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 ?
5751	(9*2^272243-1)/7	81954	Lelio R Paula	02/2014
5752	2^272177-111223	81934	Enzo Doria	05/2014
5753	(151009^15817+1)/151010	81912	Faysal YAtim	06/2017
5754	(16*10^81896-19)/3	81897	Robert Price	03/2016
5755	(2^271922+78557)/63	81855	Lelio R Paula	12/2012
5756	(10^81848+77)/3	81848	Robert Price	01/2017
5757	(24737*2^271883+1)/3757	81846	Lelio R Paula	06/2014
5758	10^81778+39	81779	Robert Price	03/2011
5759	10^81778-171999	81778	Patrick De Geest	07/2013
5760	(14*10^81767-11)/3	81768	Erik Branger	09/2014
5761	2^271541+1868417	81742	Enzo Doria	04/2016
5762	(2^271549-1)/238749682487	81734	Jens K. Andersen	02/2009
5763	2^271484-167	81725	Lelio R Paula	06/2012
5764	(8*10^81709-611)/9	81709	Robert Price	11/2017
5765	2^271382+12909	81695	Lelio R Paula	07/2013
5766	49^48334+48	81694	Norbert Schneider	07/2014
5767	7^96668+48	81694	Lelio R Paula	10/2015
5768	11^78435-1410	81682	Enzo Doria	12/2012
5769	5*10^81653+9	81654	Dmitry Domanov	11/2010
5770	(2^271211-1)/613961495159	81631	Jens K. Andersen	02/2009
5771	3^171068+52	81621	Lelio R Paula	12/2015
5772	2^271115-110407	81614	Enzo Doria	05/2014
5773	2^271111-110635	81613	Enzo Doria	05/2014
5774	2^271098-111	81609	Lelio R Paula	06/2012
5775	(77*10^81606+13)/9	81607	Robert Price	10/2015
5776	2^271064-2790209	81599	Enzo Doria	03/2016
5777	(13*2^271053-1)/3095	81593	Lelio R Paula	02/2014
5778	2^271040-57	81592	Lelio R Paula	06/2012
5779	(14*10^81585+73)/3	81586	Robert Price	04/2016
5780	127^38779+126	81584	Norbert Schneider	02/2015
5781	18^64966-43	81551	Lelio R Paula	11/2015
5782	(2^270840+47)/591	81529	Lelio R Paula	12/2012
5783	20^62654+87	81515	Lelio R Paula	01/2016
5784	(19*10^81488+191)/3	81489	Robert Price	01/2017
5785	8*10^81487+21	81488	Robert Price	02/2017
5786	(73*10^81485+107)/9	81486	Robert Price	08/2016
5787	536^29847+29847^536	81458	Norbert Schneider	03/2017
5788	8*7^96378+9	81450	Lelio R Paula	10/2014
5789	2^270546-110345	81443	Enzo Doria	05/2014
5790	13^73105-60	81435	Lelio R Paula	11/2015
5791	44^49524+43	81391	Norbert Schneider	06/2014
5792	(3*2^270368-1)/13	81389	Lelio R Paula	02/2014
5793	(10^81363+719)/9	81363	Serge Batalov	12/2014
5794	(10^81353+449)/9	81353	Serge Batalov	12/2014
5795	14^70978-89	81350	Lelio R Paula	11/2015
5796	11^78108-2040	81342	Enzo Doria	12/2012
5797	3^170400-58	81302	Lelio R Paula	12/2015
5798	(17*10^81300-131)/3	81301	Robert Price	12/2017
5799	10^81297+36991	81298	Patrick De Geest	06/2013
5800	10^81297-57	81297	Robert Price	05/2011
5801	2^270055-113047	81295	Enzo Doria	07/2014
5802	18^64759-55	81291	Lelio R Paula	11/2015
5803	(2^269987+1)/3	81274	H.&R. Lifchitz	10/2000
5804	(31^54493-1)/30	81268	Alexander Zhirkov	10/2010
5805	(2^270059-1)/540119/6481417/7124976157756725967	81265	Dario Alpern	09/2014
5806	2^269819-4597	81224	Yves Minet	03/2019
5807	(2^269816+7)/424901	81218	Lelio R Paula	12/2012
5808	(23*10^81214+1)/3	81215	Serge Batalov	06/2009
5809	(17*2^269720+1)/303	81193	Lelio R Paula	07/2012
5810	56^46441-55^46441	81188	Robert Price	10/2013
5812	2^269664+177	81177	Lelio R Paula	06/2012
