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	2^613033-114621	184542	Enzo Doria	05/2015
1252	(9^193247+1)/10	184404	Paul Bourdelais	02/2010
1253	2^612341-1604809	184334	Enzo Doria	05/2015
1254	(2^611999-1)/18464214225958267477777390354183	184199	Dario Alpern	06/2017
1255	(14*10^184150+37)/3	184151	Robert Price	12/2018
1256	2^611731-4837	184150	Yves Minet	08/2018
1257	3*10^184124-7	184125	Robert Price	08/2015
1258	2^611628-24537	184119	Enzo Doria	08/2013
1259	3*10^184110+13	184111	Robert Price	07/2018
1260	2^611460+71881	184068	Enzo Doria	04/2016
1261	4*10^184004-63	184005	Robert Price	10/2018
1262	2^610982-1867301	183924	Enzo Doria	03/2016
1263	3*10^183872-49	183873	Robert Price	07/2018
1264	2^610597+1178897	183809	Enzo Doria	05/2016
1265	(65*10^183768-29)/9	183769	Robert Price	01/2021
1266	(17*10^183764+31)/3	183765	Robert Price	01/2019
1267	(28*10^183760-1)/9	183761	Serge Batalov	10/2014
1268	2^610401+1277	183750	Lelio R Paula	07/2013
1269	2^610356-1849019	183736	Enzo Doria	08/2015
1270	(63^102103+1)/64	183717	Paul Bourdelais	10/2017
1271	23*10^183710-7	183712	Robert Price	02/2020
1272	(2^610289+1)/(3*528882550291)	183704	Gord Palameta	08/2018
1273	(4*10^183659+149)/9	183659	Robert Price	04/2018
1274	2^609846-1834251	183582	Enzo Doria	07/2015
1275	10^183546+1547323	183547	Patrick De Geest	02/2021
1277	10^183546-800000001	183546	Robert Price	09/2020
1276	10^183546-584297	183546	Patrick De Geest	02/2021
1278	(23*10^183477-71)/3	183478	Robert Price	07/2020
1279	11^176176-240	183469	Enzo Doria	11/2012
1280	(41^113749+1)/42	183451	Paul Bourdelais	11/2017
1281	6*10^183429+53	183430	Robert Price	05/2020
1282	(28*10^183403+191)/3	183404	Robert Price	02/2020
1283	(101^91463+1)/102	183320	Paul Bourdelais	11/2017
1284	2^608965-113989	183317	Enzo Doria	10/2014
1285	A005165(43592)	183312	Serge Batalov	07/2017
1286	(61*10^183294+119)/9	183295	Robert Price	05/2019
1287	2^608814-461261	183272	Enzo Doria	06/2015
1288	(163*10^183227-1)/9	183229	Serge Batalov	12/2014
1289	2^608541-608541^2	183190	Henri Lifchitz	02/2018
1290	2^608293+143807	183115	Enzo Doria	10/2016
1291	2^608164-462419	183076	Enzo Doria	08/2015
1292	2^607950-1862303	183012	Enzo Doria	12/2015
1293	(46*10^182896+683)/9	182897	Robert Price	03/2019
1294	(2*10^182787+73)/3	182787	Robert Price	09/2020
1295	2^607101+1871987	182756	Enzo Doria	05/2016
1296	2^606869-69175	182686	Enzo Doria	11/2015
1297	(23*10^182666-71)/3	182667	Robert Price	07/2020
1298	3*10^182614-11	182615	Robert Price	07/2018
1299	2^606560-357	182593	Enzo Doria	05/2014
1300	66*10^182420+7	182422	Robert Price	07/2020
1301	2^605687+1866983	182330	Enzo Doria	03/2016
1302	2^605655-114445	182321	Enzo Doria	02/2015
1303	94*10^182291-3	182293	Robert Price	05/2020
1304	(20^140053+1)/21	182212	Paul Bourdelais	04/2010
1305	(14*10^182177-221)/9	182178	Robert Price	04/2018
1306	2^605174-112751	182176	Enzo Doria	06/2014
1307	2^604761+1874507	182052	Enzo Doria	06/2016
1308	2^604705+1871957	182035	Enzo Doria	05/2016
1309	(14*10^182000+229)/9	182001	Robert Price	03/2018
1310	(10^181996+41)/3	181996	Robert Price	12/2017
1311	(5*10^181950-101)/3	181951	Robert Price	04/2018
1312	2^603915+75233	181797	Enzo Doria	04/2016
