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 ?
5501	7*3^186960-4	89204	Lelio R Paula	08/2014
5502	2^296290-112133	89193	Enzo Doria	06/2014
5503	6^114620-17003	89192	Enzo Doria	02/2013
5504	(4*10^89189+41)/9	89189	Robert Price	11/2014
5505	2^296261-161181	89184	Enzo Doria	04/2013
5506	(19*2^296269-1)/530623	89182	Lelio R Paula	02/2014
5507	3^186903-10	89176	Robert Price	09/2013
5508	7*10^89169-3	89170	Dmitry Domanov	11/2010
5509	(2^296221-1017)/35	89170	Lelio R Paula	01/2013
5510	(43*10^89169+47)/9	89170	Robert Price	12/2017
5511	(10^89160+29)/3	89160	Serge Batalov	12/2014
5512	(28*10^89141-97)/3	89142	Robert Price	07/2016
5513	2^296116-734639	89140	Paul Bourdelais	04/2013
5514	(2^296101+1250)/2	89135	Stefano Morozzi	01/2020
5515	6^114544-133	89133	Lelio R Paula	12/2015
5516	2^296076-113297	89128	Enzo Doria	07/2014
5517	(11*2^296060-1)/215	89122	Lelio R Paula	02/2014
5518	5*10^89118+81	89119	Robert Price	08/2017
5519	2^296037-1411	89117	Yves Minet	01/2013
5520	2^296020-2604809	89111	Enzo Doria	05/2015
5521	2^296016+81	89110	Henri Lifchitz	02/2007
5522	2^296010-11	89108	Lelio R Paula	10/2012
5523	2^295998-111911	89105	Enzo Doria	05/2014
5524	(2^296014+47)/93991149	89102	Lelio R Paula	01/2013
5525	2^295939-16621	89087	Enzo Doria	04/2013
5526	2^295934-109691	89086	Enzo Doria	04/2014
5527	(2^295921+2246)/2	89081	Stefano Morozzi	01/2020
5528	(185*10^89063+7)/3	89065	Robert Price	02/2017
5529	2^295831+143	89055	Lelio R Paula	10/2012
5530	31^59713-30	89054	Theodore Burton	02/2007
5531	(7*2^295834-1)/27663	89052	Lelio R Paula	02/2014
5532	79731!4-32	89049	Robert Price	11/2019
5534	123^42608+2	89047	Lelio R Paula	05/2013
5533	6^114433-114433^6	89047	Norbert Schneider	04/2017
5535	2^295800-459659	89045	Enzo Doria	05/2015
5537	(52*10^89037-1)/3	89039	Robert Price	02/2017
5536	(2^295782+1870)/2	89039	Stefano Morozzi	01/2020
5538	(6^114398-11)/5	89019	Paul Bourdelais	11/2011
5539	11^85470-5850	89008	Enzo Doria	02/2013
5540	(2^295650+522)/2	89000	Stefano Morozzi	01/2020
5541	(27*2^295634+1)/4687	88993	Lelio R Paula	01/2013
5542	(p(18424)#-4)/2	88985	Robert Price	09/2017
5543	2^295564-189	88974	Lelio R Paula	10/2012
5544	2^295557+73097	88972	Enzo Doria	04/2016
5545	11^85433-5760	88970	Enzo Doria	01/2013
5546	(2^295479+3050)/2	88948	Stefano Morozzi	01/2020
5547	6*10^88938-91	88939	Robert Price	11/2017
5548	15^75619-88	88935	Lelio R Paula	11/2015
5549	(2^295433+2234)/2	88934	Stefano Morozzi	01/2020
5550	2^295385-85	88920	Lelio R Paula	10/2012
5551	2^295385-16333	88920	Enzo Doria	04/2013
5552	79617!4+32	88909	Robert Price	09/2019
5553	2^295309+59	88897	Lelio R Paula	10/2012
5554	2^295288-109799	88891	Enzo Doria	04/2014
5555	10^88888+170373	88889	Stefano Morozzi	07/2018
5556	10^88888+271399	88889	Stefano Morozzi	07/2018
5557	10^88888+375397	88889	Stefano Morozzi	07/2018
5558	10^88888+548823	88889	Stefano Morozzi	07/2018
5559	10^88888+820861	88889	Stefano Morozzi	07/2018
5560	10^88888+1206349	88889	Stefano Morozzi	07/2018
5561	10^88888+1292047	88889	Stefano Morozzi	07/2018
5562	10^88888+1456029	88889	Stefano Morozzi	07/2018
5563	10^88888-490287	88888	Patrick De Geest	09/2018
