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 ?
6251	(2^298408+450)/2	89830	Stefano Morozzi	01/2020
6252	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
6253	2^298367+58905	89818	Lelio R Paula	11/2013
6254	21966^12269+12269^21966	89815	Hans Havermann	08/2020
6255	(2^298333+3126)/2	89807	Stefano Morozzi	01/2020
6256	2^298319-109657	89803	Enzo Doria	04/2014
6257	8*10^89800+81	89801	Robert Price	05/2017
6258	21354^16037+16037^21354	89797	Hans Havermann	08/2020
6259	(2^298249+714)/2	89782	Stefano Morozzi	01/2020
6260	21227^16954+16954^21227	89775	Hans Havermann	08/2020
6261	(733^31333-1)/732	89770	Serge Batalov	08/2020
6264	18^71505-91	89759	Lelio R Paula	12/2015
6262	(2^298171+1586)/2	89759	Stefano Morozzi	01/2020
6263	(4788^24391-1)/4787	89759	Serge Batalov	08/2020
6265	(2^298161+3530)/2	89756	Stefano Morozzi	01/2020
6266	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
6267	2^298079-109531	89731	Enzo Doria	04/2014
6268	(9255^22621-1)/9254	89720	Serge Batalov	08/2020
6269	117^43380+116	89718	Norbert Schneider	08/2018
6270	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
6271	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
6272	2^298003-66945	89708	Lelio R Paula	11/2013
6273	(23*10^89705-83)/3	89706	Robert Price	09/2017
6274	17^72900-54	89700	Lelio R Paula	11/2015
6275	(2^297968+2482)/2	89698	Stefano Morozzi	01/2020
6276	3*2^297956+5	89695	Lelio R Paula	08/2014
6277	(2^297952+3558)/2	89693	Stefano Morozzi	01/2020
6278	(3992^24907-1)/3991	89692	Serge Batalov	08/2020
6279	20^68938-11	89691	Lelio R Paula	01/2016
6280	89*10^89687-7	89689	Robert Price	03/2017
6281	(6882^23371-1)/6881	89688	Serge Batalov	08/2020
6282	(297847^16384+1)/2	89686	Richard Fischer	08/2019
6283	2^297923+77783	89684	Enzo Doria	05/2016
6284	(2^297893+1694)/2	89675	Stefano Morozzi	01/2020
6285	11^86107-24576000	89672	Enzo Doria	02/2013
6286	2^297878-111911	89671	Enzo Doria	05/2014
6287	20823^20236+20236^20823	89667	Hans Havermann	08/2020
6288	25708^3075+3075^25708	89666	Hans Havermann	08/2020
6289	21002^18585+18585^21002	89661	Hans Havermann	08/2020
6290	(2^297830+3670)/2	89656	Stefano Morozzi	01/2020
6291	7^106084+40	89652	Lelio R Paula	10/2015
6292	(2^297815+618)/2	89651	Stefano Morozzi	01/2020
6293	21223^16752+16752^21223	89648	Hans Havermann	08/2020
6295	(86*10^89640-311)/9	89641	Robert Price	10/2017
6294	(2^297781+2094)/2	89641	Stefano Morozzi	01/2020
6296	(2^297741+3326)/2	89629	Stefano Morozzi	01/2020
6297	(2^297724+3606)/2	89624	Stefano Morozzi	01/2020
6298	3*10^89608-59	89609	Robert Price	10/2017
6299	(2^297650+3250)/2	89602	Stefano Morozzi	01/2020
6300	3^187780-11038	89594	Enzo Doria	05/2014
6301	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
6302	5^128141-36	89567	Lelio R Paula	10/2015
6303	4*7^105951+9	89540	Lelio R Paula	10/2014
6304	(7*10^89539-439)/9	89539	Robert Price	09/2017
6305	(9772^22441-1)/9771	89536	Serge Batalov	08/2020
6306	22823^8374+8374^22823	89534	Hans Havermann	08/2020
6307	(2^297401+2954)/2	89527	Stefano Morozzi	01/2020
6308	(2^297403+1670)/2	89527	Stefano Morozzi	01/2020
6309	2^297397+177257	89526	Enzo Doria	05/2016
6311	2^297346-16241	89511	Enzo Doria	04/2013
