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	5^211959-12874	148153	Enzo Doria	05/2014
1252	2^491851+1871453	148062	Enzo Doria	05/2016
1253	2^491521-1865323	147963	Enzo Doria	02/2016
1254	(2^491476+7)/71	147948	Lelio R Paula	10/2015
1255	2^491391-7807	147924	Lelio R Paula	01/2013
1256	2^491370-113297	147918	Enzo Doria	07/2014
1257	(32760^32760+32759^32759)/95546586737133567708319	147900	Robert Price	07/2016
1258	2^490550+1179439	147671	Enzo Doria	06/2016
1259	2^490303+2793653	147596	Enzo Doria	03/2016
1260	2^489871-286987	147466	Enzo Doria	07/2015
1261	2^489864-351899	147464	Enzo Doria	07/2015
1262	2^489712+1874851	147419	Enzo Doria	06/2016
1263	2^489305-59815	147296	Enzo Doria	10/2015
1264	(2^489280-7)/6381	147285	Lelio R Paula	09/2015
1265	2^489125+80357	147242	Enzo Doria	06/2016
1266	2^488648-112799	147098	Enzo Doria	07/2014
1267	2^488627-350317	147092	Enzo Doria	06/2015
1268	(2^488441-1)/(61543567*30051203516986199)	147012	Dario Alpern	12/2014
1269	2^488280-2165	146987	Yves Minet	07/2014
1270	2^487726-1863341	146821	Enzo Doria	12/2015
1271	2^487121-39523	146639	Enzo Doria	09/2015
1272	(7*2^486967+1)/39	146591	Lelio R Paula	09/2015
1273	2^486893-79	146570	Yves Minet	09/2017
1274	2^486840+1879141	146554	Enzo Doria	08/2016
1275	96^73877-95^73877	146445	Robert Price	10/2015
1276	2^485531-114621	146160	Enzo Doria	05/2015
1277	(2^485461-9)/4249	146135	Lelio R Paula	09/2015
1278	2^485389+81887	146117	Enzo Doria	08/2016
1279	(10^146063+71)/9	146063	Serge Batalov	07/2015
1280	(2^485119+7)/2745	146032	Lelio R Paula	09/2015
1281	2^484743+1872923	145923	Enzo Doria	05/2016
1282	2^484341+1879157	145802	Enzo Doria	08/2016
1283	70^78989-69^78989	145743	Robert Price	01/2014
1284	51^85334+2	145714	Robert Price	07/2015
1285	2^483886-1857101	145665	Enzo Doria	10/2015
1286	2^483563-1863457	145567	Enzo Doria	12/2015
1287	2^483516-1861409	145553	Enzo Doria	11/2015
1288	2^483384-115019	145514	Enzo Doria	06/2015
1289	2^483302-3221	145489	Lelio R Paula	12/2012
1290	2^483046+1874029	145412	Enzo Doria	06/2016
1291	2^482991-2789317	145395	Enzo Doria	12/2015
1292	2^482978-2789711	145391	Enzo Doria	12/2015
1293	2^482966-2789711	145388	Enzo Doria	12/2015
1294	2^482817-1858843	145343	Enzo Doria	10/2015
1295	2^482751-113635	145323	Enzo Doria	08/2014
1296	2^482705-459763	145309	Enzo Doria	05/2015
1297	(4^241306+11)/3	145281	Robert Price	03/2017
1298	(19*2^482534+1)/7	145258	Lelio R Paula	09/2015
1299	53^84239-52^84239	145252	Robert Price	01/2013
1300	(2^482333+5)/9287	145193	Lelio R Paula	09/2015
1301	2^482087+72623	145123	Enzo Doria	04/2016
1302	2^482016-286565	145102	Enzo Doria	07/2015
1303	2^481840+15	145049	Robert Price	09/2015
1304	2^481801-481801	145037	Henri Lifchitz	03/2005
1305	2^481775+1869083	145029	Enzo Doria	05/2016
1306	29^99167+2	145022	Ray Chandler	08/2011
1307	2^481663+1875653	144996	Enzo Doria	07/2016
1308	2^481149-459073	144841	Enzo Doria	05/2015
1309	2^481045-113215	144809	Enzo Doria	07/2014
1310	2^480859-113695	144753	Enzo Doria	09/2014
1311	2^480766-2787191	144725	Enzo Doria	11/2015
1312	(21*27^101106-151)/26	144720	Curtis Bright	05/2015
1313	2^480678+1874239	144699	Enzo Doria	06/2016
