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	(29*10^180432-17)/3	180433	Robert Price	09/2019
1252	4*10^180360+93	180361	Robert Price	08/2018
1253	2^598942+80779	180300	Enzo Doria	07/2016
1254	(38*10^180296+403)/9	180297	Robert Price	10/2018
1255	2^598591-1844797	180194	Enzo Doria	06/2015
1256	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
1257	6*10^179970+91	179971	Robert Price	05/2019
1258	(4*10^179963-79)/3	179964	Robert Price	02/2018
1259	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
1260	2^597424-1859729	179843	Enzo Doria	11/2015
1261	Phi(180683,10)	179760	Maksym Voznyy	09/2015
1262	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
1263	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
1264	(29*10^179697+223)/9	179698	Robert Price	09/2018
1265	(68*10^179656+7)/3	179658	Robert Price	01/2020
1266	2^596690-461261	179622	Enzo Doria	07/2015
1267	2^596684-113939	179620	Enzo Doria	10/2014
1268	2*10^179602+63	179603	Robert Price	05/2018
1269	3^375887-112696	179344	Enzo Doria	07/2014
1270	4*10^179265-71	179266	Robert Price	12/2018
1271	2^595144-1850429	179157	Enzo Doria	08/2015
1272	3*10^179138+89	179139	Robert Price	10/2018
1273	2^594531+82253	178972	Enzo Doria	09/2016
1274	2^594260-2787899	178891	Enzo Doria	11/2015
1275	2^593631+101381	178701	Jorge Menendez	04/2018
1276	10^178695+136719	178696	Patrick De Geest	05/2016
1277	10^178695-71	178695	Serge Batalov	12/2014
1278	(691^62903-1)/690	178609	Michael Stocker	05/2020
1279	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
1280	2^593222-14145	178578	Jorge Menendez	10/2017
1281	7*10^178566+33	178567	Robert Price	06/2020
1282	2^593178+1867219	178565	Enzo Doria	03/2016
1283	(302*10^178369+13)/9	178371	Robert Price	02/2020
1284	(26*10^178296-113)/3	178297	Robert Price	06/2020
1285	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
1286	(5*10^178206+91)/3	178207	Robert Price	04/2018
1287	2^591872-291929	178172	Enzo Doria	07/2015
1288	2^591682-286871	178115	Enzo Doria	07/2015
1289	4*10^178091+9	178092	Robert Price	05/2015
1290	410747#+478483	178007	Makoto Morimoto	02/2016
1291	3*10^177872+73	177873	Robert Price	08/2018
1292	2^590762-396765	177838	Enzo Doria	08/2013
1293	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
1294	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
1295	(266*10^177577-11)/3	177579	Robert Price	04/2020
1296	(11*10^177466-113)/3	177467	Robert Price	10/2018
1297	3*10^177373-97	177374	Robert Price	07/2018
1298	2^589204+1881151	177369	Enzo Doria	11/2016
1299	2^589132-69479	177347	Enzo Doria	01/2016
1300	(101*10^177302-17)/3	177304	Robert Price	02/2020
1301	2^588912-113519	177281	Enzo Doria	08/2014
1302	15^150706+2	177245	Robert Price	06/2015
1303	2^588194-1861001	177065	Enzo Doria	11/2015
1304	(23*10^176964-47)/3	176965	Robert Price	09/2019
1305	(19*10^176932+521)/9	176933	Robert Price	05/2018
1306	(8*10^176908+43)/3	176909	Robert Price	06/2018
1307	(85*10^176900+203)/9	176901	Robert Price	09/2020
1308	2^587560-113699	176874	Enzo Doria	09/2014
1309	(101*10^176815-17)/3	176817	Robert Price	02/2020
1310	(25*10^176715-37)/3	176716	Robert Price	10/2019
1311	5^252763-12862	176674	Enzo Doria	05/2014
1312	2^586804+81721	176646	Enzo Doria	08/2016
