170843	Robert Price	02/2017
1308	3*10^170800+73	170801	Robert Price	08/2018
1309	11^164009-270	170798	Enzo Doria	10/2012
1310	2*10^170767+41	170768	Robert Price	05/2018
1311	3^357706-112358	170670	Enzo Doria	07/2014
1312	TheodorusPrime(170657)	170657	Eric W. Weisstein	08/2013
1313	2^566871+1876163	170646	Enzo Doria	07/2016
1314	(10657#+(404267#)/(10657#))/(1675379)	170624	Makoto Morimoto	10/2017
1315	2^566496+7	170533	Donovan Johnson	07/2006
1316	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
1317	2^565183-352021	170138	Enzo Doria	07/2015
1318	2^565143-114457	170125	Enzo Doria	02/2015
1319	2^564976-49869	170075	Enzo Doria	10/2015
1320	2^564526-351401	169940	Enzo Doria	07/2015
1321	4*10^169759+19	169760	Robert Price	10/2018
1322	21^128327-20^128327	169677	Jean-Louis Charton	11/2014
1323	(4*10^169559+83)/3	169560	Robert Price	02/2018
1324	2^562749+2793047	169405	Enzo Doria	02/2016
1325	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
1326	(56*10^169311+691)/9	169312	Robert Price	05/2019
1327	2^562369-29503	169290	Enzo Doria	08/2015
1328	(22*10^169019+383)/9	169020	Robert Price	05/2018
1329	5*10^168807+87	168808	Robert Price	02/2019
1330	2^560405-39943	168699	Enzo Doria	09/2015
1331	(23*10^168608-83)/3	168609	Robert Price	08/2019
1332	2^559686-350471	168483	Enzo Doria	06/2015
1333	2^559672-1855889	168479	Enzo Doria	09/2015
1334	(5*10^168379-473)/9	168379	Robert Price	01/2018
1335	2^559000-59939	168276	Enzo Doria	11/2015
1336	(16*10^168181+41)/3	168182	Robert Price	03/2019
1337	(19*10^168173+77)/3	168174	Robert Price	05/2019
1338	2^558640-114149	168168	Enzo Doria	12/2014
1339	2^558498-1849277	168125	Enzo Doria	08/2015
1340	2^558476-1850249	168119	Enzo Doria	08/2015
1341	(7*10^168067+71)/3	168068	Robert Price	05/2018
1342	2^558150-1852211	168020	Enzo Doria	08/2015
1343	2^558125-113661	168013	Enzo Doria	09/2014
1344	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
1345	(13*10^167911+179)/3	167912	Robert Price	11/2018
1346	(26*10^167861-167)/3	167862	Robert Price	10/2019
1347	39^105456+2	167788	Robert Price	04/2015
1348	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
1349	10^167639+121911	167640	Patrick De Geest	07/2018
1350	10^167639-8001	167639	Robert Price	03/2018
1351	2^556504-462059	167525	Enzo Doria	07/2015
1352	5*10^167510+9	167511	Robert Price	08/2015
1353	2^555343+1874333	167175	Enzo Doria	06/2016
1354	2^555210-461261	167135	Enzo Doria	07/2015
1355	9*10^166996+59	166997	Robert Price	01/2020
1356	2^554372+1880527	166883	Enzo Doria	11/2016
1357	2^554299+72173	166861	Enzo Doria	04/2016
1358	(185*10^166837+7)/3	166839	Robert Price	03/2020
1359	2^554037-2797063	166782	Enzo Doria	03/2016
1360	(49*10^166721-139)/9	166722	Robert Price	03/2019
1361	2^553484-29819	166616	Enzo Doria	08/2015
1362	(188*10^166611+7)/3	166613	Robert Price	03/2020
1363	2^553383-2784217	166585	Enzo Doria	10/2015
1364	2^553069+76427	166491	Enzo Doria	05/2016
1365	2*10^166458+51	166459	Robert Price	05/2018
1366	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
1367	11^159756-2424	166369	Mike Oakes	06/2010
1368	2^552649-361275	166364	Enzo Doria	05/2014
1369	2^552628-113669	166358	Enzo Doria	09/2014
1370	10^166324+550603	166325	Patrick De Geest	07/2018
1371	10^166324-801	166324	Robert Price	02/2018