5564	2^295245+65	88878	Lelio R Paula	10/2012
5565	Padovan(727734)	88874	Eric W. Weisstein	04/2011
5566	(2^295231+1554)/2	88874	Stefano Morozzi	01/2020
5567	79585!4-32	88870	Robert Price	11/2019
5568	18^70793-17	88865	Lelio R Paula	11/2015
5569	6^114196-17573	88862	Enzo Doria	02/2013
5570	302^35829+35829^302	88857	Norbert Schneider	12/2014
5571	3^186223+16	88851	Robert Price	10/2013
5572	3*2^295139+7	88847	Lelio R Paula	08/2014
5573	3^186212-113008	88846	Enzo Doria	07/2014
5574	87^45803-86	88836	Norbert Schneider	11/2015
5575	2^295094-110273	88833	Enzo Doria	05/2014
5576	2^295080+1869151	88828	Enzo Doria	05/2016
5577	(2^295061+2174)/2	88822	Stefano Morozzi	01/2020
5578	2^295027-113407	88812	Enzo Doria	07/2014
5579	(2*10^88808-71)/3	88808	Robert Price	01/2017
5580	(2^295009+2102)/2	88807	Stefano Morozzi	01/2020
5581	13^79722-80	88806	Lelio R Paula	11/2015
5582	3^186103+104	88794	Lelio R Paula	12/2015
5583	(3*2^294971+1)/25565	88792	Lelio R Paula	01/2013
5584	2^294937-115003	88785	Enzo Doria	06/2015
5585	(2^294923+3134)/2	88781	Stefano Morozzi	01/2020
5586	2551^26056+26056^2551	88766	Norbert Schneider	01/2020
5587	2^294868-109709	88765	Enzo Doria	04/2014
5588	2^294864-2985	88763	Yves Minet	09/2014
5589	(17*10^88761-41)/3	88762	Robert Price	09/2017
5590	(2^294834+2854)/2	88754	Stefano Morozzi	01/2020
5591	(2^294823+2466)/2	88751	Stefano Morozzi	01/2020
5592	(2^294764+642)/2	88733	Stefano Morozzi	01/2020
5593	2^294754+15015	88730	Lelio R Paula	10/2013
5594	(3^185951-7)/20	88720	Lelio R Paula	01/2013
5595	(2^294688+3186)/2	88710	Stefano Morozzi	01/2020
5596	(2^294673+3906)/2	88706	Stefano Morozzi	01/2020
5597	(2^294661+5)/443693383	88694	Lelio R Paula	01/2013
5598	(2^294631+2514)/2	88693	Stefano Morozzi	01/2020
5599	(10^88680+11)/3	88680	Robert Price	11/2014
5600	2*7^104928-9	88675	Lelio R Paula	10/2014
5601	11^85150+12	88675	Lelio R Paula	11/2015
5602	8*6^113951+5	88673	Lelio R Paula	10/2014
5603	(2^294549+3110)/2	88668	Stefano Morozzi	01/2020
5605	6^113940-18563	88663	Enzo Doria	03/2013
5604	38^56123-56123^38	88663	Norbert Schneider	02/2017
5606	2^294492-65	88651	Lelio R Paula	10/2012
5607	(2^294481+2822)/2	88648	Stefano Morozzi	01/2020
5608	(2^294469+1466)/2	88644	Stefano Morozzi	01/2020
5609	7*10^88634-27	88635	Dylan Delgado	08/2019
5610	20^68120-53	88627	Lelio R Paula	01/2016
5611	122^42477-121	88623	Norbert Schneider	10/2018
5612	2^294391-113257	88621	Enzo Doria	07/2014
5613	5^126784-15476	88619	Enzo Doria	02/2013
5614	(2^294335+554)/2	88604	Stefano Morozzi	01/2020
5615	2^294327+9	88602	Lelio R Paula	10/2012
5616	2^294320+18915	88600	Lelio R Paula	10/2013
5617	(98*10^88595-89)/99	88595	Ray Chandler	07/2011
5618	(2^294268+1402)/2	88584	Stefano Morozzi	01/2020
5619	(17*2^294262-1)/13	88582	Lelio R Paula	02/2014
5620	(2^294145+1346)/2	88547	Stefano Morozzi	01/2020
5621	(2*10^88545+7)/9	88545	Erik Branger	03/2011
5622	2^294137-133	88545	Lelio R Paula	10/2012
5623	(2^294109+3494)/2	88536	Stefano Morozzi	01/2020
5624	(2^294092-1017)/1171	88528	Lelio R Paula	01/2013
5625	4^147036+147036^4+1	88525	Robert Price	04/2014
5626	(14^77213-5^77213)/9	88496	Robert Price	04/2013
