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 ?
6751	2^296377-16245	89219	Enzo Doria	04/2013
6752	2^296372-64875	89217	Lelio R Paula	11/2013
6753	5*6^114648-7	89215	Lelio R Paula	10/2014
6754	(2^296361+1262)/2	89214	Stefano Morozzi	01/2020
6755	3*10^89206+13	89207	Robert Price	08/2017
6756	7*3^186960-4	89204	Lelio R Paula	08/2014
6757	2^296290-112133	89193	Enzo Doria	06/2014
6758	6^114620-17003	89192	Enzo Doria	02/2013
6759	(4*10^89189+41)/9	89189	Robert Price	11/2014
6760	2^296261-161181	89184	Enzo Doria	04/2013
6761	(19*2^296269-1)/530623	89182	Lelio R Paula	02/2014
6762	3^186903-10	89176	Robert Price	09/2013
6763	7*10^89169-3	89170	Dmitry Domanov	11/2010
6764	(2^296221-1017)/35	89170	Lelio R Paula	01/2013
6765	(43*10^89169+47)/9	89170	Robert Price	12/2017
6766	(10^89160+29)/3	89160	Serge Batalov	12/2014
6767	(28*10^89141-97)/3	89142	Robert Price	07/2016
6768	2^296116-734639	89140	Paul Bourdelais	04/2013
6769	(2^296101+1250)/2	89135	Stefano Morozzi	01/2020
6770	22574^8883+8883^22574	89135	Hans Havermann	08/2020
6771	6^114544-133	89133	Lelio R Paula	12/2015
6772	2^296076-113297	89128	Enzo Doria	07/2014
6773	(11*2^296060-1)/215	89122	Lelio R Paula	02/2014
6774	5*10^89118+81	89119	Robert Price	08/2017
6775	2^296037-1411	89117	Yves Minet	01/2013
6776	2^296020-2604809	89111	Enzo Doria	05/2015
6777	2^296016+81	89110	Henri Lifchitz	02/2007
6778	2^296010-11	89108	Lelio R Paula	10/2012
6779	2^295998-111911	89105	Enzo Doria	05/2014
6780	(2^296014+47)/93991149	89102	Lelio R Paula	01/2013
6781	29529^1040+1040^29529	89090	Hans Havermann	08/2020
6782	2^295939-16621	89087	Enzo Doria	04/2013
6783	2^295934-109691	89086	Enzo Doria	04/2014
6784	(2^295921+2246)/2	89081	Stefano Morozzi	01/2020
6785	(185*10^89070-11)/3	89072	Robert Price	10/2020
6786	(185*10^89063+7)/3	89065	Robert Price	02/2017
6787	2^295831+143	89055	Lelio R Paula	10/2012
6788	31^59713-30	89054	Theodore Burton	02/2007
6789	(7*2^295834-1)/27663	89052	Lelio R Paula	02/2014
6790	79731!4-32	89049	Robert Price	11/2019
6792	123^42608+2	89047	Lelio R Paula	05/2013
6791	6^114433-114433^6	89047	Norbert Schneider	04/2017
6793	2^295800-459659	89045	Enzo Doria	05/2015
6795	(52*10^89037-1)/3	89039	Robert Price	02/2017
6794	(2^295782+1870)/2	89039	Stefano Morozzi	01/2020
6796	(6^114398-11)/5	89019	Paul Bourdelais	11/2011
6797	11^85470-5850	89008	Enzo Doria	02/2013
6798	(2^295650+522)/2	89000	Stefano Morozzi	01/2020
6799	(27*2^295634+1)/4687	88993	Lelio R Paula	01/2013
6800	(p(18424)#-4)/2	88985	Robert Price	09/2017
6801	2^295564-189	88974	Lelio R Paula	10/2012
6802	2^295557+73097	88972	Enzo Doria	04/2016
6803	11^85433-5760	88970	Enzo Doria	01/2013
6804	23074^7165+7165^23074	88956	Hans Havermann	08/2020
6805	(2^295479+3050)/2	88948	Stefano Morozzi	01/2020
6806	6*10^88938-91	88939	Robert Price	11/2017
6807	15^75619-88	88935	Lelio R Paula	11/2015
6808	(2^295433+2234)/2	88934	Stefano Morozzi	01/2020
6809	(15589^21211-1)/15588	88930	Serge Batalov	08/2020
6810	23776^5499+5499^23776	88929	Hans Havermann	08/2020
6811	21112^16291+16291^21112	88923	Hans Havermann	08/2020
6812	2^295385-85	88920	Lelio R Paula	10/2012
6813	2^295385-16333	88920	Enzo Doria	04/2013
6814	79617!4+32	88909	Robert Price	09/2019