1313	7*10^181594-57	181595	Robert Price	06/2020
1314	(194*10^181369-11)/3	181371	Robert Price	09/2020
1315	11^174145-360	181354	Enzo Doria	10/2012
1316	2^602351-396765	181326	Enzo Doria	08/2013
1317	6*10^181306+17	181307	Robert Price	04/2019
1318	(286*10^181220-1)/3	181222	Robert Price	11/2020
1319	2^601957-113833	181208	Enzo Doria	09/2014
1320	66^99581-65^99581	181193	Robert Price	09/2013
1321	10^181182+383973	181183	Patrick De Geest	04/2016
1322	10^181182-21	181182	Serge Batalov	12/2014
1323	(5*10^181127-29)/3	181128	Robert Price	03/2018
1324	2^601521-29143	181076	Enzo Doria	07/2015
1325	2^601442-2797811	181053	Enzo Doria	04/2016
1326	44*10^181029+3	181031	Robert Price	04/2020
1327	5*10^180992-9	180993	Robert Price	05/2015
1328	10^180979+79477	180980	Patrick De Geest	04/2016
1329	10^180979+107739	180980	Patrick De Geest	04/2016
1330	10^180979-11	180979	Serge Batalov	12/2014
1331	2^601023-113851	180926	Enzo Doria	10/2014
1332	(23*10^180862-143)/3	180863	Robert Price	12/2019
1333	3*10^180852+29	180853	Robert Price	05/2018
1334	(79*10^180710-1)/3	180712	Robert Price	02/2020
1335	2^600300-1852559	180709	Enzo Doria	08/2015
1336	(2*10^180706-77)/3	180706	Robert Price	02/2021
1337	(10^180689+71)/9	180689	Serge Batalov	07/2015
1338	2^600209+76487	180681	Enzo Doria	05/2016
1339	2^599702-369885	180529	Enzo Doria	11/2013
1340	Tau(643^11688)	180524	Nik Lygeros / Olivier Rozier	05/2015
1341	(2951*29^123418-3)/4	180490	Curtis Bright	05/2015
1342	(29*10^180432-17)/3	180433	Robert Price	09/2019
1343	4*10^180360+93	180361	Robert Price	08/2018
1344	2^598942+80779	180300	Enzo Doria	07/2016
1345	(38*10^180296+403)/9	180297	Robert Price	10/2018
1346	2^598591-1844797	180194	Enzo Doria	06/2015
1347	(100^90089+1)/101	180176	Paul Bourdelais	08/2017
1348	6*10^179970+91	179971	Robert Price	05/2019
1349	(4*10^179963-79)/3	179964	Robert Price	02/2018
1350	Gamma-Prime(179849)	179849	Eric W. Weisstein	06/2011
1351	2^597424-1859729	179843	Enzo Doria	11/2015
1352	Phi(180683,10)	179760	Maksym Voznyy	09/2015
1353	(10^180683-1)*9/(10^643-1)/(10^281-1)	179760	Robert Price	07/2016
1354	(3^376657-2^376657)/22301107657	179701	Mike Oakes	04/2017
1355	(29*10^179697+223)/9	179698	Robert Price	09/2018
1356	(68*10^179656+7)/3	179658	Robert Price	01/2020
1357	2^596690-461261	179622	Enzo Doria	07/2015
1358	2^596684-113939	179620	Enzo Doria	10/2014
1359	2*10^179602+63	179603	Robert Price	05/2018
1360	(25*10^179488-403)/9	179489	Robert Price	01/2021
1361	3^375887-112696	179344	Enzo Doria	07/2014
1362	4*10^179265-71	179266	Robert Price	12/2018
1363	2^595144-1850429	179157	Enzo Doria	08/2015
1364	3*10^179138+89	179139	Robert Price	10/2018
1365	2^594531+82253	178972	Enzo Doria	09/2016
1366	2^594260-2787899	178891	Enzo Doria	11/2015
1367	2^593631+101381	178701	Jorge Menendez	04/2018
1368	10^178695+136719	178696	Patrick De Geest	05/2016
1369	10^178695-71	178695	Serge Batalov	12/2014
1370	(2*10^178649-161)/3	178649	Robert Price	12/2020
1371	(691^62903-1)/690	178609	Michael Stocker	05/2020
1372	(2^148330+1)^4-2	178608	Cletus Emmanuel	12/2003
1373	2^593222-14145	178578	Jorge Menendez	10/2017
1374	7*10^178566+33	178567	Robert Price	06/2020
1375	2^593178+1867219	178565	Enzo Doria	03/2016
