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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	2^754038+25	226989	Stefano Morozzi	05/2021
1252	7*10^226479-9	226480	Robert Price	02/2023
1253	2^751426-764321	226202	Enzo Doria	12/2013
1254	(18^180181-1)/17	226176	Andy Steward	04/2007
1255	2^750740-3	225996	Paul Bourdelais	03/2012
1256	2^750725+60227	225991	Enzo Doria	02/2016
1257	2^750525-113743	225931	Enzo Doria	09/2014
1258	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
1259	2^749444-1861889	225606	Enzo Doria	12/2015
1260	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
1261	2^749096+1876861	225501	Enzo Doria	07/2016
1262	(519643#+43033)/(2318712706283)	225379	Makoto Morimoto	08/2019
1263	2^748657+79607	225369	Enzo Doria	06/2016
1264	(2^746920-11)/5	224845	Stefano Morozzi	08/2022
1265	2^746653-291583	224765	Enzo Doria	07/2015
1266	2^746461-114043	224708	Enzo Doria	11/2014
1267	2^746302+25	224660	Stefano Morozzi	05/2021
1268	(202*10^224545-1)/3	224547	Robert Price	06/2023
1269	2^745098-350471	224297	Enzo Doria	06/2015
1270	2^745039-4897	224280	Yves Minet	03/2021
1271	23*10^224232-7	224234	Robert Price	10/2022
1272	(154*10^224061-1)/9	224063	Serge Batalov	12/2014
1273	2^744211-1845787	224030	Enzo Doria	07/2015
1274	2^743592-134579	223844	Hans Havermann	10/2018
1275	2^742452+3	223501	Paul Bourdelais	06/2019
1276	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
1277	2^741651-461197	223260	Enzo Doria	07/2015
1278	10^223236-1001	223236	Robert Price	10/2022
1279	2^741362-1845251	223173	Enzo Doria	07/2015
1280	3^467546-5*2^467546	223077	Jon Grantham	08/2023
1281	2^740455-1863877	222900	Enzo Doria	12/2015
1282	(14*10^222718-41)/9	222719	Serge Batalov	01/2023
1283	2^739636-2792219	222653	Enzo Doria	02/2016
1284	11^213654-180	222498	Enzo Doria	01/2013
1285	2^738957-1859743	222449	Enzo Doria	11/2015
1286	4*10^222253-21	222254	Robert Price	12/2022
1287	2^737825+57	222108	Stefano Morozzi	05/2021
1288	(54^128189+1)/55	222073	Paul Bourdelais	11/2018
1289	(10^221654+179)/9	221654	Serge Batalov	12/2014
1290	2^736281+79817	221643	Enzo Doria	06/2016
1291	10^221631+247617	221632	Patrick De Geest	10/2013
1292	10^221631-9	221631	Alexander Gramolin	02/2011
1293	10^221628+7	221629	Alfred Reich	04/2021
1294	2^735970-1839821	221550	Enzo Doria	06/2015
1295	2^735367+60293	221368	Enzo Doria	03/2016
1296	(202*10^221092-1)/3	221094	Robert Price	06/2023
1297	(29^151153+1)/30	221045	Paul Bourdelais	09/2017
1298	2^733264-2784089	220735	Enzo Doria	10/2015
1299	2^733114-24555	220690	Enzo Doria	09/2013
1300	2^731891-636259	220322	Enzo Doria	12/2013
1301	98*10^220185-9	220187	Robert Price	05/2023
1302	2^731124-25539	220091	Enzo Doria	09/2013
1303	2^730972-462029	220045	Enzo Doria	07/2015
1304	2^730833+1868627	220003	Enzo Doria	04/2016
1305	2^730645-2787133	219947	Enzo Doria	11/2015
1306	2^730547-25581	219917	Enzo Doria	09/2013
1307	(113*13^197420-5)/12	219916	Anonymous	11/2022
1308	2^730460+82291	219891	Enzo Doria	09/2016
1309	(5*10^219847-101)/3	219848	Robert Price	08/2023
1310	(2^730339+1)/(3278390620037943469324347)	219831	Gord Palameta	12/2018
1311	L(1051849)	219824	Renaud Lifchitz	03/2009
1312	3*2^730149+5	219798	Jon Grantham	07/2023