1313	(10^176584+77)/3	176584	Robert Price	01/2018
1314	2^586570+1874419	176576	Enzo Doria	06/2016
1315	2^585994-3311	176402	Yves Minet	12/2014
1316	2^585832-112799	176354	Enzo Doria	07/2014
1317	2^585336-461039	176204	Enzo Doria	06/2015
1318	(25*10^176164+143)/3	176165	Robert Price	08/2020
1319	2^585095-1848127	176132	Enzo Doria	08/2015
1320	6*10^176092+77	176093	Robert Price	06/2020
1321	2^584950-115451	176088	Enzo Doria	07/2015
1322	2^584671-3697	176004	Yves Minet	03/2017
1323	(13*10^175965-37)/3	175966	Robert Price	01/2019
1324	2*10^175860-87	175861	Robert Price	04/2018
1325	(86*10^175774-221)/9	175775	Robert Price	09/2019
1326	10^175608+2971	175609	Mike Oakes	05/2010
1327	10^175608-55829	175608	Patrick De Geest	09/2013
1328	2^583051+1879793	175516	Enzo Doria	09/2016
1329	2^582860-23829	175459	Enzo Doria	08/2013
1330	2^582670-23913	175402	Enzo Doria	08/2013
1331	2^582573-29563	175372	Enzo Doria	08/2015
1332	2^582435-1862767	175331	Enzo Doria	12/2015
1333	(11*10^175250-149)/3	175251	Robert Price	09/2018
1334	2^582072-1848599	175222	Enzo Doria	08/2015
1335	(404267#+465)/(3^45^231)	175208	Makoto Morimoto	06/2019
1336	(220221^32768+1)/2	175075	Serge Batalov	03/2018
1337	2^581560+1874911	175068	Enzo Doria	06/2016
1338	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
1339	(47*10^174790+493)/9	174791	Robert Price	03/2019
1340	2^580528-114035	174757	Enzo Doria	11/2014
1341	(19*10^174754+737)/9	174755	Robert Price	07/2018
1342	(35*10^174704-377)/9	174705	Robert Price	07/2018
1343	3*10^174665-97	174666	Robert Price	07/2018
1344	2^580046-459161	174612	Enzo Doria	05/2015
1345	2^579992-39779	174595	Enzo Doria	09/2015
1346	(2*10^174301-71)/3	174301	Robert Price	12/2017
1347	(2^578696+1)/257	174203	Lelio R Paula	09/2015
1348	2^578656-1851809	174193	Enzo Doria	08/2015
1349	2^578583-113917	174171	Enzo Doria	10/2014
1350	2^578434-83	174126	Yves Minet	07/2017
1351	15^148048-2	174118	Robert Price	06/2015
1352	5*10^174101+81	174102	Robert Price	03/2019
1353	2^578346+2794249	174100	Enzo Doria	03/2016
1354	5*10^173904-13	173905	Robert Price	01/2019
1355	(71*10^173854-287)/9	173855	Robert Price	09/2019
1356	(43*10^173826+101)/9	173827	Robert Price	11/2018
1357	2*10^173809-87	173810	Robert Price	04/2018
1358	(L!41532)/2	173772	Serge Batalov	07/2017
1359	2^577146-49877	173739	Enzo Doria	10/2015
1360	2^576889+49727	173661	Enzo Doria	09/2016
1361	(167*10^173571-17)/3	173573	Robert Price	03/2020
1362	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
1363	(13*10^173467-37)/3	173468	Robert Price	01/2019
1364	2^576016-113919	173399	Enzo Doria	11/2014
1365	2^575911-1849387	173367	Enzo Doria	08/2015
1366	(16*10^173251+107)/3	173252	Robert Price	03/2019
1367	2^575196-114053	173152	Enzo Doria	11/2014
1368	7*10^173135-53	173136	Robert Price	06/2020
1369	2^574591-115387	172970	Enzo Doria	07/2015
1370	(202*10^172940-13)/9	172942	Robert Price	01/2020
1371	2^574328+81121	172890	Enzo Doria	07/2016
1372	(115*10^172862-1)/3	172864	Serge Batalov	12/2014
1373	3*10^172812+13	172813	Robert Price	07/2018
1374	4*5^247217-9	172798	Lelio R Paula	10/2015
1375	6*10^172772-31	172773	Robert Price	07/2020
1376	69061#+(467617#)/(69061#)	172766	Makoto Morimoto	10/2017
