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	2^1069788+26587	322039	Enzo Doria	12/2023
1252	2^1069293-1147195	321890	Enzo Doria	05/2015
1253	2^1065968+1880941	320889	Enzo Doria	10/2016
1254	2^1065897-1147195	320867	Enzo Doria	05/2015
1255	2^1063427+1882103	320124	Enzo Doria	12/2016
1256	2^1061095-1061095	319422	Henri Lifchitz	10/2013
1257	2^1060950+653119	319378	Enzo Doria	12/2016
1258	2^1060363+782753	319202	Enzo Doria	11/2016
1259	2^1060028+31771	319101	Enzo Doria	04/2024
1260	(71^172259-1)/70	318895	Paul Bourdelais	08/2020
1261	2^1058425+38507	318618	Enzo Doria	11/2024
1262	-30*Bern(85996)/236037521	318354	Sergey Batalov	10/2023
1263	(13^285707-1)/870834948	318253	Paul Vanderveen	05/2025
1264	2^1055665+30407	317787	Enzo Doria	03/2024
1265	2^1054736+483061	317508	Enzo Doria	12/2016
1266	2^1053965+1879667	317276	Enzo Doria	10/2016
1267	(43^194119-1)/42	317086	Paul Bourdelais	08/2020
1268	2^1052899+225413	316955	Enzo Doria	08/2024
1269	2^1052186-458165	316740	Enzo Doria	03/2015
1270	11^303909+2	316489	Paul Bourdelais	08/2023
1271	2^1049026+214609	315789	Enzo Doria	11/2023
1272	2^1048576+69661	315653	Boyan Hu	08/2024
1273	2^1046613-114685	315062	Enzo Doria	04/2015
1274	2^1045625-459373	314765	Enzo Doria	06/2015
1275	10^(2157363+1)-810^157363-1	314727	Robert Price	07/2023
1276	(7*10^314564-61)/9	314564	Erik Branger	09/2016
1277	2^1044771+228023	314508	Enzo Doria	11/2024
1278	2^1044206+7	314338	Stefano Morozzi	10/2022
1279	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
1280	(53^181981-1)/52	313784	Paul Bourdelais	08/2020
1281	(8^347437-5^347437)/3	313767	Jon Grantham	08/2023
1282	(10^313741+1)/11/11294677	313733	Alfred Reich	04/2024
1283	2^1041944+283051	313657	Enzo Doria	12/2016
1284	(1624^97969-1)/(1624^313-1)	313533	Sergey Batalov	11/2023
1285	2^1041153-114391	313419	Enzo Doria	02/2015
1286	(2^1039700+9)/5	312981	Stefano Morozzi	09/2022
1287	(74^167311+1)/75	312742	Paul Bourdelais	12/2020
1288	2^1038871+1866983	312732	Enzo Doria	04/2016
1289	2^1038545+71657	312634	Enzo Doria	08/2023
1290	(55^179573-1)/54	312521	Paul Bourdelais	08/2020
1291	2^1037647+1881263	312363	Enzo Doria	11/2016
1292	2^1037226+1879699	312237	Enzo Doria	10/2016
1293	2^1036867+1865843	312129	Enzo Doria	02/2016
1294	(76^165947+1)/77	312114	Paul Bourdelais	01/2021
1295	2^1036324+39091	311965	Enzo Doria	11/2024
1296	2^1036020-114539	311874	Enzo Doria	02/2015
1297	(90^159463-1)/89	311628	Paul Bourdelais	08/2020
1298	2^1034546+28819	311430	Enzo Doria	02/2024
1299	2^1032240+1883431	310736	Enzo Doria	01/2017
1300	64211^64588+64588^64211	310514	Norbert Schneider	11/2023
1301	2^1031450+29629	310498	Enzo Doria	03/2024
1302	2^1030352+1870021	310167	Enzo Doria	06/2016
1303	2^1030046+1882843	310075	Enzo Doria	11/2016
1304	2^1029120+227971	309796	Enzo Doria	11/2024
1305	3^648872+16	309591	Robert Price	04/2020
1306	(16976^73441-1)/(16976^271-1)	309498	Ryan Propper	11/2023
1307	64221^64366+64366^64221	309451	Norbert Schneider	06/2023
1308	(11121^76729-1)/(11121^277-1)	309336	Ryan Propper	11/2023
1309	2^1027478+219259	309302	Enzo Doria	02/2024
1310	2^1026999+20513	309158	Enzo Doria	07/2023
1311	5^442281+2	309142	Paul Bourdelais	01/2021
1312	2^1026204+22741	308919	Enzo Doria	09/2023
1313	2^1026190+15	308914	Stefano Morozzi	10/2022
1314	2^1025108+20851	308589	Enzo Doria	08/2023
