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	4*5^247217-9	172798	Lelio R Paula	10/2015
1252	69061#+(467617#)/(69061#)	172766	Makoto Morimoto	10/2017
1253	5*10^172692+57	172693	Robert Price	12/2018
1254	2^573668-2782319	172692	Enzo Doria	09/2015
1255	2^573444-1855109	172624	Enzo Doria	09/2015
1256	3^361608+2	172531	Robert Price	08/2014
1257	(54^99563+1)/55	172481	Paul Bourdelais	11/2017
1258	2^572592-114893	172368	Enzo Doria	05/2015
1259	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
1260	(38^109037-1)/37	172254	Paul Bourdelais	10/2017
1261	3*10^172219+73	172220	Robert Price	08/2018
1262	(36^110503+1)/37	171975	Lelio R Paula	04/2017
1263	(22*10^171929-73)/3	171930	Robert Price	04/2019
1264	4*10^171891-63	171892	Robert Price	10/2018
1265	2^570980-2782289	171883	Enzo Doria	09/2015
1266	(25*10^171849-37)/3	171850	Robert Price	10/2019
1267	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
1268	7*10^171535-99	171536	Robert Price	06/2019
1269	2^569563-1854607	171456	Enzo Doria	09/2015
1270	3*10^171391+59	171392	Robert Price	08/2018
1271	(13*10^171306-37)/3	171307	Robert Price	01/2019
1272	8*10^171296+87	171297	Robert Price	10/2019
1273	(55^98419-1)/54	171284	Paul Bourdelais	12/2017
1274	2^568642+1876129	171179	Enzo Doria	07/2016
1275	(46*10^170932+143)/9	170933	Robert Price	01/2019
1276	(58*10^170842+221)/9	170843	Robert Price	02/2017
1277	3*10^170800+73	170801	Robert Price	08/2018
1278	11^164009-270	170798	Enzo Doria	10/2012
1279	2*10^170767+41	170768	Robert Price	05/2018
1280	3^357706-112358	170670	Enzo Doria	07/2014
1281	TheodorusPrime(170657)	170657	Eric W. Weisstein	08/2013
1282	2^566871+1876163	170646	Enzo Doria	07/2016
1283	(10657#+(404267#)/(10657#))/(1675379)	170624	Makoto Morimoto	10/2017
1284	2^566496+7	170533	Donovan Johnson	07/2006
1285	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
1286	2^565183-352021	170138	Enzo Doria	07/2015
1287	2^565143-114457	170125	Enzo Doria	02/2015
1288	2^564976-49869	170075	Enzo Doria	10/2015
1289	2^564526-351401	169940	Enzo Doria	07/2015
1290	4*10^169759+19	169760	Robert Price	10/2018
1291	21^128327-20^128327	169677	Jean-Louis Charton	11/2014
1292	(4*10^169559+83)/3	169560	Robert Price	02/2018
1293	2^562749+2793047	169405	Enzo Doria	02/2016
1294	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
1295	(56*10^169311+691)/9	169312	Robert Price	05/2019
1296	2^562369-29503	169290	Enzo Doria	08/2015
1297	(22*10^169019+383)/9	169020	Robert Price	05/2018
1298	5*10^168807+87	168808	Robert Price	02/2019
1299	2^560405-39943	168699	Enzo Doria	09/2015
1300	(23*10^168608-83)/3	168609	Robert Price	08/2019
1301	2^559686-350471	168483	Enzo Doria	06/2015
1302	2^559672-1855889	168479	Enzo Doria	09/2015
1303	(5*10^168379-473)/9	168379	Robert Price	01/2018
1304	2^559000-59939	168276	Enzo Doria	11/2015
1305	(16*10^168181+41)/3	168182	Robert Price	03/2019
1306	(19*10^168173+77)/3	168174	Robert Price	05/2019
1307	2^558640-114149	168168	Enzo Doria	12/2014
1308	2^558498-1849277	168125	Enzo Doria	08/2015
1309	2^558476-1850249	168119	Enzo Doria	08/2015
1310	(7*10^168067+71)/3	168068	Robert Price	05/2018
1311	2^558150-1852211	168020	Enzo Doria	08/2015
