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	2^1014775+27113	305478	Enzo Doria	12/2023
1252	2^1014450+7	305380	Stefano Morozzi	10/2022
1253	2^1014404+46171	305367	Enzo Doria	05/2025
1254	2^1014336+215731	305346	Enzo Doria	12/2023
1255	2^1014224-2791229	305312	Enzo Doria	01/2016
1256	(10^304986+7)/673	304984	Alfred Reich	11/2021
1257	65473^45250+45250^65473	304818	Hans Havermann	02/2022
1258	66012^41423+41423^66012	304794	Hans Havermann	03/2022
1259	65073^48202+48202^65073	304742	Hans Havermann	04/2022
1260	2^1012054+31669	304659	Enzo Doria	06/2024
1261	238176^19+19^238176	304569	Hans Havermann	03/2022
1262	73122^14615+14615^73122	304539	Hans Havermann	05/2022
1263	64492^52639+52639^64492	304487	Hans Havermann	03/2022
1264	65955^41288+41288^65955	304437	Hans Havermann	04/2022
1265	71729^17530+17530^71729	304403	Hans Havermann	03/2022
1266	70170^21733+21733^70170	304336	Hans Havermann	03/2022
1267	2^1010751-107709	304267	Enzo Doria	03/2014
1268	84473^3994+3994^84473	304222	Hans Havermann	03/2022
1269	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
1270	74442^12125+12125^74442	303998	Hans Havermann	02/2022
1271	77842^8039+8039^77842	303989	Hans Havermann	01/2022
1272	64209^54140+54140^64209	303935	Hans Havermann	02/2022
1273	2^1009577+1869587	303913	Enzo Doria	06/2016
1274	67389^32338+32338^67389	303906	Hans Havermann	02/2022
1275	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
1276	2^1009168+15	303790	Stefano Morozzi	10/2022
1277	80766^5771+5771^80766	303782	Hans Havermann	01/2022
1278	66094^39385+39385^66094	303724	Hans Havermann	01/2022
1279	69147^24574+24574^69147	303589	Hans Havermann	02/2022
1280	78390^7459+7459^78390	303580	Hans Havermann	01/2022
1281	2^1008301+1869377	303529	Enzo Doria	06/2016
1282	65008^46615+46615^65008	303492	Hans Havermann	02/2022
1283	(2^1007838+5)/3	303389	Serge Batalov	08/2015
1284	65018^46293+46293^65018	303343	Hans Havermann	01/2022
1285	6^389756+5	303290	Paul Bourdelais	02/2021
1286	71016^18649+18649^71016	303285	Hans Havermann	01/2022
1287	2^1007065+29231	303157	Enzo Doria	03/2024
1288	80160^6047+6047^80160	303129	Hans Havermann	01/2022
1289	67434^31237+31237^67434	303094	Hans Havermann	03/2022
1290	65537^42102+42102^65537	303063	Hans Havermann	02/2022
1291	71790^16553+16553^71790	302874	Hans Havermann	11/2021
1292	65208^44129+44129^65208	302874	Hans Havermann	11/2021
1293	84181^3960+3960^84181	302858	Hans Havermann	11/2021
1294	(13703^73441-1)/(13703^271-1)	302691	Ryan Propper	11/2023
1295	71956^16087+16087^71956	302682	Hans Havermann	11/2021
1296	2^1005326+383059	302634	Enzo Doria	12/2016
1297	2^1004929+1877567	302514	Enzo Doria	08/2016
1298	69341^22978+22978^69341	302418	Hans Havermann	12/2021
1299	111443^516+516^111443	302306	Hans Havermann	12/2021
1300	67638^29387+29387^67638	302218	Hans Havermann	11/2021
1301	2^1003494+1874899	302082	Enzo Doria	06/2016
1302	75189^10400+10400^75189	302037	Hans Havermann	12/2021
1303	67237^31042+31042^67237	302026	Hans Havermann	12/2021
1304	64540^47791+47791^64540	302005	Hans Havermann	11/2021
1305	2^1003046+60529	301947	Enzo Doria	04/2016
1306	83278^4209+4209^83278	301815	Hans Havermann	09/2021
1307	64431^48250+48250^64431	301763	Hans Havermann	09/2021
1308	67237^30714+30714^67237	301716	Hans Havermann	09/2021
1309	2^1002144+235861	301676	Enzo Doria	05/2025
