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	3*10^182614-11	182615	Robert Price	07/2018
1252	2^606560-357	182593	Enzo Doria	05/2014
1253	66*10^182420+7	182422	Robert Price	07/2020
1254	2^605687+1866983	182330	Enzo Doria	03/2016
1255	2^605655-114445	182321	Enzo Doria	02/2015
1256	94*10^182291-3	182293	Robert Price	05/2020
1257	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
1258	(14*10^182177-221)/9	182178	Robert Price	04/2018
1259	2^605174-112751	182176	Enzo Doria	06/2014
1260	2^604761+1874507	182052	Enzo Doria	06/2016
1261	2^604705+1871957	182035	Enzo Doria	05/2016
1262	(14*10^182000+229)/9	182001	Robert Price	03/2018
1263	(10^181996+41)/3	181996	Robert Price	12/2017
1264	(5*10^181950-101)/3	181951	Robert Price	04/2018
1265	2^603915+75233	181797	Enzo Doria	04/2016
1266	7*10^181594-57	181595	Robert Price	06/2020
1267	(194*10^181369-11)/3	181371	Robert Price	09/2020
1268	11^174145-360	181354	Enzo Doria	10/2012
1269	2^602351-396765	181326	Enzo Doria	08/2013
1270	6*10^181306+17	181307	Robert Price	04/2019
1271	(286*10^181220-1)/3	181222	Robert Price	11/2020
1272	2^601957-113833	181208	Enzo Doria	09/2014
1273	66^99581-65^99581	181193	Robert Price	09/2013
1274	10^181182+383973	181183	Patrick De Geest	04/2016
1275	10^181182-21	181182	Serge Batalov	12/2014
1276	(5*10^181127-29)/3	181128	Robert Price	03/2018
1277	2^601521-29143	181076	Enzo Doria	07/2015
1278	2^601442-2797811	181053	Enzo Doria	04/2016
1279	44*10^181029+3	181031	Robert Price	04/2020
1280	5*10^180992-9	180993	Robert Price	05/2015
1281	10^180979+79477	180980	Patrick De Geest	04/2016
1282	10^180979+107739	180980	Patrick De Geest	04/2016
1283	10^180979-11	180979	Serge Batalov	12/2014
1284	2^601023-113851	180926	Enzo Doria	10/2014
1285	(23*10^180862-143)/3	180863	Robert Price	12/2019
1286	3*10^180852+29	180853	Robert Price	05/2018
1287	(79*10^180710-1)/3	180712	Robert Price	02/2020
1288	2^600300-1852559	180709	Enzo Doria	08/2015
1289	(10^180689+71)/9	180689	Serge Batalov	07/2015
1290	2^600209+76487	180681	Enzo Doria	05/2016
1291	2^599702-369885	180529	Enzo Doria	11/2013
1292	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
1293	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
1294	(29*10^180432-17)/3	180433	Robert Price	09/2019
1295	4*10^180360+93	180361	Robert Price	08/2018
1296	2^598942+80779	180300	Enzo Doria	07/2016
1297	(38*10^180296+403)/9	180297	Robert Price	10/2018
1298	2^598591-1844797	180194	Enzo Doria	06/2015
1299	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
1300	6*10^179970+91	179971	Robert Price	05/2019
1301	(4*10^179963-79)/3	179964	Robert Price	02/2018
1302	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
1303	2^597424-1859729	179843	Enzo Doria	11/2015
1304	Phi(180683,10)	179760	Maksym Voznyy	09/2015
1305	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
1306	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
1307	(29*10^179697+223)/9	179698	Robert Price	09/2018
1308	(68*10^179656+7)/3	179658	Robert Price	01/2020
1309	2^596690-461261	179622	Enzo Doria	07/2015
1310	2^596684-113939	179620	Enzo Doria	10/2014
1311	2*10^179602+63	179603	Robert Price	05/2018
1312	(25*10^179488-403)/9	179489	Robert Price	01/2021