1312	2^558125-113661	168013	Enzo Doria	09/2014
1313	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
1314	(13*10^167911+179)/3	167912	Robert Price	11/2018
1315	(26*10^167861-167)/3	167862	Robert Price	10/2019
1316	39^105456+2	167788	Robert Price	04/2015
1317	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
1318	10^167639+121911	167640	Patrick De Geest	07/2018
1319	10^167639-8001	167639	Robert Price	03/2018
1320	2^556504-462059	167525	Enzo Doria	07/2015
1321	5*10^167510+9	167511	Robert Price	08/2015
1322	2^555343+1874333	167175	Enzo Doria	06/2016
1323	2^555210-461261	167135	Enzo Doria	07/2015
1324	2^554372+1880527	166883	Enzo Doria	11/2016
1325	2^554299+72173	166861	Enzo Doria	04/2016
1326	2^554037-2797063	166782	Enzo Doria	03/2016
1327	(49*10^166721-139)/9	166722	Robert Price	03/2019
1328	2^553484-29819	166616	Enzo Doria	08/2015
1329	2^553383-2784217	166585	Enzo Doria	10/2015
1330	2^553069+76427	166491	Enzo Doria	05/2016
1331	2*10^166458+51	166459	Robert Price	05/2018
1332	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
1333	11^159756-2424	166369	Mike Oakes	06/2010
1334	2^552649-361275	166364	Enzo Doria	05/2014
1335	2^552628-113669	166358	Enzo Doria	09/2014
1336	10^166324+550603	166325	Patrick De Geest	07/2018
1337	10^166324-801	166324	Robert Price	02/2018
1338	8*10^166227+87	166228	Robert Price	10/2019
1339	2^552137+1879397	166210	Enzo Doria	09/2016
1340	(23^121949-1)/22	166061	Paul Bourdelais	10/2017
1341	2^551542+19249	166031	Payam Samidoost	08/2002
1342	2^551535-23821	166029	Enzo Doria	08/2013
1343	2^551507-23557	166021	Enzo Doria	08/2013
1344	7*10^165916-3	165917	Robert Price	08/2015
1345	81^86837-80^86837	165728	Robert Price	01/2015
1346	(71*10^165663-539)/9	165664	Robert Price	07/2019
1347	2^550270-69551	165648	Enzo Doria	12/2015
1348	2^550000-23625	165567	Enzo Doria	08/2013
1349	2^549675-1852057	165469	Enzo Doria	08/2015
1350	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
1351	(28*10^165358-1)/9	165359	Serge Batalov	10/2014
1353	2^549278+1879669	165350	Enzo Doria	09/2016
1352	(7*10^165350-439)/9	165350	Robert Price	02/2018
1354	2^549252-351269	165342	Enzo Doria	06/2015
1355	(14*10^165282+73)/3	165283	Robert Price	12/2018
1356	2^549049+2797607	165281	Enzo Doria	04/2016
1357	(7*10^165239+107)/3	165240	Robert Price	02/2018
1358	(44^100511-1)/43	165184	Paul Bourdelais	11/2017
1359	(7*10^165134+107)/3	165135	Robert Price	02/2018
1360	(23*10^165060-83)/3	165061	Robert Price	08/2019
1361	(76*10^164984+77)/9	164985	Robert Price	10/2019
1362	2^547178-1856501	164717	Enzo Doria	10/2015
1363	11^158160-60	164707	Enzo Doria	07/2012
1364	(26*10^164643-167)/3	164644	Robert Price	10/2019
1365	2^546398-59201	164483	Enzo Doria	10/2015
1366	2^546332-114893	164463	Enzo Doria	05/2015
1367	2^545958+1876189	164350	Enzo Doria	07/2016
1368	2^545878-49841	164326	Enzo Doria	10/2015
1369	(10^164284+77)/3	164284	Robert Price	01/2018
1370	2^545668-4019	164263	Yves Minet	04/2017
1371	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
1372	(16*10^164122+197)/3	164123	Robert Price	04/2019
1373	2^545185+76757	164118	Enzo Doria	05/2016
1374	2^545076-114329	164085	Enzo Doria	01/2015
1375	(2*10^164043-143)/3	164043	Robert Price	03/2018