1310	64641^46288+46288^64641	301581	Hans Havermann	09/2021
1311	71513^16482+16482^71513	301572	Hans Havermann	10/2021
1312	72017^15396+15396^72017	301565	Hans Havermann	09/2021
1313	65534^39927+39927^65534	301540	Hans Havermann	10/2021
1314	(23^221411-1)/22	301501	Paul Bourdelais	08/2020
1315	63169^59152+59152^63169	301441	Hans Havermann	09/2021
1316	75055^10348+10348^75055	301336	Hans Havermann	09/2021
1317	2^1000647+1881353	301225	Enzo Doria	11/2016
1318	83686^3961+3961^83686	301086	Hans Havermann	10/2021
1319	68529^24742+24742^68529	301078	Hans Havermann	09/2021
1320	65207^41416+41416^65207	301072	Hans Havermann	10/2021
1322	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
1321	2^999999+77151	301030	Norman Luhn	09/2023
1323	90762^2071+2071^90762	300984	Hans Havermann	06/2021
1324	63909^51142+51142^63909	300934	Hans Havermann	08/2021
1325	2^999646+1874029	300924	Enzo Doria	06/2016
1326	66280^34607+34607^66280	300856	Hans Havermann	06/2021
1327	65534^38925+38925^65534	300817	Hans Havermann	07/2021
1328	63296^56517+56517^63296	300794	Hans Havermann	06/2021
1329	110610^523+523^110610	300694	Hans Havermann	06/2021
1330	66428^33609+33609^66428	300684	Hans Havermann	06/2021
1331	74247^11210+11210^74247	300672	Hans Havermann	06/2021
1332	(59^169777-1)/58	300649	Paul Bourdelais	08/2020
1333	10^300476+3	300477	Ed Trice	10/2012
1334	10^300476-530913	300476	Patrick De Geest	03/2016
1335	66703^31960+31960^66703	300471	Hans Havermann	06/2021
1336	63722^51915+51915^63722	300468	Hans Havermann	06/2021
1337	2^998053+1879667	300444	Enzo Doria	09/2016
1338	77018^7959+7959^77018	300437	Hans Havermann	07/2021
1339	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
1340	2^997689+217787	300335	Enzo Doria	01/2024
1341	69478^20987+20987^69478	300281	Hans Havermann	07/2021
1342	64088^48393+48393^64088	300239	Hans Havermann	07/2021
1343	2^997369+237917	300238	Enzo Doria	06/2025
1344	64605^44146+44146^64605	300084	Hans Havermann	08/2021
1345	2^996845+29027	300081	Enzo Doria	02/2024
1346	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
1347	67594^27465+27465^67594	300035	Hans Havermann	06/2021
1348	10^300000+287389	300001	Patrick De Geest	10/2019
1349	10^300000-83657	300000	Patrick De Geest	10/2019
1350	70599^17756+17756^70599	300000	Hans Havermann	06/2021
1351	numbpart(72526161452)	299999	Serge Batalov	04/2017
1352	2^996182-114431	299881	Enzo Doria	02/2015
1353	3*2^996126+5	299865	Jon Grantham	07/2023
1354	2^996034-17	299837	Stefano Morozzi	07/2022
1355	2^995793+36587	299764	Enzo Doria	09/2024
1356	(19*10^299640+77)/3	299641	Robert Price	03/2023
1357	2^995214-2788361	299590	Enzo Doria	12/2015
1358	2^994791-114319	299462	Enzo Doria	01/2015
1359	2^994490-1863791	299372	Enzo Doria	01/2016
1360	2^993322+1885729	299020	Enzo Doria	03/2017
1361	2^993227+230033	298992	Enzo Doria	12/2024
1362	(36395^65536+36393^65536)/2	298913	Kellen Shenton	04/2022
1363	2^992711-2788807	298836	Enzo Doria	12/2015
1364	2^992525-114199	298780	Enzo Doria	12/2014
1365	(7^353501-3^353501)/4	298743	Jon Grantham	08/2023
1366	2^992329+1884707	298721	Enzo Doria	02/2017
1367	2^992292+229801	298710	Enzo Doria	12/2024
1368	2^992052+215491	298638	Enzo Doria	11/2023
1369	2^991968-23	298613	Stefano Morozzi	07/2022
1370	2^991715-19	298536	Stefano Morozzi	07/2022
1371	2^991387+237383	298438	Enzo Doria	06/2025