6310	(5*10^89510+79)/3	89511	Robert Price	11/2017
6312	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
6313	2^297328-869688105	89505	Lelio R Paula	07/2016
6314	2^297325-459043	89504	Enzo Doria	05/2015
6315	2^297310-112391	89500	Enzo Doria	06/2014
6316	2^297296-112157	89496	Enzo Doria	06/2014
6317	57^50966-2	89490	Lelio R Paula	08/2013
6318	(266*10^89482+1)/3	89484	Robert Price	02/2016
6319	(14*10^89480-101)/3	89481	Robert Price	04/2017
6320	2618^26175+26175^2618	89466	Norbert Schneider	01/2020
6321	(2^297150+3922)/2	89451	Stefano Morozzi	01/2020
6322	(2^297141+1842)/2	89449	Stefano Morozzi	01/2020
6323	(2^297140+1458)/2	89448	Stefano Morozzi	01/2020
6324	(2^297129+726)/2	89445	Stefano Morozzi	01/2020
6325	2^297122+99	89443	Lelio R Paula	10/2012
6326	(3^187435-5)/1286	89427	Lelio R Paula	01/2013
6327	(28*10^89425+101)/3	89426	Robert Price	09/2020
6328	(2^297037+3522)/2	89417	Stefano Morozzi	01/2020
6329	(25*10^89413+161)/3	89414	Robert Price	01/2017
6330	29080^1187+1187^29080	89406	Hans Havermann	08/2020
6331	2^296990+1870699	89403	Enzo Doria	05/2016
6332	2^296972-1017	89398	Lelio R Paula	11/2013
6333	(7*10^89383+167)/3	89384	Robert Kinser	10/2017
6334	(85*10^89375-31)/9	89376	Robert Price	11/2015
6335	9*2^296870+7	89368	Lelio R Paula	08/2014
6336	100^44683-99^44683	89366	Robert Price	07/2013
6337	2^296810+76519	89349	Enzo Doria	05/2016
6338	(2747^25981-1)/2746	89342	Serge Batalov	08/2020
6339	8^98928+7^(98928+1)	89341	Robert Price	06/2016
6341	(3^187247+4)/1027	89337	Lelio R Paula	01/2013
6340	21832^12359+12359^21832	89337	Hans Havermann	08/2020
6342	(3^187235-2)/2045	89331	Lelio R Paula	01/2013
6343	2^296736-432149	89327	Paul Bourdelais	05/2013
6344	2^296737-112519	89327	Enzo Doria	06/2014
6345	2^296718-3645	89322	Lelio R Paula	11/2013
6346	(2^296702+2338)/2	89316	Stefano Morozzi	01/2020
6347	2^296681-16221	89310	Enzo Doria	04/2013
6348	2^296669-16513	89307	Enzo Doria	04/2013
6349	(2^296626+1282)/2	89294	Stefano Morozzi	01/2020
6350	2^296619-16357	89292	Enzo Doria	04/2013
6351	2^296614-110051	89290	Enzo Doria	04/2014
6352	(2^296601+1730)/2	89286	Stefano Morozzi	01/2020
6353	(3^187138+8)/83147	89283	Lelio R Paula	01/2013
6354	(2*10^89279+457)/9	89279	Robert Price	01/2017
6355	(2^296568+1222)/2	89276	Stefano Morozzi	01/2020
6356	15^75907-28	89274	Lelio R Paula	11/2015
6357	2^296547-37	89270	Yves Minet	01/2012
6358	2^296485+191	89251	Lelio R Paula	10/2012
6359	2^296467-75	89246	Lelio R Paula	10/2012
6360	(2^296462+1674)/2	89244	Stefano Morozzi	01/2020
6361	2^296416-109535	89231	Enzo Doria	04/2014
6362	(23*2^296406+1)/3	89228	Lelio R Paula	01/2013
6363	66^49037-65	89225	Norbert Schneider	11/2014
6364	2^296377-16245	89219	Enzo Doria	04/2013
6365	2^296372-64875	89217	Lelio R Paula	11/2013
6366	5*6^114648-7	89215	Lelio R Paula	10/2014
6367	(2^296361+1262)/2	89214	Stefano Morozzi	01/2020
6368	3*10^89206+13	89207	Robert Price	08/2017
6369	7*3^186960-4	89204	Lelio R Paula	08/2014
6370	2^296290-112133	89193	Enzo Doria	06/2014
6371	6^114620-17003	89192	Enzo Doria	02/2013
6372	(4*10^89189+41)/9	89189	Robert Price	11/2014
6373	2^296261-161181	89184	Enzo Doria	04/2013
6374	(19*2^296269-1)/530623	89182	Lelio R Paula	02/2014
