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 (> 30000)	Who ?	When ?
1251	2^488627-350317	147092	Enzo Doria	06/2015
1252	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
1253	2^488280-2165	146987	Yves Minet	07/2014
1254	2^487726-1863341	146821	Enzo Doria	12/2015
1255	2^487121-39523	146639	Enzo Doria	09/2015
1256	(7*2^486967+1)/39	146591	Lelio R Paula	09/2015
1257	2^486840+1879141	146554	Enzo Doria	08/2016
1258	96^73877-95^73877	146445	Robert Price	10/2015
1259	2^485531-114621	146160	Enzo Doria	05/2015
1260	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
1261	2^485389+81887	146117	Enzo Doria	08/2016
1262	(10^146063+71)/9	146063	Serge Batalov	07/2015
1263	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
1264	2^484743+1872923	145923	Enzo Doria	05/2016
1265	2^484341+1879157	145802	Enzo Doria	08/2016
1266	70^78989-69^78989	145743	Robert Price	01/2014
1267	51^85334+2	145714	Robert Price	07/2015
1268	2^483886-1857101	145665	Enzo Doria	10/2015
1269	2^483563-1863457	145567	Enzo Doria	12/2015
1270	2^483516-1861409	145553	Enzo Doria	11/2015
1271	2^483384-115019	145514	Enzo Doria	06/2015
1272	2^483302-3221	145489	Lelio R Paula	12/2012
1273	2^483046+1874029	145412	Enzo Doria	06/2016
1274	2^482991-2789317	145395	Enzo Doria	12/2015
1275	2^482978-2789711	145391	Enzo Doria	12/2015
1276	2^482966-2789711	145388	Enzo Doria	12/2015
1277	2^482817-1858843	145343	Enzo Doria	10/2015
1278	2^482751-113635	145323	Enzo Doria	08/2014
1279	2^482705-459763	145309	Enzo Doria	05/2015
1280	(4^241306+11)/3	145281	Robert Price	03/2017
1281	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
1282	53^84239-52^84239	145252	Robert Price	01/2013
1283	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
1284	2^482087+72623	145123	Enzo Doria	04/2016
1285	2^482016-286565	145102	Enzo Doria	07/2015
1286	2^481840+15	145049	Robert Price	09/2015
1287	2^481801-481801	145037	Henri Lifchitz	03/2005
1288	2^481775+1869083	145029	Enzo Doria	05/2016
1289	29^99167+2	145022	Ray Chandler	08/2011
1290	2^481663+1875653	144996	Enzo Doria	07/2016
1291	2^481149-459073	144841	Enzo Doria	05/2015
1292	2^481045-113215	144809	Enzo Doria	07/2014
1293	2^480859-113695	144753	Enzo Doria	09/2014
1294	2^480766-2787191	144725	Enzo Doria	11/2015
1295	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
1296	2^480678+1874239	144699	Enzo Doria	06/2016
1297	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
1298	L(692147)	144651	Henri Lifchitz	10/2008
1299	2^480417+35	144620	Robert Price	11/2015
1300	2^480296-59879	144584	Enzo Doria	10/2015
1301	2^479844+3	144448	Donovan Johnson	06/2006
1302	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
1303	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
1304	2^479348-2792219	144299	Enzo Doria	02/2016
1305	3^302389-6242	144277	Enzo Doria	05/2014
1306	2*10^144220-3	144221	Robert Price	07/2015
1307	2^478904-109109	144165	Enzo Doria	04/2014
1308	2^478337-115333	143994	Enzo Doria	07/2015
1309	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
1310	88^74047-87^74047	143984	Robert Price	05/2015
1311	2^478088+27	143919	Robert Price	11/2015
1312	2^477475-22071	143735	Enzo Doria	07/2013
1313	2^477417-22123	143717	Enzo Doria	07/2013
1314	2^477359-3577	143700	Yves Minet	03/2017
1315	2^476936-396765	143573	Enzo Doria	07/2013
1316	2^476888-2791229	143558	Enzo Doria	01/2016
1317	2^476868-1859939	143552	Enzo Doria	11/2015
1318	2^476558-113627	143459	Enzo Doria	08/2014
1319	(2^475854+9)/73	143245	Lelio R Paula	08/2015
1320	2^475813-113239	143234	Enzo Doria	07/2014
1321	2^475624-114059	143178	Enzo Doria	11/2014
1322	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
1323	2^475480-2786129	143134	Enzo Doria	10/2015
1324	2^475299-111937	143080	Enzo Doria	05/2014
1325	2^475160-2797859	143038	Enzo Doria	04/2016
1326	(2^475069+3)/395	143008	Lelio R Paula	08/2015
1327	2^475027-461437	142998	Enzo Doria	07/2015
1328	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
1329	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
1330	2^474417-59923	142814	Enzo Doria	10/2015
1331	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
1332	2^474053+2897	142705	Lelio R Paula	08/2012
1333	(10^142699+359)/9	142699	Serge Batalov	12/2014
1334	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