5627	2^293965+2793377	88493	Enzo Doria	03/2016
5628	(2^293956+3306)/2	88490	Stefano Morozzi	01/2020
5629	11^84971-150	88489	Enzo Doria	08/2012
5630	(2^293944+1066)/2	88486	Stefano Morozzi	01/2020
5631	48^52626-47	88478	Norbert Schneider	08/2018
5632	(2^293956-1017)/39851376696677	88476	Lelio R Paula	01/2013
5633	11^84958-2190	88475	Enzo Doria	12/2012
5634	(2^293902+3070)/2	88474	Stefano Morozzi	01/2020
5635	2^293880-111347	88467	Enzo Doria	05/2014
5636	(106*10^88459-1)/3	88461	Serge Batalov	12/2014
5637	10^88457+278733	88458	Patrick De Geest	07/2017
5638	10^88457-401	88457	Robert Price	06/2017
5639	(2^293834+3018)/2	88453	Stefano Morozzi	01/2020
5640	(2^293747+1626)/2	88427	Stefano Morozzi	01/2020
5641	11^84908-1680	88423	Enzo Doria	12/2012
5642	(2^293703+3486)/2	88414	Stefano Morozzi	01/2020
5643	2^293679-112075	88407	Enzo Doria	06/2014
5644	6^113608-65	88405	Lelio R Paula	12/2015
5645	2^293624+82875	88390	Lelio R Paula	10/2013
5646	(2^293618+918)/2	88388	Stefano Morozzi	01/2020
5647	2^293612-112337	88387	Enzo Doria	06/2014
5648	758^30693+30693^758	88386	Norbert Schneider	05/2017
5649	gcd(V(1062695),5F(212539)(F(212539)-1)+1)	88383	Serge Batalov	04/2015
5651	5*10^88377+77	88378	Robert Price	06/2016
5650	(2^293584+1558)/2	88378	Stefano Morozzi	01/2020
5652	(5*2^293526+1)/303	88359	Lelio R Paula	01/2013
5653	(2^293499+2390)/2	88352	Stefano Morozzi	01/2020
5654	2^293461-2785843	88341	Enzo Doria	03/2016
5655	2^293416-1037	88328	Yves Minet	11/2012
5656	(2^293384-7)/3	88317	Lelio R Paula	01/2013
5657	(3^185092-5)/4	88311	Lelio R Paula	01/2013
5658	(5*10^88303-173)/3	88304	Robert Price	11/2017
5659	14^77039-57	88297	Lelio R Paula	11/2015
5660	3*10^88293-59	88294	Robert Price	10/2017
5661	5^126303+42	88283	Lelio R Paula	10/2015
5663	19^69025-18	88266	Theodore Burton	01/2006
5662	140^41128+139	88266	Norbert Schneider	04/2019
5664	5*10^88261-3	88262	Dmitry Domanov	11/2010
5665	(2^293195+2238)/2	88261	Stefano Morozzi	01/2020
5666	8^97731-7^(97731-1)	88260	Robert Price	04/2016
5667	5*10^88254+59	88255	Robert Price	09/2016
5668	4*3^184968-7	88253	Lelio R Paula	08/2014
5669	7^104426+88	88251	Lelio R Paula	10/2015
5670	2^293142+99	88245	Lelio R Paula	10/2012
5671	11^84736-2130	88244	Enzo Doria	12/2012
5672	(10^110315+1)/(10^22063+1)/5824812682167648578460281641	88225	Makoto Kamada	04/2019
5673	2^293068-89	88223	Lelio R Paula	10/2012
5674	2126^26511+26511^2126	88218	Norbert Schneider	02/2020
5675	2^293014-109655	88207	Enzo Doria	04/2014
5676	8*7^104371-3	88205	Lelio R Paula	10/2014
5677	2^292995-2145	88201	Lelio R Paula	10/2013
5678	5*10^88182+77	88183	Robert Price	06/2016
5680	2^292929+43877	88181	Donovan Johnson	04/2005
5679	6^113321+131	88181	Lelio R Paula	12/2015
5681	(2^292919+3366)/2	88178	Stefano Morozzi	01/2020
5682	2^292904-583949	88173	Paul Bourdelais	04/2013
5683	2^292894-111851	88170	Enzo Doria	05/2014
5684	2^292872-2797349	88164	Enzo Doria	03/2016
5685	(2^292864+1042)/2	88161	Stefano Morozzi	01/2020
5686	2^292860-109685	88160	Enzo Doria	04/2014
5687	9*6^113288-5	88157	Lelio R Paula	10/2014
5688	(2^292735+2166)/2	88122	Stefano Morozzi	01/2020
5689	(2^292735+2346)/2	88122	Stefano Morozzi	01/2020