6375	3^186903-10	89176	Robert Price	09/2013
6376	7*10^89169-3	89170	Dmitry Domanov	11/2010
6377	(2^296221-1017)/35	89170	Lelio R Paula	01/2013
6378	(43*10^89169+47)/9	89170	Robert Price	12/2017
6379	(10^89160+29)/3	89160	Serge Batalov	12/2014
6380	(28*10^89141-97)/3	89142	Robert Price	07/2016
6381	2^296116-734639	89140	Paul Bourdelais	04/2013
6382	(2^296101+1250)/2	89135	Stefano Morozzi	01/2020
6383	22574^8883+8883^22574	89135	Hans Havermann	08/2020
6384	6^114544-133	89133	Lelio R Paula	12/2015
6385	2^296076-113297	89128	Enzo Doria	07/2014
6386	(11*2^296060-1)/215	89122	Lelio R Paula	02/2014
6387	5*10^89118+81	89119	Robert Price	08/2017
6388	2^296037-1411	89117	Yves Minet	01/2013
6389	2^296020-2604809	89111	Enzo Doria	05/2015
6390	2^296016+81	89110	Henri Lifchitz	02/2007
6391	2^296010-11	89108	Lelio R Paula	10/2012
6392	2^295998-111911	89105	Enzo Doria	05/2014
6393	(2^296014+47)/93991149	89102	Lelio R Paula	01/2013
6394	29529^1040+1040^29529	89090	Hans Havermann	08/2020
6395	2^295939-16621	89087	Enzo Doria	04/2013
6396	2^295934-109691	89086	Enzo Doria	04/2014
6397	(2^295921+2246)/2	89081	Stefano Morozzi	01/2020
6398	(185*10^89063+7)/3	89065	Robert Price	02/2017
6399	2^295831+143	89055	Lelio R Paula	10/2012
6400	31^59713-30	89054	Theodore Burton	02/2007
6401	(7*2^295834-1)/27663	89052	Lelio R Paula	02/2014
6402	79731!4-32	89049	Robert Price	11/2019
6404	123^42608+2	89047	Lelio R Paula	05/2013
6403	6^114433-114433^6	89047	Norbert Schneider	04/2017
6405	2^295800-459659	89045	Enzo Doria	05/2015
6406	(52*10^89037-1)/3	89039	Robert Price	02/2017
6407	(2^295782+1870)/2	89039	Stefano Morozzi	01/2020
6408	(6^114398-11)/5	89019	Paul Bourdelais	11/2011
6409	11^85470-5850	89008	Enzo Doria	02/2013
6410	(2^295650+522)/2	89000	Stefano Morozzi	01/2020
6411	(27*2^295634+1)/4687	88993	Lelio R Paula	01/2013
6412	(p(18424)#-4)/2	88985	Robert Price	09/2017
6413	2^295564-189	88974	Lelio R Paula	10/2012
6414	2^295557+73097	88972	Enzo Doria	04/2016
6415	11^85433-5760	88970	Enzo Doria	01/2013
6416	23074^7165+7165^23074	88956	Hans Havermann	08/2020
6417	(2^295479+3050)/2	88948	Stefano Morozzi	01/2020
6418	6*10^88938-91	88939	Robert Price	11/2017
6419	15^75619-88	88935	Lelio R Paula	11/2015
6420	(2^295433+2234)/2	88934	Stefano Morozzi	01/2020
6421	(15589^21211-1)/15588	88930	Serge Batalov	08/2020
6422	23776^5499+5499^23776	88929	Hans Havermann	08/2020
6423	21112^16291+16291^21112	88923	Hans Havermann	08/2020
6424	2^295385-85	88920	Lelio R Paula	10/2012
6425	2^295385-16333	88920	Enzo Doria	04/2013
6426	79617!4+32	88909	Robert Price	09/2019
6427	22077^10640+10640^22077	88903	Hans Havermann	08/2020
6428	2^295309+59	88897	Lelio R Paula	10/2012
6429	2^295288-109799	88891	Enzo Doria	04/2014
6430	10^88888+170373	88889	Stefano Morozzi	07/2018
6431	10^88888+271399	88889	Stefano Morozzi	07/2018
6432	10^88888+375397	88889	Stefano Morozzi	07/2018
6433	10^88888+548823	88889	Stefano Morozzi	07/2018
6434	10^88888+820861	88889	Stefano Morozzi	07/2018
6435	10^88888+1206349	88889	Stefano Morozzi	07/2018
6436	10^88888+1292047	88889	Stefano Morozzi	07/2018
6437	10^88888+1456029	88889	Stefano Morozzi	07/2018
6438	10^88888-490287	88888	Patrick De Geest	09/2018