1314	(8*10^144683+1)/9	144683	Serge Batalov	05/2010
1315	L(692147)	144651	Henri Lifchitz	10/2008
1316	2^480417+35	144620	Robert Price	11/2015
1317	2^480296-59879	144584	Enzo Doria	10/2015
1318	2^479844+3	144448	Donovan Johnson	06/2006
1319	(27*2^479642+1)/733	144386	Lelio R Paula	08/2015
1320	(21*2^479605-1)/11	144376	Lelio R Paula	09/2015
1321	2^479348-2792219	144299	Enzo Doria	02/2016
1322	3^302389-6242	144277	Enzo Doria	05/2014
1323	2*10^144220-3	144221	Robert Price	07/2015
1324	2^478904-109109	144165	Enzo Doria	04/2014
1325	2^478337-115333	143994	Enzo Doria	07/2015
1326	(7*2^478330-1)/3	143993	Lelio R Paula	08/2015
1327	88^74047-87^74047	143984	Robert Price	05/2015
1328	2^478088+27	143919	Robert Price	11/2015
1329	2^477475-22071	143735	Enzo Doria	07/2013
1330	2^477417-22123	143717	Enzo Doria	07/2013
1331	2^477359-3577	143700	Yves Minet	03/2017
1332	2^476936-396765	143573	Enzo Doria	07/2013
1333	2^476888-2791229	143558	Enzo Doria	01/2016
1334	2^476868-1859939	143552	Enzo Doria	11/2015
1335	2^476558-113627	143459	Enzo Doria	08/2014
1336	(2^475854+9)/73	143245	Lelio R Paula	08/2015
1337	2^475813-113239	143234	Enzo Doria	07/2014
1338	2^475624-114059	143178	Enzo Doria	11/2014
1339	(11*2^475553-7)/15	143156	Renaud Lifchitz	03/2011
1340	2^475480-2786129	143134	Enzo Doria	10/2015
1341	2^475299-111937	143080	Enzo Doria	05/2014
1342	2^475160-2797859	143038	Enzo Doria	04/2016
1343	(2^475069+3)/395	143008	Lelio R Paula	08/2015
1344	2^475027-461437	142998	Enzo Doria	07/2015
1345	(2^474958+78557)/3	142977	Lelio R Paula	07/2015
1346	(11*2^474432-1)/95	142818	Lelio R Paula	09/2015
1347	2^474417-59923	142814	Enzo Doria	10/2015
1348	(3*2^474166+1)/7	142738	Lelio R Paula	08/2015
1349	2^474053+2897	142705	Lelio R Paula	08/2012
1350	(10^142699+359)/9	142699	Serge Batalov	12/2014
1351	898^48311-897^48311	142676	Jean-Louis Charton	12/2012
1352	2^473740-1856639	142610	Enzo Doria	09/2015
1353	2^473617-114223	142573	Enzo Doria	12/2014
1354	2^473257+1873217	142465	Enzo Doria	06/2016
1355	(19*2^473242+1)/11	142461	Lelio R Paula	09/2015
1356	(10^142425+359)/9	142425	Serge Batalov	12/2014
1357	2^473101+773027	142418	Enzo Doria	05/2016
1358	(13*2^472838-1)/3	142340	Lelio R Paula	09/2015
1359	(17*2^472789-1)/187347	142320	Lelio R Paula	09/2015
1360	2^472634-109511	142278	Enzo Doria	04/2014
1361	(48^84589+1)/49	142213	Robert Price	01/2014
1362	2^472258+7	142164	Lelio R Paula	08/2015
1363	tau(317^10330)	142098	Nik Lygeros / Olivier Rozier / LR team	10/2013
1364	(11*2^471913-1)/21	142060	Lelio R Paula	09/2015
1365	2^471792+1880881	142024	Enzo Doria	11/2016
1366	(31*2^471580-1)/135	141960	Lelio R Paula	08/2015
1367	(904*19^110984-1)/3	141924	Curtis Bright	05/2015
1368	4*5^202913-9	141831	Lelio R Paula	04/2015
1369	2*7^167812-3	141818	Lelio R Paula	12/2014
1370	2^471043+35	141799	Robert Price	11/2015
1371	(11*2^470956-1)/7945	141770	Lelio R Paula	08/2015
1372	2^470692+76771	141693	Enzo Doria	05/2016
1373	(21*2^470391+1)/533	141601	Lelio R Paula	09/2015
1374	2^470305-459373	141576	Enzo Doria	05/2015
1375	2^470183+72623	141540	Enzo Doria	04/2016
1376	2^470173-16465	141537	Enzo Doria	04/2013