1313	3^375887-112696	179344	Enzo Doria	07/2014
1314	4*10^179265-71	179266	Robert Price	12/2018
1315	2^595144-1850429	179157	Enzo Doria	08/2015
1316	3*10^179138+89	179139	Robert Price	10/2018
1317	2^594531+82253	178972	Enzo Doria	09/2016
1318	2^594260-2787899	178891	Enzo Doria	11/2015
1319	2^593631+101381	178701	Jorge Menendez	04/2018
1320	10^178695+136719	178696	Patrick De Geest	05/2016
1321	10^178695-71	178695	Serge Batalov	12/2014
1322	(2*10^178649-161)/3	178649	Robert Price	12/2020
1323	(691^62903-1)/690	178609	Michael Stocker	05/2020
1324	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
1325	2^593222-14145	178578	Jorge Menendez	10/2017
1326	7*10^178566+33	178567	Robert Price	06/2020
1327	2^593178+1867219	178565	Enzo Doria	03/2016
1328	(302*10^178369+13)/9	178371	Robert Price	02/2020
1329	(26*10^178296-113)/3	178297	Robert Price	06/2020
1330	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
1331	(5*10^178206+91)/3	178207	Robert Price	04/2018
1332	2^591872-291929	178172	Enzo Doria	07/2015
1333	2^591682-286871	178115	Enzo Doria	07/2015
1334	4*10^178091+9	178092	Robert Price	05/2015
1335	410747#+478483	178007	Makoto Morimoto	02/2016
1336	3*10^177872+73	177873	Robert Price	08/2018
1337	2^590762-396765	177838	Enzo Doria	08/2013
1338	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
1339	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
1340	(266*10^177577-11)/3	177579	Robert Price	04/2020
1341	(11*10^177466-113)/3	177467	Robert Price	10/2018
1342	3*10^177373-97	177374	Robert Price	07/2018
1343	2^589204+1881151	177369	Enzo Doria	11/2016
1344	2^589132-69479	177347	Enzo Doria	01/2016
1345	(101*10^177302-17)/3	177304	Robert Price	02/2020
1346	2^588912-113519	177281	Enzo Doria	08/2014
1347	15^150706+2	177245	Robert Price	06/2015
1348	2^588194-1861001	177065	Enzo Doria	11/2015
1349	(23*10^176964-47)/3	176965	Robert Price	09/2019
1350	(19*10^176932+521)/9	176933	Robert Price	05/2018
1351	(8*10^176908+43)/3	176909	Robert Price	06/2018
1352	(85*10^176900+203)/9	176901	Robert Price	09/2020
1353	2^587560-113699	176874	Enzo Doria	09/2014
1354	(101*10^176815-17)/3	176817	Robert Price	02/2020
1355	(25*10^176715-37)/3	176716	Robert Price	10/2019
1356	5^252763-12862	176674	Enzo Doria	05/2014
1357	2^586804+81721	176646	Enzo Doria	08/2016
1358	(10^176584+77)/3	176584	Robert Price	01/2018
1359	2^586570+1874419	176576	Enzo Doria	06/2016
1360	2^585994-3311	176402	Yves Minet	12/2014
1361	2^585832-112799	176354	Enzo Doria	07/2014
1362	2^585336-461039	176204	Enzo Doria	06/2015
1363	(25*10^176164+143)/3	176165	Robert Price	08/2020
1364	2^585095-1848127	176132	Enzo Doria	08/2015
1365	6*10^176092+77	176093	Robert Price	06/2020
1366	2^584950-115451	176088	Enzo Doria	07/2015
1367	2^584671-3697	176004	Yves Minet	03/2017
1368	(13*10^175965-37)/3	175966	Robert Price	01/2019
1369	2*10^175860-87	175861	Robert Price	04/2018
1370	(86*10^175774-221)/9	175775	Robert Price	09/2019
1371	10^175608+2971	175609	Mike Oakes	05/2010
1372	10^175608-55829	175608	Patrick De Geest	09/2013
1373	2^583051+1879793	175516	Enzo Doria	09/2016
1374	2^582860-23829	175459	Enzo Doria	08/2013
1375	(28*10^175417-67)/3	175418	Robert Price	10/2020
1376	2^582670-23913	175402	Enzo Doria	08/2013