6439	2^295245+65	88878	Lelio R Paula	10/2012
6440	Padovan(727734)	88874	Eric W. Weisstein	04/2011
6441	(2^295231+1554)/2	88874	Stefano Morozzi	01/2020
6442	79585!4-32	88870	Robert Price	11/2019
6443	18^70793-17	88865	Lelio R Paula	11/2015
6444	6^114196-17573	88862	Enzo Doria	02/2013
6445	302^35829+35829^302	88857	Norbert Schneider	12/2014
6446	3^186223+16	88851	Robert Price	10/2013
6447	3*2^295139+7	88847	Lelio R Paula	08/2014
6448	3^186212-113008	88846	Enzo Doria	07/2014
6449	23415^6224+6224^23415	88839	Hans Havermann	08/2020
6450	87^45803-86	88836	Norbert Schneider	11/2015
6451	2^295094-110273	88833	Enzo Doria	05/2014
6452	2^295080+1869151	88828	Enzo Doria	05/2016
6453	(2^295061+2174)/2	88822	Stefano Morozzi	01/2020
6454	2^295027-113407	88812	Enzo Doria	07/2014
6455	(2*10^88808-71)/3	88808	Robert Price	01/2017
6456	(2^295009+2102)/2	88807	Stefano Morozzi	01/2020
6457	13^79722-80	88806	Lelio R Paula	11/2015
6458	21112^16077+16077^21112	88802	Hans Havermann	08/2020
6459	3^186103+104	88794	Lelio R Paula	12/2015
6460	(3*2^294971+1)/25565	88792	Lelio R Paula	01/2013
6461	(4025^24631-1)/4024	88786	Serge Batalov	08/2020
6462	2^294937-115003	88785	Enzo Doria	06/2015
6463	(2^294923+3134)/2	88781	Stefano Morozzi	01/2020
6464	(15326^21211-1)/15325	88773	Serge Batalov	08/2020
6465	2551^26056+26056^2551	88766	Norbert Schneider	01/2020
6466	2^294868-109709	88765	Enzo Doria	04/2014
6467	2^294864-2985	88763	Yves Minet	09/2014
6468	(17*10^88761-41)/3	88762	Robert Price	09/2017
6469	(2^294834+2854)/2	88754	Stefano Morozzi	01/2020
6470	(2^294823+2466)/2	88751	Stefano Morozzi	01/2020
6471	(2^294764+642)/2	88733	Stefano Morozzi	01/2020
6472	2^294754+15015	88730	Lelio R Paula	10/2013
6473	(3^185951-7)/20	88720	Lelio R Paula	01/2013
6474	(2^294688+3186)/2	88710	Stefano Morozzi	01/2020
6475	(2^294673+3906)/2	88706	Stefano Morozzi	01/2020
6476	(2^294661+5)/443693383	88694	Lelio R Paula	01/2013
6477	(2^294631+2514)/2	88693	Stefano Morozzi	01/2020
6478	(10^88680+11)/3	88680	Robert Price	11/2014
6479	2*7^104928-9	88675	Lelio R Paula	10/2014
6480	11^85150+12	88675	Lelio R Paula	11/2015
6481	8*6^113951+5	88673	Lelio R Paula	10/2014
6482	(2^294549+3110)/2	88668	Stefano Morozzi	01/2020
6484	6^113940-18563	88663	Enzo Doria	03/2013
6483	38^56123-56123^38	88663	Norbert Schneider	02/2017
6485	2^294492-65	88651	Lelio R Paula	10/2012
6486	(2^294481+2822)/2	88648	Stefano Morozzi	01/2020
6487	23874^5165+5165^23874	88646	Hans Havermann	08/2020
6488	(2^294469+1466)/2	88644	Stefano Morozzi	01/2020
6489	7*10^88634-27	88635	Dylan Delgado	08/2019
6490	20^68120-53	88627	Lelio R Paula	01/2016
6491	122^42477-121	88623	Norbert Schneider	10/2018
6492	2^294391-113257	88621	Enzo Doria	07/2014
6493	5^126784-15476	88619	Enzo Doria	02/2013
6494	(2^294335+554)/2	88604	Stefano Morozzi	01/2020
6495	2^294327+9	88602	Lelio R Paula	10/2012
6496	2^294320+18915	88600	Lelio R Paula	10/2013
6497	(98*10^88595-89)/99	88595	Ray Chandler	07/2011
6498	20723^18834+18834^20723	88590	Hans Havermann	08/2020
6499	(2^294268+1402)/2	88584	Stefano Morozzi	01/2020
6500	(17*2^294262-1)/13	88582	Lelio R Paula	02/2014

Find by discoverer :

PRP Records

Probable Primes Top 10000

(271067 PRPs in the top)