1377	5*10^172692+57	172693	Robert Price	12/2018
1378	2^573668-2782319	172692	Enzo Doria	09/2015
1379	2^573444-1855109	172624	Enzo Doria	09/2015
1380	3^361608+2	172531	Robert Price	08/2014
1381	(54^99563+1)/55	172481	Paul Bourdelais	11/2017
1382	2^572592-114893	172368	Enzo Doria	05/2015
1383	4*10^172354-39	172355	Robert Price	09/2020
1384	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
1385	(38^109037-1)/37	172254	Paul Bourdelais	10/2017
1386	3*10^172219+73	172220	Robert Price	08/2018
1387	(36^110503+1)/37	171975	Lelio R Paula	04/2017
1388	(22*10^171929-73)/3	171930	Robert Price	04/2019
1389	4*10^171891-63	171892	Robert Price	10/2018
1390	2^570980-2782289	171883	Enzo Doria	09/2015
1391	(25*10^171849-37)/3	171850	Robert Price	10/2019
1392	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
1393	(536*10^171601-23)/9	171603	Robert Price	02/2020
1394	7*10^171535-99	171536	Robert Price	06/2019
1395	(28*10^171534+101)/3	171535	Robert Price	09/2020
1396	2^569563-1854607	171456	Enzo Doria	09/2015
1397	3*10^171391+59	171392	Robert Price	08/2018
1398	(13*10^171306-37)/3	171307	Robert Price	01/2019
1399	8*10^171296+87	171297	Robert Price	10/2019
1400	(55^98419-1)/54	171284	Paul Bourdelais	12/2017
1401	(29*10^171275+67)/3	171276	Robert Price	12/2019
1402	2^568642+1876129	171179	Enzo Doria	07/2016
1403	(19*10^170970+131)/3	170971	Robert Price	06/2020
1404	(46*10^170932+143)/9	170933	Robert Price	01/2019
1405	(79*10^170901-1)/3	170903	Robert Price	02/2020
1406	(58*10^170842+221)/9	170843	Robert Price	02/2017
1407	3*10^170800+73	170801	Robert Price	08/2018
1408	11^164009-270	170798	Enzo Doria	10/2012
1409	2*10^170767+41	170768	Robert Price	05/2018
1410	3^357706-112358	170670	Enzo Doria	07/2014
1411	TheodorusPrime(170657)	170657	Eric W. Weisstein	08/2013
1412	2^566871+1876163	170646	Enzo Doria	07/2016
1413	(10657#+(404267#)/(10657#))/(1675379)	170624	Makoto Morimoto	10/2017
1414	2^566496+7	170533	Donovan Johnson	07/2006
1415	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
1416	7*10^170348+33	170349	Robert Price	06/2020
1417	2^565183-352021	170138	Enzo Doria	07/2015
1418	2^565143-114457	170125	Enzo Doria	02/2015
1419	2^564976-49869	170075	Enzo Doria	10/2015
1420	(7*10^169944+23)/3	169945	Robert Price	06/2020
1421	2^564526-351401	169940	Enzo Doria	07/2015
1422	4*10^169759+19	169760	Robert Price	10/2018
1423	21^128327-20^128327	169677	Jean-Louis Charton	11/2014
1424	(4*10^169559+83)/3	169560	Robert Price	02/2018
1425	(194*10^169461-17)/3	169463	Robert Price	09/2020
1426	2^562749+2793047	169405	Enzo Doria	02/2016
1427	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
1428	(56*10^169311+691)/9	169312	Robert Price	05/2019
1429	2^562369-29503	169290	Enzo Doria	08/2015
1430	(22*10^169019+383)/9	169020	Robert Price	05/2018
1431	5*10^168807+87	168808	Robert Price	02/2019
1432	2^560405-39943	168699	Enzo Doria	09/2015
1433	89*10^168614-7	168616	Robert Price	04/2020
1434	(23*10^168608-83)/3	168609	Robert Price	08/2019
1435	(94*10^168541+11)/3	168543	Robert Price	04/2020
1436	2^559686-350471	168483	Enzo Doria	06/2015
1437	2^559672-1855889	168479	Enzo Doria	09/2015
1438	(5*10^168379-473)/9	168379	Robert Price	01/2018
1439	2^559000-59939	168276	Enzo Doria	11/2015