1376	(29^112153+1)/30	164011	Lelio R Paula	03/2017
1377	2^544757+1874777	163989	Enzo Doria	06/2016
1378	2^544444-457199	163894	Enzo Doria	01/2015
1379	2^544264-343529	163840	Enzo Doria	07/2015
1380	7*10^163780+9	163781	Robert Price	09/2015
1381	2^543989+2793047	163758	Enzo Doria	02/2016
1382	2^542870-69551	163421	Enzo Doria	12/2015
1383	2^542395+72533	163278	Enzo Doria	04/2016
1384	2^542072-3683	163180	Yves Minet	03/2017
1385	2^541779-1867357	163092	Enzo Doria	04/2016
1386	8*10^162924+9	162925	Robert Price	12/2015
1387	2^540905+81557	162829	Enzo Doria	08/2016
1388	2^540628-2939	162746	Yves Minet	09/2014
1389	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
1390	3*10^162620-59	162621	Robert Price	09/2018
1391	3^340694-112960	162553	Enzo Doria	07/2014
1392	2^539807-114081	162499	Enzo Doria	12/2014
1393	2^539654-114893	162453	Enzo Doria	05/2015
1394	2^539617-1851583	162441	Enzo Doria	08/2015
1395	2^539346+81049	162360	Enzo Doria	07/2016
1396	2^539220-115499	162322	Enzo Doria	07/2015
1397	2^539217-113713	162321	Enzo Doria	09/2014
1398	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
1399	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
1400	(10^162138+11)/3	162138	Serge Batalov	07/2015
1401	2^538473-112723	162097	Enzo Doria	06/2014
1402	2^538157+79337	162002	Enzo Doria	06/2016
1403	2^538136-114749	161996	Enzo Doria	05/2015
1404	2^538104+1531	161986	Lelio R Paula	01/2013
1405	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
1406	2^537815-22737	161899	Enzo Doria	07/2013
1407	2^537804-39839	161896	Enzo Doria	09/2015
1408	2^537458-59201	161791	Enzo Doria	10/2015
1409	2*10^161766+51	161767	Robert Price	05/2018
1410	2^537209-49849	161717	Enzo Doria	10/2015
1411	(58*10^161691+329)/9	161692	Robert Price	05/2019
1412	2^536937+1879397	161635	Enzo Doria	09/2016
1413	2^536569-22881	161524	Enzo Doria	07/2013
1414	10^161253+573493	161254	Patrick De Geest	07/2018
1415	10^161253-8001	161253	Robert Price	03/2018
1416	7*10^161192-9	161193	Robert Price	10/2015
1417	2^535269-113803	161133	Enzo Doria	09/2014
1418	2^535205-23295	161113	Enzo Doria	08/2013
1419	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
1420	2^534359-23229	160859	Enzo Doria	08/2013
1421	67^88037-66^88037	160763	Robert Price	10/2013
1422	2^533948-1852559	160735	Enzo Doria	08/2015
1423	2^533665-23335	160650	Enzo Doria	08/2013
1424	(19*10^160619+77)/3	160620	Robert Price	05/2019
1425	3^336353-2^336353	160482	Mike Oakes	10/2007
1426	2^532253+1868417	160225	Enzo Doria	04/2016
1427	2^532108-291989	160181	Enzo Doria	07/2015
1428	(26*10^160166-131)/3	160167	Robert Price	10/2019
1429	(17*10^160143+67)/3	160144	Robert Price	01/2019
1430	(19*10^159921-49)/3	159922	Robert Price	05/2019
1431	2^531110-1853771	159881	Enzo Doria	09/2015
1432	2^530992-1845299	159845	Enzo Doria	07/2015
1433	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
1434	2^530417-113833	159672	Enzo Doria	09/2014
1435	2^530406-69701	159669	Enzo Doria	02/2016
1436	5*10^159656+41	159657	Robert Price	03/2019
1437	7^188858-188858^7	159604	Norbert Schneider	05/2018
1438	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
1439	(17*10^159438-377)/9	159439	Robert Price	03/2018