1372	(85*10^166297-1)/3	166299	Robert Price	02/2020
1373	8*10^166227+87	166228	Robert Price	10/2019
1374	2^552137+1879397	166210	Enzo Doria	09/2016
1375	(23^121949-1)/22	166061	Paul Bourdelais	10/2017
1376	2^551542+19249	166031	Payam Samidoost	08/2002
1377	2^551535-23821	166029	Enzo Doria	08/2013
1378	2^551507-23557	166021	Enzo Doria	08/2013
1379	7*10^165916-3	165917	Robert Price	08/2015
1380	(29*10^165796+67)/3	165797	Robert Price	12/2019
1381	81^86837-80^86837	165728	Robert Price	01/2015
1382	(71*10^165663-539)/9	165664	Robert Price	07/2019
1383	2^550270-69551	165648	Enzo Doria	12/2015
1384	(202*10^165569-13)/9	165571	Robert Price	01/2020
1385	2^550000-23625	165567	Enzo Doria	08/2013
1386	2^549675-1852057	165469	Enzo Doria	08/2015
1387	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
1388	(28*10^165358-1)/9	165359	Serge Batalov	10/2014
1390	2^549278+1879669	165350	Enzo Doria	09/2016
1389	(7*10^165350-439)/9	165350	Robert Price	02/2018
1391	2^549252-351269	165342	Enzo Doria	06/2015
1392	(14*10^165282+73)/3	165283	Robert Price	12/2018
1393	2^549049+2797607	165281	Enzo Doria	04/2016
1394	(7*10^165239+107)/3	165240	Robert Price	02/2018
1395	(44^100511-1)/43	165184	Paul Bourdelais	11/2017
1396	(7*10^165134+107)/3	165135	Robert Price	02/2018
1397	(23*10^165060-83)/3	165061	Robert Price	08/2019
1398	(76*10^164984+77)/9	164985	Robert Price	10/2019
1399	2^547178-1856501	164717	Enzo Doria	10/2015
1400	11^158160-60	164707	Enzo Doria	07/2012
1401	(26*10^164643-167)/3	164644	Robert Price	10/2019
1402	2^546398-59201	164483	Enzo Doria	10/2015
1403	2^546332-114893	164463	Enzo Doria	05/2015
1404	2^545958+1876189	164350	Enzo Doria	07/2016
1405	2^545878-49841	164326	Enzo Doria	10/2015
1406	(10^164284+77)/3	164284	Robert Price	01/2018
1407	2^545668-4019	164263	Yves Minet	04/2017
1408	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
1409	(16*10^164122+197)/3	164123	Robert Price	04/2019
1410	2^545185+76757	164118	Enzo Doria	05/2016
1411	2^545076-114329	164085	Enzo Doria	01/2015
1412	(2*10^164043-143)/3	164043	Robert Price	03/2018
1413	(29^112153+1)/30	164011	Lelio R Paula	03/2017
1414	2^544757+1874777	163989	Enzo Doria	06/2016
1415	2^544444-457199	163894	Enzo Doria	01/2015
1416	2^544264-343529	163840	Enzo Doria	07/2015
1417	7*10^163780+9	163781	Robert Price	09/2015
1418	2^543989+2793047	163758	Enzo Doria	02/2016
1419	(28*10^163709+113)/3	163710	Robert Price	03/2020
1420	2^542870-69551	163421	Enzo Doria	12/2015
1421	2^542395+72533	163278	Enzo Doria	04/2016
1422	2^542072-3683	163180	Yves Minet	03/2017
1423	2^541779-1867357	163092	Enzo Doria	04/2016
1424	8*10^162924+9	162925	Robert Price	12/2015
1425	2^540905+81557	162829	Enzo Doria	08/2016
1426	2^540628-2939	162746	Yves Minet	09/2014
1427	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
1428	(203*10^162689+1)/3	162691	Robert Price	03/2020
1429	3*10^162620-59	162621	Robert Price	09/2018
1430	3^340694-112960	162553	Enzo Doria	07/2014
1431	2^539807-114081	162499	Enzo Doria	12/2014
1432	2^539654-114893	162453	Enzo Doria	05/2015
1433	2^539617-1851583	162441	Enzo Doria	08/2015
1434	(91*10^162410+11)/3	162412	Robert Price	02/2020
1435	2^539346+81049	162360	Enzo Doria	07/2016
1436	2^539220-115499	162322	Enzo Doria	07/2015
1437	2^539217-113713	162321	Enzo Doria	09/2014