1372	(10^298414+7)/191/823/56921/1334467	298398	Alfred Reich	10/2021
1373	2^989562+25	297888	Stefano Morozzi	05/2021
1374	2^988580+214051	297593	Enzo Doria	10/2023
1375	2^988537+218837	297580	Enzo Doria	03/2024
1376	(19*10^297497+77)/3	297498	Robert Price	03/2023
1377	(2*10^297488-23)/3	297488	Robert Price	10/2022
1378	2^988148+48271	297463	Enzo Doria	07/2025
1379	2^987033+46427	297127	Enzo Doria	05/2025
1380	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
1381	2^985217-114553	296580	Enzo Doria	03/2015
1382	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
1383	2^984650+21529	296410	Enzo Doria	08/2023
1384	2^984131-1828009	296253	Enzo Doria	01/2015
1385	2^983620+60451	296100	Phil Moore	03/2008
1386	2^982721-2683	295829	Yves Minet	02/2016
1387	(23*10^295581+7)/3	295582	Robert Price	05/2023
1388	2^981298-2788421	295401	Enzo Doria	12/2015
1389	2^981163-2790967	295360	Enzo Doria	12/2015
1390	2^981016-15	295316	Stefano Morozzi	07/2022
1391	8*10^295160-13	295161	Robert Price	08/2023
1392	2^979594+1865839	294888	Enzo Doria	02/2016
1393	2^979502+221029	294860	Enzo Doria	03/2024
1394	2*10^294527-91	294528	Robert Price	02/2023
1395	(49363^63001-1)/(49363^251-1)	294511	Ryan Propper	11/2023
1396	10^294475+49	294476	Robert Price	02/2023
1397	2^977896+234601	294377	Enzo Doria	04/2025
1398	(11*10^294308+91)/3	294309	Robert Price	03/2023
1399	2^976760+1885021	294035	Enzo Doria	02/2017
1400	3*2^976518+5	293962	Jon Grantham	07/2023
1401	2^975798+218599	293745	Enzo Doria	01/2024
1402	2^974441+1878407	293336	Enzo Doria	08/2016
1403	2^974180+1876831	293258	Enzo Doria	07/2016
1404	2^974170+453319	293255	Enzo Doria	01/2017
1405	(211^126023-1)/210	292911	Anonymous	05/2024
1406	2^972744-114419	292826	Enzo Doria	03/2015
1407	11^281143+6	292781	Paul Bourdelais	03/2021
1408	(4*10^292619-91)/3	292620	Robert Price	12/2022
1409	E(69468)/13247122135	292549	Sergey Batalov	10/2023
1410	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
1411	3*10^292344-97	292345	Robert Price	01/2023
1412	2^970911+1873373	292274	Enzo Doria	07/2016
1413	2^970670+383059	292201	Enzo Doria	12/2016
1414	2^970141-100363	292042	Enzo Doria	02/2014
1415	2^969945+1874717	291983	Enzo Doria	06/2016
1416	2^969384+1880701	291814	Enzo Doria	10/2016
1417	(13*10^291721-43)/3	291722	Robert Price	08/2023
1418	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
1419	10^(2145126+1)-210^145126-1	290253	Robert Price	03/2025
1420	3*2^963892+5	290161	Jon Grantham	07/2023
1421	(151*10^289877-1)/3	289879	Robert Price	07/2023
1422	2^962194+60139	289650	Enzo Doria	02/2016
1423	2^961409+44267	289413	Enzo Doria	04/2025
1424	2^959307-1861507	288781	Enzo Doria	11/2015
1425	(17*10^288692+31)/3	288693	Robert Price	04/2023
1426	14^251797-3	288592	Paul Bourdelais	12/2020
1427	(8745^73441-1)/(8745^271-1)	288419	Ryan Propper	11/2023
1428	(2*10^288371-23)/3	288371	Robert Price	10/2022
1429	(31*10^288238-1)/3	288240	Robert Price	02/2023
1430	(7^341063-2^341063)/5	288231	Jon Grantham	08/2023
1431	2^957372+283531	288198	Enzo Doria	02/2017
1432	2^957192-1864049	288144	Enzo Doria	01/2016
1433	(95774^58081-1)/(95774^241-1)	288116	Ryan Propper	11/2023
1434	2^956446+1875199	287919	Enzo Doria	06/2016
1435	2^956283+219143	287870	Enzo Doria	02/2024
1436	7*10^287854+39	287855	Robert Price	01/2023
1437	2^956082+28309	287810	Enzo Doria	02/2024