1313	8*10^219740-3	219741	Serge Batalov	01/2023
1314	11^210961-240	219694	Enzo Doria	01/2013
1315	(26*10^219639-77)/3	219640	Robert Price	03/2023
1316	2^729611-113437	219635	Enzo Doria	08/2014
1317	7^259710-2	219481	Paul Bourdelais	01/2021
1318	F(1049897)	219416	Henri Lifchitz	10/2008
1319	(1488^69151-1)/1487	219386	Alexander Zhirkov	02/2023
1320	2^728604+1879321	219332	Enzo Doria	10/2016
1321	33^144412+2	219292	Robert Price	04/2015
1322	2^728277-183313	219234	Hans Havermann	10/2018
1323	2^727998-1862711	219150	Enzo Doria	12/2015
1324	(29*10^219124+91)/3	219125	Robert Price	12/2022
1325	2^727729-114073	219069	Enzo Doria	12/2014
1326	2^727496-1851809	218999	Enzo Doria	08/2015
1327	2^726591+2793143	218726	Enzo Doria	02/2016
1328	(7*10^218644+17)/3	218645	Robert Price	06/2023
1329	2^725534-2791931	218408	Enzo Doria	02/2016
1330	Phi(220531,10)/2686456812680882641	217774	Makoto Kamada	10/2020
1331	2^722184+1877821	217400	Enzo Doria	08/2016
1332	(109*10^217360-1)/9	217362	Serge Batalov	12/2014
1333	2^721721-4453	217260	Yves Minet	03/2021
1334	10^216950+49	216951	Robert Price	02/2023
1335	281*499979#/46410-2702372	216849	Robert Smith	08/2016
1336	281*499979#/46410+2400766	216849	Robert Smith	08/2016
1337	tau(311^15786)	216429	Nik Lygeros / Olivier Rozier / LR team	10/2013
1338	2^718756-114107	216368	Enzo Doria	12/2014
1339	2^717672+121	216041	Stefano Morozzi	05/2021
1340	2^717305+80327	215931	Enzo Doria	07/2016
1341	2^717069-59773	215860	Enzo Doria	10/2015
1342	10^215802+33	215803	Robert Price	08/2023
1343	30^146021-29^146021	215691	Jean-Louis Charton	09/2018
1344	277^88301-276^88301	215674	Jean-Louis Charton	06/2012
1345	(13*10^215592-43)/3	215593	Robert Price	08/2023
1346	227^91413-40	215372	Enzo Doria	04/2015
1347	(2^715008-21)/5	215239	Stefano Morozzi	08/2022
1348	2^714717+782897	215152	Enzo Doria	11/2016
1349	tau(373^15186)	214796	Nik Lygeros / Olivier Rozier / LR team	10/2013
1350	2^713241+1879157	214707	Enzo Doria	08/2016
1351	(23*10^214633+91)/3	214634	Robert Price	03/2023
1352	11^206081-10^206081	214612	Jean-Louis Charton	10/2011
1353	2^712801-69553	214575	Enzo Doria	01/2016
1354	2^712603-25357	214515	Enzo Doria	09/2013
1355	2^711721-1846723	214250	Enzo Doria	07/2015
1356	2^710730-396765	213952	Enzo Doria	09/2013
1357	(713^74897-1)/712	213685	Jinyuan Wang	08/2023
1358	2^708468-114329	213271	Enzo Doria	02/2015
1359	(163*10^212779-1)/9	212781	Serge Batalov	12/2014
1360	2^706838-69041	212780	Enzo Doria	11/2015
1361	22*10^212339+7	212341	Robert Price	10/2022
1362	2^704577-113871	212099	Enzo Doria	10/2014
1363	(2^704548-19)/3	212090	Stefano Morozzi	08/2022
1364	2^704110-2792441	211959	Enzo Doria	02/2016
1365	2^703943-1862947	211908	Enzo Doria	12/2015
1366	(60^119083+1)/61	211746	Paul Bourdelais	10/2018
1367	(184*10^211682-1)/3	211684	Robert Price	12/2022
1368	(10^211610-91)/9	211610	Serge Batalov	12/2014
1369	227^89797+2	211565	Lelio R Paula	08/2012
1370	2^702194-3	211382	Paul Bourdelais	03/2012
1371	2^702064+1874911	211343	Enzo Doria	07/2016
1372	2^701968-113873	211314	Enzo Doria	10/2014
1373	(14*10^211262-41)/9	211263	Serge Batalov	01/2023
1374	2^701713-113779	211237	Enzo Doria	09/2014
1375	2^701449-25201	211158	Enzo Doria	09/2013
1376	2^701403-2786977	211144	Enzo Doria	11/2015