6815	22077^10640+10640^22077	88903	Hans Havermann	08/2020
6816	2^295309+59	88897	Lelio R Paula	10/2012
6817	2^295288-109799	88891	Enzo Doria	04/2014
6818	10^88888+170373	88889	Stefano Morozzi	07/2018
6819	10^88888+271399	88889	Stefano Morozzi	07/2018
6820	10^88888+375397	88889	Stefano Morozzi	07/2018
6821	10^88888+548823	88889	Stefano Morozzi	07/2018
6822	10^88888+820861	88889	Stefano Morozzi	07/2018
6823	10^88888+1206349	88889	Stefano Morozzi	07/2018
6824	10^88888+1292047	88889	Stefano Morozzi	07/2018
6825	10^88888+1456029	88889	Stefano Morozzi	07/2018
6826	10^88888-490287	88888	Patrick De Geest	09/2018
6827	2^295245+65	88878	Lelio R Paula	10/2012
6828	Padovan(727734)	88874	Eric W. Weisstein	04/2011
6829	(2^295231+1554)/2	88874	Stefano Morozzi	01/2020
6830	79585!4-32	88870	Robert Price	11/2019
6831	18^70793-17	88865	Lelio R Paula	11/2015
6832	6^114196-17573	88862	Enzo Doria	02/2013
6833	302^35829+35829^302	88857	Norbert Schneider	12/2014
6834	3^186223+16	88851	Robert Price	10/2013
6835	3*2^295139+7	88847	Lelio R Paula	08/2014
6836	3^186212-113008	88846	Enzo Doria	07/2014
6837	2*10^88844+23	88845	Robert Price	12/2020
6838	23415^6224+6224^23415	88839	Hans Havermann	08/2020
6839	87^45803-86	88836	Norbert Schneider	11/2015
6840	2^295094-110273	88833	Enzo Doria	05/2014
6841	2^295080+1869151	88828	Enzo Doria	05/2016
6842	(2^295061+2174)/2	88822	Stefano Morozzi	01/2020
6843	2^295027-113407	88812	Enzo Doria	07/2014
6844	(2*10^88808-71)/3	88808	Robert Price	01/2017
6845	(2^295009+2102)/2	88807	Stefano Morozzi	01/2020
6846	13^79722-80	88806	Lelio R Paula	11/2015
6847	21112^16077+16077^21112	88802	Hans Havermann	08/2020
6848	3^186103+104	88794	Lelio R Paula	12/2015
6849	(3*2^294971+1)/25565	88792	Lelio R Paula	01/2013
6850	(4025^24631-1)/4024	88786	Serge Batalov	08/2020
6851	2^294937-115003	88785	Enzo Doria	06/2015
6852	(2^294923+3134)/2	88781	Stefano Morozzi	01/2020
6853	(15326^21211-1)/15325	88773	Serge Batalov	08/2020
6854	2551^26056+26056^2551	88766	Norbert Schneider	01/2020
6855	2^294868-109709	88765	Enzo Doria	04/2014
6856	2^294864-2985	88763	Yves Minet	09/2014
6857	(17*10^88761-41)/3	88762	Robert Price	09/2017
6858	(2^294834+2854)/2	88754	Stefano Morozzi	01/2020
6859	(2^294823+2466)/2	88751	Stefano Morozzi	01/2020
6860	(2^294764+642)/2	88733	Stefano Morozzi	01/2020
6861	2^294754+15015	88730	Lelio R Paula	10/2013
6862	(3^185951-7)/20	88720	Lelio R Paula	01/2013
6863	(2^294688+3186)/2	88710	Stefano Morozzi	01/2020
6864	(2^294673+3906)/2	88706	Stefano Morozzi	01/2020
6865	(2^294661+5)/443693383	88694	Lelio R Paula	01/2013
6866	(2^294631+2514)/2	88693	Stefano Morozzi	01/2020
6867	(10^88680+11)/3	88680	Robert Price	11/2014
6868	2*7^104928-9	88675	Lelio R Paula	10/2014
6869	11^85150+12	88675	Lelio R Paula	11/2015
6870	8*6^113951+5	88673	Lelio R Paula	10/2014
6871	(2^294549+3110)/2	88668	Stefano Morozzi	01/2020
6873	6^113940-18563	88663	Enzo Doria	03/2013
6872	38^56123-56123^38	88663	Norbert Schneider	02/2017
6874	2^294492-65	88651	Lelio R Paula	10/2012
6875	(2^294481+2822)/2	88648	Stefano Morozzi	01/2020
6876	23874^5165+5165^23874	88646	Hans Havermann	08/2020
6877	(2^294469+1466)/2	88644	Stefano Morozzi	01/2020
6878	7*10^88634-27	88635	Dylan Delgado	08/2019