1315	2^1022860+234121	307912	Enzo Doria	03/2025
1316	A352736(16)	306985	Kellen Shenton	05/2022
1317	2^1019777+213947	306984	Enzo Doria	10/2023
1318	2^1018820+236731	306696	Enzo Doria	05/2025
1319	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
1320	(67^167449-1)/66	305773	Paul Bourdelais	08/2020
1321	(62^170539+1)/63	305671	Paul Bourdelais	12/2020
1322	2^1015321-1015321	305643	Henri Lifchitz	08/2013
1323	2^1014775+27113	305478	Enzo Doria	12/2023
1324	2^1014450+7	305380	Stefano Morozzi	10/2022
1325	2^1014404+46171	305367	Enzo Doria	05/2025
1326	2^1014336+215731	305346	Enzo Doria	12/2023
1327	2^1014224-2791229	305312	Enzo Doria	01/2016
1328	(10^304986+7)/673	304984	Alfred Reich	11/2021
1329	65473^45250+45250^65473	304818	Hans Havermann	02/2022
1330	66012^41423+41423^66012	304794	Hans Havermann	03/2022
1331	65073^48202+48202^65073	304742	Hans Havermann	04/2022
1332	2^1012054+31669	304659	Enzo Doria	06/2024
1333	238176^19+19^238176	304569	Hans Havermann	03/2022
1334	73122^14615+14615^73122	304539	Hans Havermann	05/2022
1335	64492^52639+52639^64492	304487	Hans Havermann	03/2022
1336	65955^41288+41288^65955	304437	Hans Havermann	04/2022
1337	71729^17530+17530^71729	304403	Hans Havermann	03/2022
1338	70170^21733+21733^70170	304336	Hans Havermann	03/2022
1339	2^1010751-107709	304267	Enzo Doria	03/2014
1340	84473^3994+3994^84473	304222	Hans Havermann	03/2022
1341	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
1342	74442^12125+12125^74442	303998	Hans Havermann	02/2022
1343	77842^8039+8039^77842	303989	Hans Havermann	01/2022
1344	64209^54140+54140^64209	303935	Hans Havermann	02/2022
1345	2^1009577+1869587	303913	Enzo Doria	06/2016
1346	67389^32338+32338^67389	303906	Hans Havermann	02/2022
1347	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
1348	2^1009168+15	303790	Stefano Morozzi	10/2022
1349	80766^5771+5771^80766	303782	Hans Havermann	01/2022
1350	66094^39385+39385^66094	303724	Hans Havermann	01/2022
1351	69147^24574+24574^69147	303589	Hans Havermann	02/2022
1352	78390^7459+7459^78390	303580	Hans Havermann	01/2022
1353	2^1008301+1869377	303529	Enzo Doria	06/2016
1354	65008^46615+46615^65008	303492	Hans Havermann	02/2022
1355	(2^1007838+5)/3	303389	Serge Batalov	08/2015
1356	65018^46293+46293^65018	303343	Hans Havermann	01/2022
1357	6^389756+5	303290	Paul Bourdelais	02/2021
1358	71016^18649+18649^71016	303285	Hans Havermann	01/2022
1359	2^1007065+29231	303157	Enzo Doria	03/2024
1360	80160^6047+6047^80160	303129	Hans Havermann	01/2022
1361	67434^31237+31237^67434	303094	Hans Havermann	03/2022
1362	65537^42102+42102^65537	303063	Hans Havermann	02/2022
1363	71790^16553+16553^71790	302874	Hans Havermann	11/2021
1364	65208^44129+44129^65208	302874	Hans Havermann	11/2021
1365	84181^3960+3960^84181	302858	Hans Havermann	11/2021
1366	(13703^73441-1)/(13703^271-1)	302691	Ryan Propper	11/2023
1367	71956^16087+16087^71956	302682	Hans Havermann	11/2021
1368	2^1005326+383059	302634	Enzo Doria	12/2016
1369	2^1004929+1877567	302514	Enzo Doria	08/2016
1370	69341^22978+22978^69341	302418	Hans Havermann	12/2021
1371	111443^516+516^111443	302306	Hans Havermann	12/2021
1372	67638^29387+29387^67638	302218	Hans Havermann	11/2021
1373	2^1003494+1874899	302082	Enzo Doria	06/2016
1374	75189^10400+10400^75189	302037	Hans Havermann	12/2021
1375	67237^31042+31042^67237	302026	Hans Havermann	12/2021