1335	2^473740-1856639	142610	Enzo Doria	09/2015
1336	2^473617-114223	142573	Enzo Doria	12/2014
1337	2^473257+1873217	142465	Enzo Doria	06/2016
1338	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
1339	(10^142425+359)/9	142425	Serge Batalov	12/2014
1340	2^473101+773027	142418	Enzo Doria	05/2016
1341	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
1342	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
1343	2^472634-109511	142278	Enzo Doria	04/2014
1344	(48^84589+1)/49	142213	Robert Price	01/2014
1345	2^472258+7	142164	Lelio R Paula	08/2015
1346	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
1347	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
1348	2^471792+1880881	142024	Enzo Doria	11/2016
1349	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
1350	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
1351	4*5^202913-9	141831	Lelio R Paula	04/2015
1352	2*7^167812-3	141818	Lelio R Paula	12/2014
1353	2^471043+35	141799	Robert Price	11/2015
1354	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
1355	2^470692+76771	141693	Enzo Doria	05/2016
1356	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
1357	2^470305-459373	141576	Enzo Doria	05/2015
1358	2^470183+72623	141540	Enzo Doria	04/2016
1359	2^470173-16465	141537	Enzo Doria	04/2013
1360	2^469974-1841	141477	Enzo Doria	05/2014
1361	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
1362	2^469630-59711	141373	Enzo Doria	10/2015
1363	(2^469564-3)/611	141351	Lelio R Paula	08/2015
1364	2^469372-112949	141296	Enzo Doria	07/2014
1365	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
1366	2^469198+782569	141243	Enzo Doria	10/2016
1367	2^469076-2786939	141206	Enzo Doria	11/2015
1368	2^468804+1874941	141125	Enzo Doria	06/2016
1369	2^468787+81353	141119	Enzo Doria	08/2016
1370	2^468595-350407	141062	Enzo Doria	06/2015
1371	2^468564+87855	141052	Lelio R Paula	01/2016
1372	2^468551-21987	141048	Enzo Doria	07/2013
1373	2^468523-7	141040	Lelio R Paula	08/2015
1374	2^468405+87855	141004	Lelio R Paula	01/2016
1375	2^467978-113051	140876	Enzo Doria	07/2014
1376	2^467780-344429	140816	Enzo Doria	07/2015
1377	2^467605-1855603	140764	Enzo Doria	09/2015
1378	5*10^140744-7	140745	Robert Price	09/2015
1379	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
1380	2^467401-1850023	140702	Enzo Doria	08/2015
1381	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
1382	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
1383	2^467166-1854941	140631	Enzo Doria	09/2015
1384	2^466866-1840571	140541	Enzo Doria	06/2015
1385	2^466829-459523	140530	Enzo Doria	05/2015
1386	2^466692-113213	140489	Enzo Doria	07/2014
1387	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
1388	2^466181-112735	140335	Enzo Doria	07/2014
1389	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
1390	2^465803-114817	140221	Enzo Doria	05/2015
1391	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
1392	2^465503-112735	140131	Enzo Doria	07/2014
1393	6^179964+179964^6-1	140040	Robert Price	04/2014
1394	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
1395	2^465072-344789	140001	Enzo Doria	07/2015
1396	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
1397	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
1398	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
1399	2^463633-2788423	139568	Enzo Doria	11/2015
1400	2^463271-109501	139459	Enzo Doria	04/2014
1401	2^463019+79463	139383	Enzo Doria	06/2016
1402	3^292129-112756	139381	Enzo Doria	07/2014
1403	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
1404	2^462855-1865707	139334	Enzo Doria	02/2016
1405	2^462786-292043	139313	Enzo Doria	08/2015
1406	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
1407	2^462238-935	139148	Yves Minet	02/2014
1408	2^461228+1870441	138844	Enzo Doria	05/2016
1409	2^461204-113675	138837	Enzo Doria	08/2014
1410	(2^461139-7)/47	138815	Lelio R Paula	08/2015
1411	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
1412	2^460567-113541	138645	Enzo Doria	08/2014
1413	7*10^138604+3	138605	Robert Price	08/2015
1414	2^460078-69581	138498	Enzo Doria	12/2015
1415	2^459768+1531	138404	Lelio R Paula	06/2012
1416	2^459343-113611	138277	Enzo Doria	08/2014
1417	2^459199+1874393	138233	Enzo Doria	06/2016
1418	2^459063-345307	138192	Enzo Doria	06/2015