1376	(302*10^178369+13)/9	178371	Robert Price	02/2020
1377	(26*10^178296-113)/3	178297	Robert Price	06/2020
1378	(18^142031-1)/17	178287	Paul Bourdelais	03/2010
1379	(5*10^178206+91)/3	178207	Robert Price	04/2018
1380	2^591872-291929	178172	Enzo Doria	07/2015
1381	2^591682-286871	178115	Enzo Doria	07/2015
1382	4*10^178091+9	178092	Robert Price	05/2015
1383	410747#+478483	178007	Makoto Morimoto	02/2016
1384	3*10^177872+73	177873	Robert Price	08/2018
1385	2^590762-396765	177838	Enzo Doria	08/2013
1386	(136*10^177754-1)/9	177756	Serge Batalov	12/2014
1387	ReverseConsecutiveIntegerPrime(37765)	177719	Eric W. Weisstein	04/2010
1388	(266*10^177577-11)/3	177579	Robert Price	04/2020
1389	(11*10^177466-113)/3	177467	Robert Price	10/2018
1390	3*10^177373-97	177374	Robert Price	07/2018
1391	2^589204+1881151	177369	Enzo Doria	11/2016
1392	2^589132-69479	177347	Enzo Doria	01/2016
1393	(101*10^177302-17)/3	177304	Robert Price	02/2020
1394	2^588912-113519	177281	Enzo Doria	08/2014
1395	15^150706+2	177245	Robert Price	06/2015
1396	2^588194-1861001	177065	Enzo Doria	11/2015
1397	(23*10^176964-47)/3	176965	Robert Price	09/2019
1398	(19*10^176932+521)/9	176933	Robert Price	05/2018
1399	(8*10^176908+43)/3	176909	Robert Price	06/2018
1400	(85*10^176900+203)/9	176901	Robert Price	09/2020
1401	2^587560-113699	176874	Enzo Doria	09/2014
1402	(101*10^176815-17)/3	176817	Robert Price	02/2020
1403	(25*10^176715-37)/3	176716	Robert Price	10/2019
1404	5^252763-12862	176674	Enzo Doria	05/2014
1405	2^586804+81721	176646	Enzo Doria	08/2016
1406	(10^176584+77)/3	176584	Robert Price	01/2018
1407	2^586570+1874419	176576	Enzo Doria	06/2016
1408	2^585994-3311	176402	Yves Minet	12/2014
1409	8*10^176383-81	176384	Robert Price	02/2021
1410	2^585832-112799	176354	Enzo Doria	07/2014
1411	2^585336-461039	176204	Enzo Doria	06/2015
1412	(25*10^176164+143)/3	176165	Robert Price	08/2020
1413	2^585095-1848127	176132	Enzo Doria	08/2015
1414	6*10^176092+77	176093	Robert Price	06/2020
1415	2^584950-115451	176088	Enzo Doria	07/2015
1416	2^584671-3697	176004	Yves Minet	03/2017
1417	(13*10^175965-37)/3	175966	Robert Price	01/2019
1418	2*10^175860-87	175861	Robert Price	04/2018
1419	(86*10^175774-221)/9	175775	Robert Price	09/2019
1420	10^175608+2971	175609	Mike Oakes	05/2010
1421	10^175608-55829	175608	Patrick De Geest	09/2013
1422	2^583051+1879793	175516	Enzo Doria	09/2016
1423	2^582860-23829	175459	Enzo Doria	08/2013
1424	(28*10^175417-67)/3	175418	Robert Price	10/2020
1425	2^582670-23913	175402	Enzo Doria	08/2013
1426	2^582573-29563	175372	Enzo Doria	08/2015
1427	2^582435-1862767	175331	Enzo Doria	12/2015
1428	(11*10^175250-149)/3	175251	Robert Price	09/2018
1429	(29*10^175236+31)/3	175237	Robert Price	04/2021
1430	2^582072-1848599	175222	Enzo Doria	08/2015
1431	(404267#+465)/(3^45^231)	175208	Makoto Morimoto	06/2019
1432	(220221^32768+1)/2	175075	Serge Batalov	03/2018
1433	2^581560+1874911	175068	Enzo Doria	06/2016
1434	(75^93307-1)/74	174955	Paul Bourdelais	09/2017
1435	(47*10^174790+493)/9	174791	Robert Price	03/2019
1436	2^580528-114035	174757	Enzo Doria	11/2014
1437	(19*10^174754+737)/9	174755	Robert Price	07/2018
1438	(35*10^174704-377)/9	174705	Robert Price	07/2018