1377	2^701189-25423	211079	Enzo Doria	09/2013
1378	2^701162-459161	211071	Enzo Doria	05/2015
1379	(24^152783-1)/23	210872	Paul Bourdelais	04/2018
1380	2^700400+9385	210842	Lelio R Paula	01/2014
1381	2^700304-17	210813	Stefano Morozzi	07/2022
1382	2^700131+1874693	210761	Enzo Doria	06/2016
1383	(2^700095+225414)/2	210750	Stefano Morozzi	04/2020
1384	(2^700090+278254)/2	210748	Stefano Morozzi	04/2020
1385	(2^700075+303666)/2	210744	Stefano Morozzi	04/2020
1386	(2^700073+75882)/2	210743	Stefano Morozzi	04/2020
1387	(2^700074+328890)/2	210743	Stefano Morozzi	04/2020
1388	(2^700052+79162)/2	210737	Stefano Morozzi	04/2020
1389	(2^700052+304458)/2	210737	Stefano Morozzi	04/2020
1390	(2^700048+376578)/2	210736	Stefano Morozzi	04/2020
1391	11^202357-1140	210734	Enzo Doria	12/2012
1392	(2^700021+25874)/2	210728	Stefano Morozzi	04/2020
1393	(2^700018+377518)/2	210727	Stefano Morozzi	04/2020
1394	2^699999+300729	210721	Norman Luhn	09/2023
1395	(238*10^210712-1)/3	210714	Robert Price	09/2023
1396	2^699740+25	210643	Stefano Morozzi	05/2021
1397	2^698929-2788423	210399	Enzo Doria	11/2015
1398	(5^300893+4^300893)/9	210315	Jean-Louis Charton	11/2011
1399	2^698316+1878601	210215	Enzo Doria	08/2016
1400	34*10^210097-9	210099	Robert Price	05/2023
1401	(19*10^210011-49)/3	210012	Robert Price	06/2023
1402	6*10^209846-91	209847	Robert Price	05/2023
1403	2^697036+1878751	209829	Enzo Doria	08/2016
1404	(238*10^209715-1)/3	209717	Robert Price	09/2023
1405	6^269407+5	209640	Paul Bourdelais	02/2021
1406	(2^696343-1)/11141489/36009913139329	209600	Tony Prest / Never Odd Or Even	02/2014
1407	2^696254-115151	209594	Enzo Doria	06/2015
1408	(35^135623+1)/36	209410	Paul Bourdelais	07/2018
1409	7*10^209161+39	209162	Robert Price	01/2023
1410	2^694633+1887257	209106	Enzo Doria	05/2017
1411	fibonacci(999790)-4	208944	Jon Grantham	08/2023
1412	2^693959+180923	208903	Enzo Doria	07/2016
1413	(2^693747-11)/3	208839	Stefano Morozzi	08/2022
1414	2^693462-1847561	208753	Enzo Doria	07/2015
1415	2^690890-59981	207979	Enzo Doria	11/2015
1416	(38^131591+1)/39	207884	Paul Bourdelais	07/2018
1417	3*2^690484+5	207857	Jon Grantham	07/2023
1418	2^690163+1877063	207760	Enzo Doria	07/2016
1419	7^245608-2	207563	Paul Bourdelais	01/2021
1420	(67*10^207556+23)/9	207557	Serge Batalov	01/2023
1421	2^689286-29381	207496	Enzo Doria	08/2015
1422	2^689122-114521	207447	Enzo Doria	04/2015
1423	9*10^207254-89	207255	Robert Price	02/2023
1424	2^688373+6077	207221	Enzo Doria	02/2016
1425	2^688201+1875527	207170	Enzo Doria	07/2016
1426	(42^127609+1)/43	207140	Paul Bourdelais	07/2018
1427	2^687619+81563	206994	Enzo Doria	08/2016
1428	3*10^206927+37	206928	Robert Price	08/2023
1429	2^687383+21803	206923	Enzo Doria	09/2023
1430	2^686572-1845299	206679	Enzo Doria	07/2015
1431	(21^156217-1)/20	206552	Paul Bourdelais	04/2010
1432	(2^685739+1)/(3*87774593)	206420	Gord Palameta	08/2018
1433	2^685578+3	206380	Paul Bourdelais	04/2012
1434	2^684836-49349	206157	Enzo Doria	10/2015
1435	(73^110603-1)/72	206088	Paul Bourdelais	06/2018
1436	2^684163-2790967	205954	Enzo Doria	12/2015
1437	326^81943-325^81943	205941	Jean-Louis Charton	07/2012
1438	(2^684127-1)/23765203727	205933	Jens K. Andersen	04/2009