1377	2^582573-29563	175372	Enzo Doria	08/2015
1378	2^582435-1862767	175331	Enzo Doria	12/2015
1379	(11*10^175250-149)/3	175251	Robert Price	09/2018
1380	2^582072-1848599	175222	Enzo Doria	08/2015
1381	(404267#+465)/(3^45^231)	175208	Makoto Morimoto	06/2019
1382	(220221^32768+1)/2	175075	Serge Batalov	03/2018
1383	2^581560+1874911	175068	Enzo Doria	06/2016
1384	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
1385	(47*10^174790+493)/9	174791	Robert Price	03/2019
1386	2^580528-114035	174757	Enzo Doria	11/2014
1387	(19*10^174754+737)/9	174755	Robert Price	07/2018
1388	(35*10^174704-377)/9	174705	Robert Price	07/2018
1389	3*10^174665-97	174666	Robert Price	07/2018
1390	2^580046-459161	174612	Enzo Doria	05/2015
1391	2^579992-39779	174595	Enzo Doria	09/2015
1392	(2*10^174301-71)/3	174301	Robert Price	12/2017
1393	14^152048+3	174267	Paul Bourdelais	12/2020
1394	(2^578696+1)/257	174203	Lelio R Paula	09/2015
1395	2^578656-1851809	174193	Enzo Doria	08/2015
1396	2^578583-113917	174171	Enzo Doria	10/2014
1397	2^578434-83	174126	Yves Minet	07/2017
1398	15^148048-2	174118	Robert Price	06/2015
1399	5*10^174101+81	174102	Robert Price	03/2019
1400	2^578346+2794249	174100	Enzo Doria	03/2016
1401	10^173947-500000001	173947	Robert Price	12/2020
1402	5*10^173904-13	173905	Robert Price	01/2019
1403	(71*10^173854-287)/9	173855	Robert Price	09/2019
1404	(43*10^173826+101)/9	173827	Robert Price	11/2018
1405	2*10^173809-87	173810	Robert Price	04/2018
1406	(L!41532)/2	173772	Serge Batalov	07/2017
1407	2^577146-49877	173739	Enzo Doria	10/2015
1408	2^576889+49727	173661	Enzo Doria	09/2016
1409	(167*10^173571-17)/3	173573	Robert Price	03/2020
1410	5*10^173534+29	173535	Robert Price	12/2020
1411	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
1412	4*10^173509+99	173510	Robert Price	12/2020
1413	(13*10^173467-37)/3	173468	Robert Price	01/2019
1414	2^576016-113919	173399	Enzo Doria	11/2014
1415	2^575911-1849387	173367	Enzo Doria	08/2015
1416	(16*10^173251+107)/3	173252	Robert Price	03/2019
1417	2^575196-114053	173152	Enzo Doria	11/2014
1418	7*10^173135-53	173136	Robert Price	06/2020
1419	2^574591-115387	172970	Enzo Doria	07/2015
1420	(202*10^172940-13)/9	172942	Robert Price	01/2020
1421	2^574328+81121	172890	Enzo Doria	07/2016
1422	(115*10^172862-1)/3	172864	Serge Batalov	12/2014
1423	3*10^172812+13	172813	Robert Price	07/2018
1424	4*5^247217-9	172798	Lelio R Paula	10/2015
1425	6*10^172772-31	172773	Robert Price	07/2020
1426	69061#+(467617#)/(69061#)	172766	Makoto Morimoto	10/2017
1427	5*10^172692+57	172693	Robert Price	12/2018
1428	2^573668-2782319	172692	Enzo Doria	09/2015
1429	2^573444-1855109	172624	Enzo Doria	09/2015
1430	3^361608+2	172531	Robert Price	08/2014
1431	(54^99563+1)/55	172481	Paul Bourdelais	11/2017
1432	2^572592-114893	172368	Enzo Doria	05/2015
1433	4*10^172354-39	172355	Robert Price	09/2020
1434	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
1435	(38^109037-1)/37	172254	Paul Bourdelais	10/2017
1436	3*10^172219+73	172220	Robert Price	08/2018
1437	(36^110503+1)/37	171975	Lelio R Paula	04/2017
1438	(22*10^171929-73)/3	171930	Robert Price	04/2019
1439	4*10^171891-63	171892	Robert Price	10/2018
1440	2^570980-2782289	171883	Enzo Doria	09/2015