5811	(13*2^269665-1)/185	81177	Lelio R Paula	02/2014
5813	2^269539-112249	81140	Enzo Doria	06/2014
5814	((2170026-3)3^(170026-1)+1)/4	81128	Robert Price	01/2015
5815	(2^269495-5)/9	81126	Lelio R Paula	12/2012
5816	2^269490-3623	81125	Yves Minet	10/2009
5817	(55459*2^269444+1)/35	81114	Lelio R Paula	06/2014
5818	(2^269417+78557)/5257	81099	Lelio R Paula	12/2012
5819	4*5^116011-7	81089	Lelio R Paula	10/2014
5820	7*10^81058+79	81059	Robert Price	02/2017
5821	2^269236-109907	81049	Enzo Doria	04/2014
5822	(8*10^81029-11)/3	81030	Erik Branger	03/2014
5823	3*10^81021+7	81022	Erik Branger	11/2013
5824	6^104115+103	81018	Lelio R Paula	12/2015
5825	2^269120+1869151	81014	Enzo Doria	05/2016
5826	5^115901+12	81012	Lelio R Paula	10/2015
5827	(2^269083-9)/320369	80997	Lelio R Paula	12/2012
5828	17^65810-20	80976	Lelio R Paula	11/2015
5829	20^62236-23	80971	Lelio R Paula	01/2016
5830	2^268974-112181	80970	Enzo Doria	06/2014
5832	L(387433)	80969	Renaud Lifchitz	11/2003
5831	V(387433)	80969	Serge Batalov	03/2015
5833	(2^268955-509203)/5	80963	Lelio R Paula	12/2012
5834	(87398^16384+1)/65537	80957	Lelio R Paula	11/2011
5835	329^32160+32160^329	80954	Norbert Schneider	11/2014
5836	2^268859-159	80935	Lelio R Paula	05/2012
5837	(2^268841-lucasV(1,2,268841)+1)/2	80929	Mike Oakes	11/2016
5838	2^268827+5775	80925	Lelio R Paula	07/2013
5839	2^268824-110255	80925	Enzo Doria	05/2014
5840	2^268798-1868321	80917	Enzo Doria	04/2016
5841	2^268753-114621	80903	Enzo Doria	05/2015
5842	2^268743+1605	80900	Lelio R Paula	07/2013
5843	6^103954-139	80892	Lelio R Paula	12/2015
5844	10^80883+49	80884	Robert Price	03/2011
5845	10^80883-80327	80883	Patrick De Geest	07/2013
5846	6^103937+121	80879	Lelio R Paula	12/2015
5847	148^37266+147	80877	Norbert Schneider	12/2018
5848	(26*10^80875-119)/3	80876	Robert Price	07/2016
5849	(22699*2^268657+1)/6351	80875	Lelio R Paula	06/2014
5850	2^268581-869688105	80851	Lelio R Paula	05/2016
5851	(11*2^268521-1)/3	80834	Lelio R Paula	02/2014
5852	2^268516-249	80832	Yves Minet	02/2012
5853	2^268500+16095	80827	Lelio R Paula	07/2013
5854	3^169402+100	80826	Lelio R Paula	12/2015
5855	9^84698+8^(84698-1)	80823	Robert Price	03/2016
5856	2^268472-109739	80819	Enzo Doria	04/2014
5857	(9*2^268454+1)/37	80813	Lelio R Paula	12/2012
5858	(3*2^268502+1)/377902188435353647	80811	Lelio R Paula	12/2012
5859	134^37987-133^37987	80803	Jean-Louis Charton	12/2005
5860	15^68702-76	80800	Lelio R Paula	11/2015
5861	2^268408+7	80799	Lelio R Paula	05/2012
5862	2^268375+141	80789	Lelio R Paula	05/2012
5863	12^74856-47	80784	Lelio R Paula	11/2015
5864	2^268346+524287	80781	Paul Underwood	08/2018
5865	6^103770-107	80749	Lelio R Paula	12/2015
5867	3^169224-62	80741	Lelio R Paula	12/2015
5866	p(16866)#/2+64	80741	Robert Price	03/2017
5868	5^115502-72	80733	Lelio R Paula	10/2015
5869	2^268079-1927	80700	Yves Minet	10/2009
5870	2^268028+117	80685	Lelio R Paula	05/2012
5871	121^38738+120	80683	Norbert Schneider	01/2015
5872	(3^169097-8)/835	80677	Lelio R Paula	12/2012
5873	2^267918+67	80652	Lelio R Paula	05/2012
5874	(89*10^80650-179)/9	80651	Robert Price	11/2017
5875	(302*10^80638+13)/9	80640	Robert Price	01/2017