1439	(49*10^174681+293)/9	174682	Robert Price	03/2021
1440	3*10^174665-97	174666	Robert Price	07/2018
1441	2^580046-459161	174612	Enzo Doria	05/2015
1442	2^579992-39779	174595	Enzo Doria	09/2015
1443	(2*10^174301-71)/3	174301	Robert Price	12/2017
1444	14^152048+3	174267	Paul Bourdelais	12/2020
1445	(2^578696+1)/257	174203	Lelio R Paula	09/2015
1446	2^578656-1851809	174193	Enzo Doria	08/2015
1447	2^578583-113917	174171	Enzo Doria	10/2014
1448	2^578434-83	174126	Yves Minet	07/2017
1449	15^148048-2	174118	Robert Price	06/2015
1450	5*10^174101+81	174102	Robert Price	03/2019
1451	2^578346+2794249	174100	Enzo Doria	03/2016
1452	10^173947-500000001	173947	Robert Price	12/2020
1453	5*10^173904-13	173905	Robert Price	01/2019
1454	(71*10^173854-287)/9	173855	Robert Price	09/2019
1455	(43*10^173826+101)/9	173827	Robert Price	11/2018
1456	2*10^173809-87	173810	Robert Price	04/2018
1457	(L!41532)/2	173772	Serge Batalov	07/2017
1458	2^577146-49877	173739	Enzo Doria	10/2015
1459	2^576889+49727	173661	Enzo Doria	09/2016
1460	(167*10^173571-17)/3	173573	Robert Price	03/2020
1461	5*10^173534+29	173535	Robert Price	12/2020
1462	(2^576551-1)/4612409/64758208321/242584327930759	173528	Dario Alpern	06/2014
1463	4*10^173509+99	173510	Robert Price	12/2020
1464	(13*10^173467-37)/3	173468	Robert Price	01/2019
1465	2^576016-113919	173399	Enzo Doria	11/2014
1466	2^575911-1849387	173367	Enzo Doria	08/2015
1467	(16*10^173251+107)/3	173252	Robert Price	03/2019
1468	2^575196-114053	173152	Enzo Doria	11/2014
1469	7*10^173135-53	173136	Robert Price	06/2020
1470	2^574591-115387	172970	Enzo Doria	07/2015
1471	(202*10^172940-13)/9	172942	Robert Price	01/2020
1472	2^574328+81121	172890	Enzo Doria	07/2016
1473	(115*10^172862-1)/3	172864	Serge Batalov	12/2014
1474	3*10^172812+13	172813	Robert Price	07/2018
1475	4*5^247217-9	172798	Lelio R Paula	10/2015
1476	6*10^172772-31	172773	Robert Price	07/2020
1477	69061#+(467617#)/(69061#)	172766	Makoto Morimoto	10/2017
1478	(34*10^172693-547)/9	172694	Robert Price	03/2021
1479	5*10^172692+57	172693	Robert Price	12/2018
1480	2^573668-2782319	172692	Enzo Doria	09/2015
1481	2^573444-1855109	172624	Enzo Doria	09/2015
1482	3^361608+2	172531	Robert Price	08/2014
1483	(54^99563+1)/55	172481	Paul Bourdelais	11/2017
1484	2^572592-114893	172368	Enzo Doria	05/2015
1485	4*10^172354-39	172355	Robert Price	09/2020
1486	5^246497-4^246497	172295	Jean-Louis Charton	11/2008
1487	(38^109037-1)/37	172254	Paul Bourdelais	10/2017
1488	3*10^172219+73	172220	Robert Price	08/2018
1489	(36^110503+1)/37	171975	Lelio R Paula	04/2017
1490	(22*10^171929-73)/3	171930	Robert Price	04/2019
1491	4*10^171891-63	171892	Robert Price	10/2018
1492	67*10^171882-9	171884	Robert Price	03/2021
1493	2^570980-2782289	171883	Enzo Doria	09/2015
1494	(25*10^171849-37)/3	171850	Robert Price	10/2019
1495	10^171832-10001	171832	Robert Price	02/2021
1496	(2^(12*47563+13)-9)/7	171818	Kevin Acres	11/2013
1497	(536*10^171601-23)/9	171603	Robert Price	02/2020
1498	7*10^171535-99	171536	Robert Price	06/2019
1499	(28*10^171534+101)/3	171535	Robert Price	09/2020
1500	2^569563-1854607	171456	Enzo Doria	09/2015

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Probable Primes Top 10000

(280932 PRPs in the top)