1440	2^528944-461315	159229	Enzo Doria	07/2015
1441	(13*10^159147+161)/3	159148	Robert Price	11/2018
1442	2^528620-113879	159131	Enzo Doria	10/2014
1443	2^528000-23307	158944	Enzo Doria	08/2013
1444	(29*10^158909+61)/9	158910	Robert Price	08/2018
1445	2^527817+1876817	158889	Enzo Doria	07/2016
1446	2^527774-49451	158876	Enzo Doria	10/2015
1447	2^527745-291553	158868	Enzo Doria	07/2015
1448	2^527644-1856999	158837	Enzo Doria	10/2015
1449	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
1450	2^527573-1863253	158816	Enzo Doria	12/2015
1451	2^527553-23401	158810	Enzo Doria	08/2013
1452	11^152420-210	158730	Enzo Doria	09/2012
1453	(13*10^158694+401)/9	158695	Robert Price	01/2018
1454	2^527052-69059	158659	Enzo Doria	11/2015
1455	2^526849-113233	158598	Enzo Doria	07/2014
1456	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016
1457	2^526658-3551	158540	Yves Minet	03/2017
1458	7*10^158465-11	158466	Robert Price	06/2019
1459	2^526375-23115	158455	Enzo Doria	08/2013
1460	(77*10^158407-293)/9	158408	Robert Price	09/2019
1461	2^526028-112793	158351	Enzo Doria	07/2014
1462	2^525690-9221	158249	Lelio R Paula	01/2013
1463	2*10^158242-7	158243	Robert Price	10/2015
1464	2^525667-525667^2	158242	Henri Lifchitz	12/2017
1465	2^525186-1857431	158097	Enzo Doria	10/2015
1466	2^524515-23245	157895	Enzo Doria	08/2013
1467	2^524499-109087	157890	Enzo Doria	04/2014
1468	2^18067*(2^506221+1)-1	157827	Makoto Morimoto	05/2014
1469	2^524288+189093	157827	Makoto Morimoto	01/2016
1470	(2^(2^19)-9333)/(1923463121331973)	157814	Makoto Morimoto	09/2017
1471	(10^157792+359)/9	157792	Serge Batalov	12/2014
1472	2^523924+1876591	157717	Enzo Doria	07/2016
1473	(17*10^157705+67)/3	157706	Robert Price	01/2019
1474	(46^94841+1)/47	157696	Robert Price	01/2014
1475	2^523774+77839	157672	Enzo Doria	05/2016
1476	2^523587+2799143	157616	Enzo Doria	04/2016
1477	2^523371+1872113	157551	Enzo Doria	05/2016
1478	(82*10^157319+449)/9	157320	Robert Price	11/2019
1479	2^522535-351457	157299	Enzo Doria	07/2015
1480	2^522226+2799079	157206	Enzo Doria	04/2016
1481	2^522134-1849451	157178	Enzo Doria	08/2015
1482	4*10^157150+93	157151	Robert Price	08/2018
1483	2^521401-29593	156958	Enzo Doria	08/2015
1484	7*10^156956+87	156957	Robert Price	07/2019
1485	2^521348-23397	156942	Enzo Doria	08/2013
1486	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
1487	65^86522+64	156857	Lelio R Paula	04/2016
1488	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
1489	2^520977-1858183	156830	Enzo Doria	10/2015
1490	(8*10^156718-101)/3	156719	Robert Price	08/2018
1491	2^520314-1849481	156631	Enzo Doria	08/2015
1492	(13*10^156522+89)/3	156523	Robert Price	09/2018
1493	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
1494	3*10^156435-97	156436	Robert Price	07/2018
1495	(8*10^156371-77)/3	156372	Robert Price	07/2018
1496	53^90679-52^90679	156356	Robert Price	01/2013
1497	2^519106-59141	156267	Enzo Doria	10/2015
1498	2^519053+6077	156251	Enzo Doria	02/2016
1499	2^518968-1860989	156225	Enzo Doria	11/2015
1500	(25*10^156221-7)/9	156222	Robert Price	05/2018

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PRP Records

Probable Primes Top 10000

(255312 PRPs in the top)