1438	(17^233689+1)/18	287542	Paul Bourdelais	09/2013
1439	2^955178+1883587	287538	Enzo Doria	12/2016
1440	2^954127-954127^2	287221	Henri Lifchitz	01/2021
1441	2^954001+1875257	287183	Enzo Doria	07/2016
1442	2*10^287175-49	287176	Robert Price	05/2023
1443	(22*10^287085-19)/3	287086	Robert Price	07/2023
1444	2^953667+38573	287083	Enzo Doria	11/2024
1445	2^953488+22411	287029	Enzo Doria	09/2023
1446	(23891^65536+1)/2	286932	Serge Batalov	03/2018
1447	5*3^601336-2^601336	286911	Jon Grantham	08/2023
1448	2^952268+1878601	286662	Enzo Doria	09/2016
1449	2^950801+81557	286220	Enzo Doria	08/2016
1450	2^949403+217523	285799	Enzo Doria	01/2024
1451	22845^65536+22844^65536	285658	Kellen Shenton	03/2021
1452	(19*10^285615+53)/9	285616	Rytis Slatkevicius	12/2024
1453	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
1454	(54^164839+1)/55	285565	Paul Bourdelais	07/2019
1455	2^948510+782569	285530	Enzo Doria	10/2016
1456	2^948374-114137	285490	Enzo Doria	01/2015
1457	2^947739+1872923	285298	Enzo Doria	06/2016
1458	2^946274+218407	284857	Enzo Doria	03/2024
1459	7*10^284751+9	284752	Robert Price	04/2023
1460	2^944561-21	284342	Stefano Morozzi	07/2022
1461	(4*10^284330-31)/9	284330	Serge Batalov	11/2022
1462	(32*10^283826-23)/9	283827	Serge Batalov	01/2023
1463	2^942533+82067	283731	Enzo Doria	09/2016
1464	2^941469+39	283411	Jon Grantham	08/2023
1465	(10^283342-31)/3	283342	Robert Price	03/2023
1466	2^940950+1874989	283255	Enzo Doria	06/2016
1467	2^940426-2786141	283097	Enzo Doria	11/2015
1468	2^940155+226973	283015	Enzo Doria	09/2024
1469	(2*10^282948-11)/9	282948	Serge Batalov	11/2022
1470	2^939881-114115	282933	Enzo Doria	12/2014
1471	(14*10^282673-143)/3	282674	Robert Price	05/2023
1472	10^282493+632551	282494	Patrick De Geest	02/2017
1474	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
1473	10^282493-132327	282493	Patrick De Geest	02/2017
1475	3^591827-2^591827	282374	Mike Oakes	08/2009
1476	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
1477	2^936716-1835519	281980	Enzo Doria	04/2015
1478	2^936588+79411	281942	Enzo Doria	06/2016
1479	2^936047+1877423	281779	Enzo Doria	08/2016
1480	2^935713+1869377	281678	Enzo Doria	05/2016
1481	2^933082+1877059	280886	Enzo Doria	08/2016
1482	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
1483	2^932443+225893	280694	Enzo Doria	08/2024
1484	2^932064+26521	280580	Enzo Doria	12/2023
1485	2^931976+25	280553	Stefano Morozzi	05/2021
1486	(42^172663+1)/43	280274	Paul Bourdelais	07/2019
1487	(10^279978+11)/3	279978	Serge Batalov	07/2015
1488	2^929524-1864829	279815	Enzo Doria	01/2016
1489	2^929329+22697	279756	Enzo Doria	09/2023
1490	2^929152+60181	279703	Enzo Doria	02/2016
1491	2^928621-2787883	279543	Enzo Doria	11/2015
1492	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
1493	3*10^279271+77	279272	Robert Price	06/2024
1494	2^927429+1882277	279184	Enzo Doria	12/2016
1495	2^926766-11	278985	Stefano Morozzi	07/2022
1496	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
1497	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
1498	(166*10^278633-7)/3	278635	Robert Price	02/2023
1499	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
1500	2^925330-1301	278553	Yves Minet	06/2015

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PRP Records

Probable Primes Top 10000

(301822 PRPs in the top)