1441	(25*10^171849-37)/3	171850	Robert Price	10/2019
1442	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
1443	(536*10^171601-23)/9	171603	Robert Price	02/2020
1444	7*10^171535-99	171536	Robert Price	06/2019
1445	(28*10^171534+101)/3	171535	Robert Price	09/2020
1446	2^569563-1854607	171456	Enzo Doria	09/2015
1447	3*10^171391+59	171392	Robert Price	08/2018
1448	(13*10^171306-37)/3	171307	Robert Price	01/2019
1449	8*10^171296+87	171297	Robert Price	10/2019
1450	(55^98419-1)/54	171284	Paul Bourdelais	12/2017
1451	(29*10^171275+67)/3	171276	Robert Price	12/2019
1452	2^568642+1876129	171179	Enzo Doria	07/2016
1453	(19*10^170970+131)/3	170971	Robert Price	06/2020
1454	(46*10^170932+143)/9	170933	Robert Price	01/2019
1455	(79*10^170901-1)/3	170903	Robert Price	02/2020
1456	(58*10^170842+221)/9	170843	Robert Price	02/2017
1457	3*10^170800+73	170801	Robert Price	08/2018
1458	11^164009-270	170798	Enzo Doria	10/2012
1459	2*10^170767+41	170768	Robert Price	05/2018
1460	3^357706-112358	170670	Enzo Doria	07/2014
1461	TheodorusPrime(170657)	170657	Eric W. Weisstein	08/2013
1462	2^566871+1876163	170646	Enzo Doria	07/2016
1463	(10657#+(404267#)/(10657#))/(1675379)	170624	Makoto Morimoto	10/2017
1464	2^566496+7	170533	Donovan Johnson	07/2006
1465	(7^201653+1)/8	170416	Paul Bourdelais	02/2010
1466	7*10^170348+33	170349	Robert Price	06/2020
1467	2^565183-352021	170138	Enzo Doria	07/2015
1468	2^565143-114457	170125	Enzo Doria	02/2015
1469	2^564976-49869	170075	Enzo Doria	10/2015
1470	(7*10^169944+23)/3	169945	Robert Price	06/2020
1471	2^564526-351401	169940	Enzo Doria	07/2015
1472	4*10^169759+19	169760	Robert Price	10/2018
1473	21^128327-20^128327	169677	Jean-Louis Charton	11/2014
1474	(4*10^169559+83)/3	169560	Robert Price	02/2018
1475	(194*10^169461-17)/3	169463	Robert Price	09/2020
1476	2^562749+2793047	169405	Enzo Doria	02/2016
1477	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
1478	(56*10^169311+691)/9	169312	Robert Price	05/2019
1479	2^562369-29503	169290	Enzo Doria	08/2015
1480	(22*10^169019+383)/9	169020	Robert Price	05/2018
1481	5*10^168807+87	168808	Robert Price	02/2019
1482	2^560405-39943	168699	Enzo Doria	09/2015
1483	89*10^168614-7	168616	Robert Price	04/2020
1484	(23*10^168608-83)/3	168609	Robert Price	08/2019
1485	(94*10^168541+11)/3	168543	Robert Price	04/2020
1486	2^559686-350471	168483	Enzo Doria	06/2015
1487	2^559672-1855889	168479	Enzo Doria	09/2015
1488	(5*10^168379-473)/9	168379	Robert Price	01/2018
1489	2^559000-59939	168276	Enzo Doria	11/2015
1490	(16*10^168181+41)/3	168182	Robert Price	03/2019
1491	(19*10^168173+77)/3	168174	Robert Price	05/2019
1492	2^558640-114149	168168	Enzo Doria	12/2014
1493	2^558498-1849277	168125	Enzo Doria	08/2015
1494	2^558476-1850249	168119	Enzo Doria	08/2015
1495	(7*10^168067+71)/3	168068	Robert Price	05/2018
1496	2^558150-1852211	168020	Enzo Doria	08/2015
1497	2^558125-113661	168013	Enzo Doria	09/2014
1498	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
1499	(13*10^167911+179)/3	167912	Robert Price	11/2018
1500	(26*10^167861-167)/3	167862	Robert Price	10/2019

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PRP Records

Probable Primes Top 10000

(277034 PRPs in the top)