1377	2^469974-1841	141477	Enzo Doria	05/2014
1378	(23*2^469939+1)/25	141466	Lelio R Paula	08/2015
1379	2^469630-59711	141373	Enzo Doria	10/2015
1380	(2^469564-3)/611	141351	Lelio R Paula	08/2015
1381	197^61601+2	141342	Lelio R Paula	08/2017
1382	2^469372-112949	141296	Enzo Doria	07/2014
1383	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
1384	2^469198+782569	141243	Enzo Doria	10/2016
1385	2^469076-2786939	141206	Enzo Doria	11/2015
1386	2^468804+1874941	141125	Enzo Doria	06/2016
1387	2^468787+81353	141119	Enzo Doria	08/2016
1388	2^468595-350407	141062	Enzo Doria	06/2015
1389	2^468564+87855	141052	Lelio R Paula	01/2016
1390	2^468551-21987	141048	Enzo Doria	07/2013
1391	2^468523-7	141040	Lelio R Paula	08/2015
1392	2^468405+87855	141004	Lelio R Paula	01/2016
1393	2^467978-113051	140876	Enzo Doria	07/2014
1394	2^467780-344429	140816	Enzo Doria	07/2015
1395	2^467605-1855603	140764	Enzo Doria	09/2015
1396	5*10^140744-7	140745	Robert Price	09/2015
1397	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
1398	2^467401-1850023	140702	Enzo Doria	08/2015
1399	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
1400	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
1401	2^467166-1854941	140631	Enzo Doria	09/2015
1402	2^466866-1840571	140541	Enzo Doria	06/2015
1403	2^466829-459523	140530	Enzo Doria	05/2015
1404	2^466692-113213	140489	Enzo Doria	07/2014
1405	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
1406	2^466181-112735	140335	Enzo Doria	07/2014
1407	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
1408	2^465803-114817	140221	Enzo Doria	05/2015
1409	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
1410	2^465503-112735	140131	Enzo Doria	07/2014
1411	6^179964+179964^6-1	140040	Robert Price	04/2014
1412	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
1413	2^465072-344789	140001	Enzo Doria	07/2015
1414	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
1415	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
1416	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
1417	2^463633-2788423	139568	Enzo Doria	11/2015
1418	2^463271-109501	139459	Enzo Doria	04/2014
1419	2^463019+79463	139383	Enzo Doria	06/2016
1420	3^292129-112756	139381	Enzo Doria	07/2014
1421	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
1422	2^462855-1865707	139334	Enzo Doria	02/2016
1423	2^462786-292043	139313	Enzo Doria	08/2015
1424	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
1425	2^462238-935	139148	Yves Minet	02/2014
1426	2^461228+1870441	138844	Enzo Doria	05/2016
1427	2^461204-113675	138837	Enzo Doria	08/2014
1428	(2^461139-7)/47	138815	Lelio R Paula	08/2015
1429	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
1430	2^460567-113541	138645	Enzo Doria	08/2014
1431	7*10^138604+3	138605	Robert Price	08/2015
1432	2^460330+69	138574	Lelio R Paula	09/2017
1433	2^460078-69581	138498	Enzo Doria	12/2015
1434	2^459768+1531	138404	Lelio R Paula	06/2012
1435	2^459343-113611	138277	Enzo Doria	08/2014
1436	2^459199+1874393	138233	Enzo Doria	06/2016
1437	2^459063-345307	138192	Enzo Doria	06/2015
1438	2^458927-112747	138151	Enzo Doria	06/2014