5876	3^169004+2660	80636	Lelio R Paula	12/2015
5877	2^267860-112859	80634	Enzo Doria	06/2014
5878	2^267828-110705	80625	Enzo Doria	05/2014
5879	2^267743+12705	80599	Lelio R Paula	07/2013
5880	(22*10^80595+23)/9	80596	Robert Price	03/2015
5881	2^267674-51	80578	Lelio R Paula	05/2012
5882	(86*10^80571-41)/9	80572	Robert Price	11/2015
5883	2^267612-1965	80560	Lelio R Paula	07/2013
5884	2^267553+4097	80542	Lelio R Paula	07/2013
5885	7^95276-8	80518	Robert Price	01/2014
5886	(15185*2^267457-1)/47829	80513	Lelio R Paula	04/2015
5887	6^103467+163	80513	Lelio R Paula	12/2015
5888	(7*10^80490+143)/3	80491	Robert Price	04/2016
5889	86^41597-85^41597	80470	Robert Price	04/2015
5890	13^72237+30	80468	Lelio R Paula	11/2015
5891	17^65389+14	80458	Lelio R Paula	11/2015
5892	423^30634+30634^423	80456	Norbert Schneider	05/2017
5893	2^267232+105	80445	Lelio R Paula	05/2012
5894	11^77237-3072000	80435	Enzo Doria	01/2013
5895	2^267116-459959	80410	Enzo Doria	06/2015
5896	38715!2+8	80406	Robert Price	01/2015
5897	(2^267017+1)/3	80380	H.&R. Lifchitz	09/2000
5898	2^266968-45	80366	Lelio R Paula	05/2012
5899	20^61768-63	80363	Lelio R Paula	01/2016
5900	2^266920-112967	80351	Enzo Doria	06/2014
5901	8*10^80342+87	80343	Robert Price	10/2017
5902	12^74428-13	80322	Lelio R Paula	11/2015
5903	2^266680+27	80279	Lelio R Paula	05/2012
5904	2^266630-131	80264	Lelio R Paula	05/2012
5905	2^266598+76819	80254	Enzo Doria	05/2016
5906	2^266587+1880633	80251	Enzo Doria	10/2016
5907	2^266541-110049	80237	Enzo Doria	04/2014
5908	38635!2-8	80222	Robert Price	06/2015
5909	3^168111+168111^3-1	80210	Robert Price	04/2014
5910	2^266443+513	80208	Lelio R Paula	07/2013
5911	(26*10^80200+61)/3	80201	Robert Price	06/2017
5912	2^266412-109913	80199	Enzo Doria	04/2014
5913	(10223*2^266417+1)/45091	80199	Lelio R Paula	06/2014
5914	2^266413-4693	80199	Yves Minet	05/2019
5915	13^71988+66	80191	Lelio R Paula	11/2015
5916	11^77002-4320	80190	Enzo Doria	01/2013
5917	18^63879-13	80186	Lelio R Paula	11/2015
5918	2^266368-112295	80185	Enzo Doria	06/2014
5919	(3^168050+5)/1021454	80175	Lelio R Paula	10/2012
5920	(22*10^80167+41)/9	80168	Robert Price	02/2015
5921	(34*10^80162-43)/9	80163	Ray Chandler	12/2010
5922	(38*10^80150-11)/9	80151	Robert Price	05/2015
5923	(598*10^80149-31)/9	80151	Robert Price	02/2017
5924	19^62678-80	80150	Lelio R Paula	12/2015
5925	10^80139+32343	80140	Patrick De Geest	02/2011
5926	10^80139-9	80139	Alexander Gramolin	01/2011
5927	3^167955-106	80135	Lelio R Paula	12/2015
5928	(197*10^80089-11)/3	80091	Robert Price	10/2017
5929	2^265998+75559	80074	Enzo Doria	04/2016
5930	2^265969-109801	80065	Enzo Doria	04/2014
5931	2^265888-112757	80041	Enzo Doria	06/2014
5932	2^265809+1701	80017	Lelio R Paula	07/2013
5933	gcd(V(957175),5F(191435)(F(191435)+1)+1)	80014	Serge Batalov	04/2015
5934	3^167687-104	80008	Lelio R Paula	02/2015
5935	11^76826-5790	80007	Enzo Doria	01/2013
5936	10^80000+85731	80001	Patrick De Geest	10/2009
5937	10^80000-7169	80000	Patrick De Geest	09/2009
5938	10^79999+22399	80000	Patrick De Geest	09/2009
5939	10^79999-74873	79999	Patrick De Geest	09/2009