1438	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
1439	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
1440	(10^162138+11)/3	162138	Serge Batalov	07/2015
1441	2^538473-112723	162097	Enzo Doria	06/2014
1442	2^538157+79337	162002	Enzo Doria	06/2016
1443	2^538136-114749	161996	Enzo Doria	05/2015
1444	2^538104+1531	161986	Lelio R Paula	01/2013
1445	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
1446	2^537815-22737	161899	Enzo Doria	07/2013
1447	2^537804-39839	161896	Enzo Doria	09/2015
1448	2^537458-59201	161791	Enzo Doria	10/2015
1449	2*10^161766+51	161767	Robert Price	05/2018
1450	2^537209-49849	161717	Enzo Doria	10/2015
1451	(58*10^161691+329)/9	161692	Robert Price	05/2019
1452	2^536937+1879397	161635	Enzo Doria	09/2016
1453	(31*10^161582-1)/3	161584	Robert Price	02/2020
1454	2^536569-22881	161524	Enzo Doria	07/2013
1455	10^161253+573493	161254	Patrick De Geest	07/2018
1456	10^161253-8001	161253	Robert Price	03/2018
1457	7*10^161192-9	161193	Robert Price	10/2015
1458	2^535269-113803	161133	Enzo Doria	09/2014
1459	2^535205-23295	161113	Enzo Doria	08/2013
1460	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
1461	2^534359-23229	160859	Enzo Doria	08/2013
1462	67^88037-66^88037	160763	Robert Price	10/2013
1463	2^533948-1852559	160735	Enzo Doria	08/2015
1464	2^533665-23335	160650	Enzo Doria	08/2013
1465	(19*10^160619+77)/3	160620	Robert Price	05/2019
1466	3^336353-2^336353	160482	Mike Oakes	10/2007
1467	(91*10^160249+11)/3	160251	Robert Price	02/2020
1468	2^532253+1868417	160225	Enzo Doria	04/2016
1469	2^532108-291989	160181	Enzo Doria	07/2015
1470	(26*10^160166-131)/3	160167	Robert Price	10/2019
1471	(17*10^160143+67)/3	160144	Robert Price	01/2019
1472	(19*10^159921-49)/3	159922	Robert Price	05/2019
1473	2^531110-1853771	159881	Enzo Doria	09/2015
1474	2^530992-1845299	159845	Enzo Doria	07/2015
1475	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
1476	2^530417-113833	159672	Enzo Doria	09/2014
1477	2^530406-69701	159669	Enzo Doria	02/2016
1478	5*10^159656+41	159657	Robert Price	03/2019
1479	7^188858-188858^7	159604	Norbert Schneider	05/2018
1480	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
1481	(17*10^159438-377)/9	159439	Robert Price	03/2018
1482	(203*10^159381+1)/3	159383	Robert Price	03/2020
1483	2^528944-461315	159229	Enzo Doria	07/2015
1484	(13*10^159147+161)/3	159148	Robert Price	11/2018
1485	2^528620-113879	159131	Enzo Doria	10/2014
1486	2^528000-23307	158944	Enzo Doria	08/2013
1487	(29*10^158909+61)/9	158910	Robert Price	08/2018
1488	2^527817+1876817	158889	Enzo Doria	07/2016
1489	2^527774-49451	158876	Enzo Doria	10/2015
1490	2^527745-291553	158868	Enzo Doria	07/2015
1491	(91*10^158862+11)/3	158864	Robert Price	02/2020
1492	2^527644-1856999	158837	Enzo Doria	10/2015
1493	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
1494	2^527573-1863253	158816	Enzo Doria	12/2015
1495	2^527553-23401	158810	Enzo Doria	08/2013
1496	11^152420-210	158730	Enzo Doria	09/2012
1497	(13*10^158694+401)/9	158695	Robert Price	01/2018
1498	2^527052-69059	158659	Enzo Doria	11/2015
1499	2^526849-113233	158598	Enzo Doria	07/2014
1500	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016

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Probable Primes Top 10000

(259919 PRPs in the top)