1419	2^458927-112747	138151	Enzo Doria	06/2014
1420	2^458927-69217	138151	Enzo Doria	11/2015
1421	555555*2^458524+1513	138036	Darren Bedwell	08/2009
1422	2^458465+2^32+1	138012	T. D. Noe	06/2007
1423	2^458321-113053	137969	Enzo Doria	07/2014
1424	2^458298+79459	137962	Enzo Doria	06/2016
1425	2^458248-21815	137947	Enzo Doria	07/2013
1426	2^458194+1876549	137931	Enzo Doria	07/2016
1427	2^457822+105	137819	Donovan Johnson	06/2006
1428	2^457754-113711	137798	Enzo Doria	09/2014
1429	11^132315-360	137792	Enzo Doria	09/2012
1430	2^457322-2786393	137668	Enzo Doria	10/2015
1431	gcd(Phi(699340,10),(10^34967+1)^3(10^34967+1+10^17484)-(10^69934+10^34967)(10^17484-1)+10^104901)	137664	Serge Batalov	04/2015
1432	2^457240-59939	137643	Enzo Doria	10/2015
1433	2^457120-21575	137607	Enzo Doria	07/2013
1434	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
1435	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
1436	2^456796-113513	137510	Enzo Doria	08/2014
1437	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
1438	2^456503-114361	137422	Enzo Doria	01/2015
1439	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
1440	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
1441	2^455922+76249	137247	Enzo Doria	05/2016
1442	14^119741-119741^14	137239	Serge Batalov	04/2016
1443	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
1444	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
1445	2^455689+72677	137177	Enzo Doria	04/2016
1446	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
1447	(37^87421-1)/36	137093	Robert Price	03/2012
1448	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
1449	2^455025-112723	136977	Enzo Doria	06/2014
1450	2^454675-1777	136871	Yves Minet	10/2011
1451	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
1452	31^91680-2	136729	Lelio R Paula	05/2017
1453	2^454199-113697	136728	Enzo Doria	09/2014
1454	2^453935-2791357	136649	Enzo Doria	01/2016
1455	2^453906-69131	136640	Enzo Doria	11/2015
1456	2^453791+1873913	136605	Enzo Doria	06/2016
1457	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
1458	2^453503-2788297	136519	Enzo Doria	11/2015
1459	2^453267-113827	136447	Enzo Doria	09/2014
1460	2^453102+1877629	136398	Enzo Doria	08/2016
1461	L(651821)	136223	Henri Lifchitz	09/2008
1462	2^452460+77701	136205	Enzo Doria	05/2016
1463	2^452440-114755	136199	Enzo Doria	04/2015
1464	(2^451956-5)/181	136051	Lelio R Paula	07/2015
1465	2^451947-22165	136050	Enzo Doria	07/2013
1466	2^451787-21805	136002	Enzo Doria	07/2013
1467	2^451734-112817	135986	Enzo Doria	06/2014
1468	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
1469	2^451705-21879	135977	Enzo Doria	07/2013
1470	2^451560-112349	135934	Enzo Doria	06/2014
1471	2^451450-21743	135900	Enzo Doria	07/2013
1472	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
1473	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
1474	2^449944-113247	135447	Enzo Doria	07/2014
1475	2^449770-113247	135395	Enzo Doria	07/2014
1476	2^449637-21471	135355	Enzo Doria	07/2013
1477	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
1478	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
1479	2^449049-115309	135178	Enzo Doria	07/2015
1480	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
1481	2^448762-351401	135091	Enzo Doria	07/2015
1482	(10^135011+719)/9	135011	Serge Batalov	12/2014
1483	2^448386-2786261	134978	Enzo Doria	03/2016
1484	2^448113-113949	134896	Enzo Doria	11/2014
1485	2^447888-2786639	134828	Enzo Doria	03/2016
1486	2^447870-396765	134823	Enzo Doria	07/2013
1487	2^447766-21791	134791	Enzo Doria	07/2013
1488	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
1489	2^447552-1019	134727	Yves Minet	02/2014
1490	2^447437-113569	134692	Enzo Doria	08/2014
1491	2^447357-2797573	134668	Enzo Doria	04/2016
1492	2^447094-113193	134589	Enzo Doria	07/2014
1493	3^282041-9934	134568	Enzo Doria	05/2014
1494	2^447019-109039	134567	Enzo Doria	04/2014
1495	2^446990-22041	134558	Enzo Doria	07/2013
1496	2^446782-39701	134495	Enzo Doria	09/2015
1497	2^446494-16485	134409	Enzo Doria	04/2013
1498	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
1499	(10^134385+719)/9	134385	Serge Batalov	12/2014
1500	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015

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