1440	(16*10^168181+41)/3	168182	Robert Price	03/2019
1441	(19*10^168173+77)/3	168174	Robert Price	05/2019
1442	2^558640-114149	168168	Enzo Doria	12/2014
1443	2^558498-1849277	168125	Enzo Doria	08/2015
1444	2^558476-1850249	168119	Enzo Doria	08/2015
1445	(7*10^168067+71)/3	168068	Robert Price	05/2018
1446	2^558150-1852211	168020	Enzo Doria	08/2015
1447	2^558125-113661	168013	Enzo Doria	09/2014
1448	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
1449	(13*10^167911+179)/3	167912	Robert Price	11/2018
1450	(26*10^167861-167)/3	167862	Robert Price	10/2019
1451	39^105456+2	167788	Robert Price	04/2015
1452	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
1453	10^167639+121911	167640	Patrick De Geest	07/2018
1454	10^167639-8001	167639	Robert Price	03/2018
1455	2^556504-462059	167525	Enzo Doria	07/2015
1456	5*10^167510+9	167511	Robert Price	08/2015
1457	7*10^167437-93	167438	Robert Price	08/2020
1458	2^555343+1874333	167175	Enzo Doria	06/2016
1459	2^555210-461261	167135	Enzo Doria	07/2015
1460	9*10^166996+59	166997	Robert Price	01/2020
1461	2^554372+1880527	166883	Enzo Doria	11/2016
1462	2^554299+72173	166861	Enzo Doria	04/2016
1463	(185*10^166837+7)/3	166839	Robert Price	03/2020
1464	2^554037-2797063	166782	Enzo Doria	03/2016
1465	(49*10^166721-139)/9	166722	Robert Price	03/2019
1466	2*10^166646+69	166647	Robert Price	06/2020
1467	2^553484-29819	166616	Enzo Doria	08/2015
1468	(188*10^166611+7)/3	166613	Robert Price	03/2020
1469	2^553383-2784217	166585	Enzo Doria	10/2015
1470	2^553069+76427	166491	Enzo Doria	05/2016
1471	2*10^166458+51	166459	Robert Price	05/2018
1472	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
1473	11^159756-2424	166369	Mike Oakes	06/2010
1474	2^552649-361275	166364	Enzo Doria	05/2014
1475	2^552628-113669	166358	Enzo Doria	09/2014
1476	10^166324+550603	166325	Patrick De Geest	07/2018
1477	10^166324-801	166324	Robert Price	02/2018
1478	(85*10^166297-1)/3	166299	Robert Price	02/2020
1479	8*10^166227+87	166228	Robert Price	10/2019
1480	2^552137+1879397	166210	Enzo Doria	09/2016
1481	(23^121949-1)/22	166061	Paul Bourdelais	10/2017
1482	2^551542+19249	166031	Payam Samidoost	08/2002
1483	2^551535-23821	166029	Enzo Doria	08/2013
1484	2^551507-23557	166021	Enzo Doria	08/2013
1485	7*10^165916-3	165917	Robert Price	08/2015
1486	(29*10^165796+67)/3	165797	Robert Price	12/2019
1487	81^86837-80^86837	165728	Robert Price	01/2015
1488	(71*10^165663-539)/9	165664	Robert Price	07/2019
1489	2^550270-69551	165648	Enzo Doria	12/2015
1490	(202*10^165569-13)/9	165571	Robert Price	01/2020
1491	2^550000-23625	165567	Enzo Doria	08/2013
1492	2^549675-1852057	165469	Enzo Doria	08/2015
1493	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
1494	(28*10^165358-1)/9	165359	Serge Batalov	10/2014
1495	2^549278+1879669	165350	Enzo Doria	09/2016
1496	(7*10^165350-439)/9	165350	Robert Price	02/2018
1497	2^549252-351269	165342	Enzo Doria	06/2015
1498	(14*10^165282+73)/3	165283	Robert Price	12/2018
1499	2^549049+2797607	165281	Enzo Doria	04/2016
1500	(7*10^165239+107)/3	165240	Robert Price	02/2018

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PRP Records

Probable Primes Top 10000

(271067 PRPs in the top)