1439	(68*10^205510+13)/9	205511	Serge Batalov	01/2023
1440	4^341233-3^341233	205443	Jean-Louis Charton	01/2006
1441	2^681545+467	205166	Lelio R Paula	11/2013
1442	2^681306+81049	205094	Enzo Doria	07/2016
1443	2^680697+1877057	204911	Enzo Doria	07/2016
1444	2^680415+71783	204826	Enzo Doria	04/2016
1445	10^204764-8001	204764	Robert Price	03/2023
1446	(26*10^204730-77)/3	204731	Robert Price	03/2023
1447	2^679860-459995	204659	Enzo Doria	06/2015
1448	2^679593+1879547	204578	Enzo Doria	09/2016
1449	2^678753+21677	204326	Enzo Doria	08/2023
1450	2^678651+1875023	204295	Enzo Doria	07/2016
1451	2^678561+678561	204268	Henri Lifchitz	05/2006
1452	5*3^427884+2^427884	204154	Jon Grantham	08/2023
1453	2^678101-114043	204129	Enzo Doria	11/2014
1454	2^678028+1875631	204107	Enzo Doria	06/2016
1455	2^676992-59783	203795	Enzo Doria	10/2015
1456	2^676972+1866871	203789	Enzo Doria	03/2016
1457	2^676761-9	203726	Robert Price	01/2017
1458	2^676592-23	203675	Stefano Morozzi	07/2022
1459	2^676563-2792407	203666	Enzo Doria	02/2016
1460	2^676306-114713	203589	Enzo Doria	04/2015
1461	(2^675977-1)/(1686378749257*7171117283326998925471)	203456	Dario Alpern	07/2015
1462	6*10^203365+53	203366	Robert Price	09/2023
1463	10247^50678-50678^10247	203250	Norbert Schneider	03/2022
1464	2^674627-25161	203083	Enzo Doria	09/2013
1465	2^674603-69337	203076	Enzo Doria	12/2015
1466	(182*10^203048+1)/3	203050	Robert Price	09/2023
1467	2^674459+74213	203033	Enzo Doria	04/2016
1468	2^674116-458879	202930	Enzo Doria	04/2015
1469	2^674076-114755	202918	Enzo Doria	04/2015
1470	5^289937-4^289937	202658	Jean-Louis Charton	03/2013
1471	(2^673184-7)/3	202649	Stefano Morozzi	08/2022
1472	(467617#+14534)/(2^21343)	202603	Makoto Morimoto	06/2019
1473	2^672556-1835519	202460	Enzo Doria	04/2015
1474	(7*10^202267+179)/3	202268	Robert Price	02/2023
1475	2^671446-351401	202126	Enzo Doria	07/2015
1476	2^671373+77747	202104	Enzo Doria	05/2016
1477	(2*10^202059+7)/9	202059	Rytis Slatkevicius	01/2023
1478	98*10^202021-9	202023	Robert Price	05/2023
1479	2^670726-114845	201909	Enzo Doria	05/2015
1480	2^670539-25045	201853	Enzo Doria	09/2013
1481	10^201801-93	201801	Robert Price	02/2023
1482	43284^43519-43519^43284	201769	Norbert Schneider	08/2018
1483	2^670213+282317	201755	Enzo Doria	09/2016
1484	2^670133+89	201731	Stefano Morozzi	05/2021
1485	2^669854-113501	201647	Enzo Doria	08/2014
1486	2^669718+81619	201606	Enzo Doria	08/2016
1487	(299*10^201547-17)/3	201549	Robert Price	02/2023
1488	(145*10^201504-1)/9	201506	Serge Batalov	12/2014
1489	2^668938-1839821	201371	Enzo Doria	06/2015
1490	2^668492+1879303	201237	Enzo Doria	08/2016
1491	7*10^201140-87	201141	Robert Price	03/2023
1492	6^258413-5^258413	201085	Jean-Louis Charton	03/2013
1493	10194^50161-50161^10194	201063	Norbert Schneider	09/2020
1494	2^667894+1875589	201057	Enzo Doria	06/2016
1495	2^667569-1836559	200959	Enzo Doria	05/2015
1496	(172*10^200746-1)/9	200748	Serge Batalov	12/2014
1497	2^666430+782569	200616	Enzo Doria	10/2016
1498	(13*10^200610-43)/3	200611	Robert Price	08/2023
1499	(8*10^200408-11)/3	200409	Robert Price	07/2023
1500	(19*10^200260+101)/3	200261	Robert Price	06/2023

Find by discoverer :

PRP Records

Probable Primes Top 10000

(293510 PRPs in the top)