1439	2^458927-69217	138151	Enzo Doria	11/2015
1440	555555*2^458524+1513	138036	Darren Bedwell	08/2009
1441	2^458465+2^32+1	138012	T. D. Noe	06/2007
1442	2^458321-113053	137969	Enzo Doria	07/2014
1443	2^458298+79459	137962	Enzo Doria	06/2016
1444	2^458248-21815	137947	Enzo Doria	07/2013
1445	2^458194+1876549	137931	Enzo Doria	07/2016
1446	2^457937+57	137853	Lelio R Paula	09/2017
1447	2^457822+105	137819	Donovan Johnson	06/2006
1448	2^457754-113711	137798	Enzo Doria	09/2014
1449	11^132315-360	137792	Enzo Doria	09/2012
1450	2^457347-37	137676	Lelio R Paula	09/2017
1451	2^457322-2786393	137668	Enzo Doria	10/2015
1452	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
1453	2^457240-59939	137643	Enzo Doria	10/2015
1454	2^457120-21575	137607	Enzo Doria	07/2013
1455	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
1456	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
1457	2^456796-113513	137510	Enzo Doria	08/2014
1458	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
1459	2^456503-114361	137422	Enzo Doria	01/2015
1460	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
1461	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
1462	2^455922+76249	137247	Enzo Doria	05/2016
1463	14^119741-119741^14	137239	Serge Batalov	04/2016
1464	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015
1465	124^(2^16)+57^(2^16)	137195	Valeryi Kuryshev	02/2011
1466	2^455689+72677	137177	Enzo Doria	04/2016
1467	(17948!)^2+Prime(17948)	137118	Robert Price	08/2014
1468	(37^87421-1)/36	137093	Robert Price	03/2012
1469	2^455323-57	137066	Lelio R Paula	09/2017
1470	(73*17^111333-9)/16	136991	Curtis Bright	05/2015
1471	2^455025-112723	136977	Enzo Doria	06/2014
1472	2^454675-1777	136871	Yves Minet	10/2011
1473	(6092*28^94536-143)/9	136812	Curtis Bright	05/2015
1474	2^454348-53	136773	Lelio R Paula	09/2017
1475	31^91680-2	136729	Lelio R Paula	05/2017
1476	2^454199-113697	136728	Enzo Doria	09/2014
1477	2^453935-2791357	136649	Enzo Doria	01/2016
1478	2^453906-69131	136640	Enzo Doria	11/2015
1479	2^453791+1873913	136605	Enzo Doria	06/2016
1480	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
1481	2^453503-2788297	136519	Enzo Doria	11/2015
1482	2^453267-113827	136447	Enzo Doria	09/2014
1483	2^453102+1877629	136398	Enzo Doria	08/2016
1484	L(651821)	136223	Henri Lifchitz	09/2008
1485	2^452460+77701	136205	Enzo Doria	05/2016
1486	2^452440-114755	136199	Enzo Doria	04/2015
1487	(2^451956-5)/181	136051	Lelio R Paula	07/2015
1488	2^451947-22165	136050	Enzo Doria	07/2013
1489	2^451787-21805	136002	Enzo Doria	07/2013
1490	2^451734-112817	135986	Enzo Doria	06/2014
1491	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
1492	2^451705-21879	135977	Enzo Doria	07/2013
1493	2^451560-112349	135934	Enzo Doria	06/2014
1494	2^451530+45	135925	Lelio R Paula	08/2017
1495	2^451450-21743	135900	Enzo Doria	07/2013
1496	2^450805+65	135706	Lelio R Paula	08/2017
1497	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
1498	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
1499	2^449944-113247	135447	Enzo Doria	07/2014
1500	2^449770-113247	135395	Enzo Doria	07/2014

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