5940	3^167668+58	79998	Lelio R Paula	02/2015
5941	155^36506-2	79961	Lelio R Paula	10/2017
5942	2^265612+4257	79958	Lelio R Paula	07/2013
5943	5*3^167577+4	79956	Lelio R Paula	06/2014
5944	(9179*2^265593-1)/9	79955	Lelio R Paula	04/2015
5945	6^102723-43	79935	Lelio R Paula	04/2015
5946	11^76748-3360	79925	Enzo Doria	12/2012
5947	(13*2^265498-1)/187119	79919	Lelio R Paula	02/2014
5948	2^265399-109855	79894	Enzo Doria	04/2014
5949	(20^61403-1)/19	79886	Paul Bourdelais	03/2010
5950	18^63635+59	79880	Lelio R Paula	02/2015
5951	(11*10^79867-107)/3	79868	Robert Price	11/2016
5952	3^167375+80	79859	Lelio R Paula	02/2015
5953	5^114240-14486	79851	Enzo Doria	02/2013
5954	49^47238+48	79842	Norbert Schneider	07/2014
5955	2^265212-3779	79837	Yves Minet	04/2017
5956	91^40746+40746^91	79824	Norbert Schneider	12/2014
5957	(68*10^79813-257)/9	79814	Robert Price	06/2017
5958	(5*2^265118-1)/61	79808	Lelio R Paula	02/2014
5959	2^265074+28425	79796	Lelio R Paula	07/2013
5960	2^265072+1185	79795	Lelio R Paula	07/2013
5961	p(16682)#/2-128	79771	Robert Price	05/2017
5962	3^167167-34	79759	Robert Price	11/2013
5963	12^73906+29	79758	Lelio R Paula	02/2015
5964	2^264934+255	79754	Lelio R Paula	07/2013
5965	4*10^79729-87	79730	Robert Price	03/2017
5966	2^264846-111701	79727	Enzo Doria	05/2014
5967	2^264831-112041	79723	Enzo Doria	06/2014
5968	2^264816-455	79718	Yves Minet	03/2012
5969	(55*10^79711+89)/9	79712	Robert Price	09/2017
5970	47^47667-46	79704	Theodore Burton	02/2007
5971	13^71547+96	79700	Lelio R Paula	03/2015
5972	2^264752-112883	79699	Enzo Doria	06/2014
5973	2^264732+133	79693	Lelio R Paula	05/2012
5974	8*3^167010+7	79685	Lelio R Paula	06/2014
5975	42^49087-41	79681	Norbert Schneider	06/2014
5976	(26*10^79678-119)/3	79679	Robert Price	07/2016
5977	2^264683-21	79678	Lelio R Paula	05/2012
5978	7^94279+18	79675	Lelio R Paula	02/2015
5979	2^264655-127	79670	Lelio R Paula	02/2012
5980	2^264597-459043	79652	Enzo Doria	05/2015
5981	(21*2^264566+1)/5	79643	Lelio R Paula	10/2012
5982	2^264536+1870021	79634	Enzo Doria	05/2016
5983	(17*2^264512-1)/359	79625	Lelio R Paula	02/2014
5984	2^264477-109783	79616	Enzo Doria	04/2014
5985	18^63419-1333	79609	Enzo Doria	03/2013
5986	13^71451-36	79593	Lelio R Paula	03/2015
5987	(2^264410-5)/128002609121	79585	Lelio R Paula	10/2012
5988	19^62234+90	79582	Lelio R Paula	03/2015
5989	12^73714+49	79551	Lelio R Paula	02/2015
5990	(3*2^264184-1)/1433339	79522	Lelio R Paula	02/2014
5991	2^264103-112531	79503	Enzo Doria	06/2014
5992	19^62170+78	79501	Lelio R Paula	03/2015
5993	11^76340-2580	79500	Enzo Doria	12/2012
5994	(23*10^79492-11)/3	79493	Robert Price	10/2015
5995	((2^132049+13650)^2+(2^132049+13650)+41)/2003/23841473	79491	Makoto Morimoto	05/2016
5996	2^264060-112133	79490	Enzo Doria	06/2014
5997	((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/10426147	79488	Makoto Morimoto	05/2016
5998	9^83298+6^83298-2^83298	79487	Mike Oakes	08/2010
5999	18^63319+35	79483	Lelio R Paula	02/2015
6000	38303!2+256	79461	Robert Price	01/2015

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PRP Records

Probable Primes Top 10000

(252932 PRPs in the top)