6879	20^68120-53	88627	Lelio R Paula	01/2016
6880	122^42477-121	88623	Norbert Schneider	10/2018
6881	2^294391-113257	88621	Enzo Doria	07/2014
6882	5^126784-15476	88619	Enzo Doria	02/2013
6883	(2^294335+554)/2	88604	Stefano Morozzi	01/2020
6884	2^294327+9	88602	Lelio R Paula	10/2012
6885	2^294320+18915	88600	Lelio R Paula	10/2013
6886	(98*10^88595-89)/99	88595	Ray Chandler	07/2011
6887	20723^18834+18834^20723	88590	Hans Havermann	08/2020
6888	(2^294268+1402)/2	88584	Stefano Morozzi	01/2020
6889	(17*2^294262-1)/13	88582	Lelio R Paula	02/2014
6890	6*10^88571+77	88572	Robert Price	06/2020
6891	(2^294145+1346)/2	88547	Stefano Morozzi	01/2020
6892	(2*10^88545+7)/9	88545	Erik Branger	03/2011
6893	2^294137-133	88545	Lelio R Paula	10/2012
6894	(2^294109+3494)/2	88536	Stefano Morozzi	01/2020
6895	23515^5818+5818^23515	88529	Hans Havermann	08/2020
6896	(2^294092-1017)/1171	88528	Lelio R Paula	01/2013
6898	4^147036+147036^4+1	88525	Robert Price	04/2014
6897	22541^8458+8458^22541	88525	Hans Havermann	08/2020
6899	(14^77213-5^77213)/9	88496	Robert Price	04/2013
6900	2^293965+2793377	88493	Enzo Doria	03/2016
6901	(2^293956+3306)/2	88490	Stefano Morozzi	01/2020
6902	11^84971-150	88489	Enzo Doria	08/2012
6903	(2^293944+1066)/2	88486	Stefano Morozzi	01/2020
6904	9*10^88485+91	88486	Robert Price	10/2020
6905	48^52626-47	88478	Norbert Schneider	08/2018
6906	(2^293956-1017)/39851376696677	88476	Lelio R Paula	01/2013
6907	11^84958-2190	88475	Enzo Doria	12/2012
6908	(2^293902+3070)/2	88474	Stefano Morozzi	01/2020
6909	2^293880-111347	88467	Enzo Doria	05/2014
6910	(106*10^88459-1)/3	88461	Serge Batalov	12/2014
6911	10^88457+278733	88458	Patrick De Geest	07/2017
6912	10^88457-401	88457	Robert Price	06/2017
6913	(2^293834+3018)/2	88453	Stefano Morozzi	01/2020
6914	(2^293747+1626)/2	88427	Stefano Morozzi	01/2020
6915	22080^10109+10109^22080	88424	Hans Havermann	08/2020
6916	11^84908-1680	88423	Enzo Doria	12/2012
6917	(2^293703+3486)/2	88414	Stefano Morozzi	01/2020
6918	2^293679-112075	88407	Enzo Doria	06/2014
6919	6^113608-65	88405	Lelio R Paula	12/2015
6920	2^293624+82875	88390	Lelio R Paula	10/2013
6921	(2^293618+918)/2	88388	Stefano Morozzi	01/2020
6922	2^293612-112337	88387	Enzo Doria	06/2014
6923	758^30693+30693^758	88386	Norbert Schneider	05/2017
6924	gcd(V(1062695),5F(212539)(F(212539)-1)+1)	88383	Serge Batalov	04/2015
6926	5*10^88377+77	88378	Robert Price	06/2016
6925	(2^293584+1558)/2	88378	Stefano Morozzi	01/2020
6927	(5*2^293526+1)/303	88359	Lelio R Paula	01/2013
6928	20918^16743+16743^20918	88355	Hans Havermann	08/2020
6929	(2^293499+2390)/2	88352	Stefano Morozzi	01/2020
6930	20727^18292+18292^20727	88344	Hans Havermann	08/2020
6931	2^293461-2785843	88341	Enzo Doria	03/2016
6933	2^293416-1037	88328	Yves Minet	11/2012
6932	6*10^88327+43	88328	Robert Price	07/2020
6934	25109^3292+3292^25109	88320	Hans Havermann	08/2020
6935	(2^293384-7)/3	88317	Lelio R Paula	01/2013
6936	(3^185092-5)/4	88311	Lelio R Paula	01/2013
6937	(5*10^88303-173)/3	88304	Robert Price	11/2017
6938	14^77039-57	88297	Lelio R Paula	11/2015
6939	3*10^88293-59	88294	Robert Price	10/2017
6940	5^126303+42	88283	Lelio R Paula	10/2015
6942	19^69025-18	88266	Theodore Burton	01/2006