1376	64540^47791+47791^64540	302005	Hans Havermann	11/2021
1377	2^1003046+60529	301947	Enzo Doria	04/2016
1378	83278^4209+4209^83278	301815	Hans Havermann	09/2021
1379	64431^48250+48250^64431	301763	Hans Havermann	09/2021
1380	67237^30714+30714^67237	301716	Hans Havermann	09/2021
1381	2^1002144+235861	301676	Enzo Doria	05/2025
1382	64641^46288+46288^64641	301581	Hans Havermann	09/2021
1383	71513^16482+16482^71513	301572	Hans Havermann	10/2021
1384	72017^15396+15396^72017	301565	Hans Havermann	09/2021
1385	65534^39927+39927^65534	301540	Hans Havermann	10/2021
1386	(23^221411-1)/22	301501	Paul Bourdelais	08/2020
1387	63169^59152+59152^63169	301441	Hans Havermann	09/2021
1388	75055^10348+10348^75055	301336	Hans Havermann	09/2021
1389	2^1000647+1881353	301225	Enzo Doria	11/2016
1390	83686^3961+3961^83686	301086	Hans Havermann	10/2021
1391	68529^24742+24742^68529	301078	Hans Havermann	09/2021
1392	65207^41416+41416^65207	301072	Hans Havermann	10/2021
1394	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
1393	2^999999+77151	301030	Norman Luhn	09/2023
1395	90762^2071+2071^90762	300984	Hans Havermann	06/2021
1396	63909^51142+51142^63909	300934	Hans Havermann	08/2021
1397	2^999646+1874029	300924	Enzo Doria	06/2016
1398	66280^34607+34607^66280	300856	Hans Havermann	06/2021
1399	65534^38925+38925^65534	300817	Hans Havermann	07/2021
1400	63296^56517+56517^63296	300794	Hans Havermann	06/2021
1401	110610^523+523^110610	300694	Hans Havermann	06/2021
1402	66428^33609+33609^66428	300684	Hans Havermann	06/2021
1403	74247^11210+11210^74247	300672	Hans Havermann	06/2021
1404	(59^169777-1)/58	300649	Paul Bourdelais	08/2020
1405	10^300476+3	300477	Ed Trice	10/2012
1406	10^300476-530913	300476	Patrick De Geest	03/2016
1407	66703^31960+31960^66703	300471	Hans Havermann	06/2021
1408	63722^51915+51915^63722	300468	Hans Havermann	06/2021
1409	2^998053+1879667	300444	Enzo Doria	09/2016
1410	77018^7959+7959^77018	300437	Hans Havermann	07/2021
1411	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
1412	2^997689+217787	300335	Enzo Doria	01/2024
1413	69478^20987+20987^69478	300281	Hans Havermann	07/2021
1414	64088^48393+48393^64088	300239	Hans Havermann	07/2021
1415	2^997369+237917	300238	Enzo Doria	06/2025
1416	64605^44146+44146^64605	300084	Hans Havermann	08/2021
1417	2^996845+29027	300081	Enzo Doria	02/2024
1418	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
1419	67594^27465+27465^67594	300035	Hans Havermann	06/2021
1420	10^300000+287389	300001	Patrick De Geest	10/2019
1421	10^300000-83657	300000	Patrick De Geest	10/2019
1422	70599^17756+17756^70599	300000	Hans Havermann	06/2021
1423	numbpart(72526161452)	299999	Serge Batalov	04/2017
1424	2^996182-114431	299881	Enzo Doria	02/2015
1425	3*2^996126+5	299865	Jon Grantham	07/2023
1426	2^996034-17	299837	Stefano Morozzi	07/2022
1427	2^995793+36587	299764	Enzo Doria	09/2024
1428	(19*10^299640+77)/3	299641	Robert Price	03/2023
1429	2^995214-2788361	299590	Enzo Doria	12/2015
1430	2^994791-114319	299462	Enzo Doria	01/2015
1431	2^994490-1863791	299372	Enzo Doria	01/2016
1432	2^993322+1885729	299020	Enzo Doria	03/2017
1433	2^993227+230033	298992	Enzo Doria	12/2024
1434	(36395^65536+36393^65536)/2	298913	Kellen Shenton	04/2022
1435	2^992711-2788807	298836	Enzo Doria	12/2015
1436	2^992525-114199	298780	Enzo Doria	12/2014