5690	(2^292705+1934)/2	88113	Stefano Morozzi	01/2020
5691	(2*10^88112-23)/3	88112	Robert Price	09/2017
5692	(73*10^88105+17)/9	88106	Robert Price	10/2015
5693	(2^292673+3026)/2	88104	Stefano Morozzi	01/2020
5694	11^84588+78	88090	Lelio R Paula	11/2015
5695	(265*10^88077+11)/3	88079	Robert Price	03/2017
5696	91^44959-90^44959	88077	Robert Price	07/2015
5697	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
5698	(2^292543+2234)/2	88064	Stefano Morozzi	01/2020
5699	(10^88020+101)/3	88020	Robert Price	04/2016
5700	52^51285-51	88006	Norbert Schneider	09/2018
5701	(2^292324+2346)/2	87998	Stefano Morozzi	01/2020
5702	(10^(243982+1)-610^43982-1)/3	87965	Robert Price	02/2016
5703	(424*10^87930-1)/9	87932	Robert Price	11/2017
5704	(2^292100+3070)/2	87931	Stefano Morozzi	01/2020
5705	p(18225)#/2+128	87929	Robert Price	04/2017
5706	(2^292047+1550)/2	87915	Stefano Morozzi	01/2020
5707	4*6^112977+7	87914	Lelio R Paula	10/2014
5708	(2^292016+1062)/2	87906	Stefano Morozzi	01/2020
5709	14^76677+69	87882	Lelio R Paula	11/2015
5710	(22*10^87863-1)/3	87864	Robert Price	12/2014
5711	2^291822-2797811	87848	Enzo Doria	04/2016
5712	(2^291730+1614)/2	87820	Stefano Morozzi	01/2020
5713	2^291716-111389	87816	Enzo Doria	05/2014
5714	(782*10^87809-71)/9	87811	Robert Price	06/2017
5715	3^184039+1820	87809	Lelio R Paula	12/2015
5716	12^81356+41	87798	Lelio R Paula	11/2015
5717	(2^291596+1986)/2	87779	Stefano Morozzi	01/2020
5718	6^112792-18983	87770	Enzo Doria	03/2013
5719	3*6^112787-5	87766	Lelio R Paula	10/2014
5720	7^103848+82	87762	Lelio R Paula	10/2015
5721	(19*2^291534-1)/178696395	87754	Lelio R Paula	02/2014
5722	(2^291506+918)/2	87752	Stefano Morozzi	01/2020
5723	(3^183915+5)/128	87748	Lelio R Paula	01/2013
5724	19^68619+24	87747	Lelio R Paula	12/2015
5726	2^291480+1185	87745	Lelio R Paula	10/2013
5725	2^291482+1867369	87745	Enzo Doria	03/2016
5727	2^291467-937	87741	Yves Minet	05/2013
5728	(25*10^87726+161)/3	87727	Robert Price	01/2017
5729	11^84239-2850	87726	Enzo Doria	12/2012
5730	10^87720+215541	87721	Patrick De Geest	01/2011
5731	10^87720-3	87720	Markus Tervooren	07/2010
5732	(2^291383+3078)/2	87715	Stefano Morozzi	01/2020
5734	(5*10^87712-473)/9	87712	Robert Price	12/2017
5733	(2^291373+2946)/2	87712	Stefano Morozzi	01/2020
5735	(2^291357+5)/6847	87704	Lelio R Paula	01/2013
5736	(2^291280+462)/2	87684	Stefano Morozzi	01/2020
5738	93^44541-2	87679	Lelio R Paula	09/2013
5737	2^291261-109561	87679	Enzo Doria	04/2014
5739	(4*10^87669+149)/9	87669	Robert Price	03/2017
5740	2^291217+4257	87666	Lelio R Paula	10/2013
5741	2*12^81214-5^81214	87645	Mike Oakes	12/2010
5742	(5*10^87622-473)/9	87622	Robert Price	12/2017
5743	12^81188+85	87617	Lelio R Paula	11/2015
5744	(2^291030+3462)/2	87609	Stefano Morozzi	01/2020
5745	(21*2^290980-1)/5	87595	Lelio R Paula	02/2014
5746	(2^290980+1150)/2	87594	Stefano Morozzi	01/2020
5747	2^290958+127	87588	Lelio R Paula	09/2012
5748	78531!4-8	87580	Robert Price	11/2019
5749	2^290923-67	87577	Lelio R Paula	09/2012
5750	3*10^87573-97	87574	Robert Price	08/2017

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Probable Primes Top 10000

(259919 PRPs in the top)