6941	140^41128+139	88266	Norbert Schneider	04/2019
6943	5*10^88261-3	88262	Dmitry Domanov	11/2010
6944	(2^293195+2238)/2	88261	Stefano Morozzi	01/2020
6945	8^97731-7^(97731-1)	88260	Robert Price	04/2016
6946	5*10^88254+59	88255	Robert Price	09/2016
6948	4*3^184968-7	88253	Lelio R Paula	08/2014
6947	34*10^88251-9	88253	Robert Price	06/2020
6949	7^104426+88	88251	Lelio R Paula	10/2015
6950	2^293142+99	88245	Lelio R Paula	10/2012
6951	11^84736-2130	88244	Enzo Doria	12/2012
6952	23884^4945+4945^23884	88232	Hans Havermann	08/2020
6953	22080^9907+9907^22080	88231	Hans Havermann	08/2020
6954	(10^110315+1)/(10^22063+1)/5824812682167648578460281641	88225	Makoto Kamada	04/2019
6955	2^293068-89	88223	Lelio R Paula	10/2012
6956	2126^26511+26511^2126	88218	Norbert Schneider	02/2020
6957	2^293014-109655	88207	Enzo Doria	04/2014
6958	8*7^104371-3	88205	Lelio R Paula	10/2014
6959	2^292995-2145	88201	Lelio R Paula	10/2013
6960	28534^1233+1233^28534	88198	Hans Havermann	08/2020
6961	5*10^88182+77	88183	Robert Price	06/2016
6963	2^292929+43877	88181	Donovan Johnson	04/2005
6962	6^113321+131	88181	Lelio R Paula	12/2015
6964	(2^292919+3366)/2	88178	Stefano Morozzi	01/2020
6965	2^292904-583949	88173	Paul Bourdelais	04/2013
6966	2^292894-111851	88170	Enzo Doria	05/2014
6967	2^292872-2797349	88164	Enzo Doria	03/2016
6968	(2^292864+1042)/2	88161	Stefano Morozzi	01/2020
6969	2^292860-109685	88160	Enzo Doria	04/2014
6970	9*6^113288-5	88157	Lelio R Paula	10/2014
6971	(2^292735+2166)/2	88122	Stefano Morozzi	01/2020
6972	(2^292735+2346)/2	88122	Stefano Morozzi	01/2020
6973	(2^292705+1934)/2	88113	Stefano Morozzi	01/2020
6974	(2*10^88112-23)/3	88112	Robert Price	09/2017
6975	29622^943+943^29622	88111	Hans Havermann	08/2020
6976	(73*10^88105+17)/9	88106	Robert Price	10/2015
6977	(2^292673+3026)/2	88104	Stefano Morozzi	01/2020
6978	11^84588+78	88090	Lelio R Paula	11/2015
6979	(265*10^88077+11)/3	88079	Robert Price	03/2017
6980	91^44959-90^44959	88077	Robert Price	07/2015
6981	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
6982	1316^28233+28233^1316	88066	Norbert Schneider	07/2020
6983	(2^292543+2234)/2	88064	Stefano Morozzi	01/2020
6984	(10^88020+101)/3	88020	Robert Price	04/2016
6985	52^51285-51	88006	Norbert Schneider	09/2018
6986	21002^15501+15501^21002	88006	Hans Havermann	08/2020
6987	20466^19951+19951^20466	88004	Hans Havermann	08/2020
6988	(2^292324+2346)/2	87998	Stefano Morozzi	01/2020
6989	21634^11683+11683^21634	87998	Hans Havermann	08/2020
6990	(6340^23143-1)/6339	87988	Serge Batalov	08/2020
6991	20674^18013+18013^20674	87980	Hans Havermann	08/2020
6992	(10^(243982+1)-610^43982-1)/3	87965	Robert Price	02/2016
6993	(424*10^87930-1)/9	87932	Robert Price	11/2017
6994	(2^292100+3070)/2	87931	Stefano Morozzi	01/2020
6995	p(18225)#/2+128	87929	Robert Price	04/2017
6996	(10607^21841-1)/10606	87919	Serge Batalov	08/2020
6997	(2^292047+1550)/2	87915	Stefano Morozzi	01/2020
6998	4*6^112977+7	87914	Lelio R Paula	10/2014
6999	(2^292016+1062)/2	87906	Stefano Morozzi	01/2020
7000	(11359^21673-1)/11358	87888	Serge Batalov	08/2020

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Probable Primes Top 10000

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