1437	(7^353501-3^353501)/4	298743	Jon Grantham	08/2023
1438	2^992329+1884707	298721	Enzo Doria	02/2017
1439	2^992292+229801	298710	Enzo Doria	12/2024
1440	2^992052+215491	298638	Enzo Doria	11/2023
1441	2^991968-23	298613	Stefano Morozzi	07/2022
1442	2^991715-19	298536	Stefano Morozzi	07/2022
1443	2^991387+237383	298438	Enzo Doria	06/2025
1444	(10^298414+7)/191/823/56921/1334467	298398	Alfred Reich	10/2021
1445	2^989562+25	297888	Stefano Morozzi	05/2021
1446	2^988580+214051	297593	Enzo Doria	10/2023
1447	2^988537+218837	297580	Enzo Doria	03/2024
1448	(19*10^297497+77)/3	297498	Robert Price	03/2023
1449	(2*10^297488-23)/3	297488	Robert Price	10/2022
1450	2^988148+48271	297463	Enzo Doria	07/2025
1451	2^987033+46427	297127	Enzo Doria	05/2025
1452	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
1453	2^985217-114553	296580	Enzo Doria	03/2015
1454	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
1455	2^984650+21529	296410	Enzo Doria	08/2023
1456	2^984131-1828009	296253	Enzo Doria	01/2015
1457	2^983620+60451	296100	Phil Moore	03/2008
1458	2^982721-2683	295829	Yves Minet	02/2016
1459	(23*10^295581+7)/3	295582	Robert Price	05/2023
1460	2^981298-2788421	295401	Enzo Doria	12/2015
1461	2^981163-2790967	295360	Enzo Doria	12/2015
1462	2^981016-15	295316	Stefano Morozzi	07/2022
1463	8*10^295160-13	295161	Robert Price	08/2023
1464	2^979594+1865839	294888	Enzo Doria	02/2016
1465	2^979502+221029	294860	Enzo Doria	03/2024
1466	2*10^294527-91	294528	Robert Price	02/2023
1467	(49363^63001-1)/(49363^251-1)	294511	Ryan Propper	11/2023
1468	10^294475+49	294476	Robert Price	02/2023
1469	2^977896+234601	294377	Enzo Doria	04/2025
1470	(11*10^294308+91)/3	294309	Robert Price	03/2023
1471	2^976760+1885021	294035	Enzo Doria	02/2017
1472	3*2^976518+5	293962	Jon Grantham	07/2023
1473	2^975798+218599	293745	Enzo Doria	01/2024
1474	2^974441+1878407	293336	Enzo Doria	08/2016
1475	2^974180+1876831	293258	Enzo Doria	07/2016
1476	2^974170+453319	293255	Enzo Doria	01/2017
1477	(211^126023-1)/210	292911	Anonymous	05/2024
1478	2^972744-114419	292826	Enzo Doria	03/2015
1479	11^281143+6	292781	Paul Bourdelais	03/2021
1480	(4*10^292619-91)/3	292620	Robert Price	12/2022
1481	E(69468)/13247122135	292549	Sergey Batalov	10/2023
1482	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
1483	3*10^292344-97	292345	Robert Price	01/2023
1484	2^970911+1873373	292274	Enzo Doria	07/2016
1485	2^970670+383059	292201	Enzo Doria	12/2016
1486	2^970141-100363	292042	Enzo Doria	02/2014
1487	2^969945+1874717	291983	Enzo Doria	06/2016
1488	2^969384+1880701	291814	Enzo Doria	10/2016
1489	(13*10^291721-43)/3	291722	Robert Price	08/2023
1490	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
1491	10^(2145126+1)-210^145126-1	290253	Robert Price	03/2025
1492	3*2^963892+5	290161	Jon Grantham	07/2023
1493	(151*10^289877-1)/3	289879	Robert Price	07/2023
1494	2^962194+60139	289650	Enzo Doria	02/2016
1495	2^961409+44267	289413	Enzo Doria	04/2025
1496	2^959307-1861507	288781	Enzo Doria	11/2015
1497	(17*10^288692+31)/3	288693	Robert Price	04/2023
1498	14^251797-3	288592	Paul Bourdelais	12/2020
1499	(8745^73441-1)/(8745^271-1)	288419	Ryan Propper	11/2023
1500	(2*10^288371-23)/3	288371	Robert Price	10/2022

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Probable Primes Top 10000

(301979 PRPs in the top)