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 ?
7751	(431^31543-1)/430	83097	Serge Batalov	08/2020
7752	(2^276028-3)*6-7	83094	Gilbert Mozzo	09/2016
7753	(26*10^83067+79)/3	83068	Robert Price	09/2020
7754	2^275926-4691	83063	Yves Minet	05/2019
7755	(2^275919+1386)/2	83060	Stefano Morozzi	01/2020
7756	(2^275897+9)/1153	83051	Lelio R Paula	12/2012
7757	2^275879-109807	83048	Enzo Doria	04/2014
7759	F(397379)	83047	Henri Lifchitz	08/2003
7758	U(397379)	83047	Serge Batalov	03/2015
7760	3^174040-14	83039	Robert Price	08/2013
7761	(86*10^83038-221)/9	83039	Robert Price	06/2017
7762	21632^6897+6897^21632	83038	Hans Havermann	05/2020
7763	2^275841-6883	83037	Lelio R Paula	07/2011
7764	19610^17127+17127^19610	83023	Hans Havermann	06/2020
7765	3^174002-140	83021	Lelio R Paula	12/2015
7766	6^106681+77	83014	Lelio R Paula	12/2015
7767	187^36539-2	83011	Lelio R Paula	10/2017
7768	1036^27529+27529^1036	83010	Norbert Schneider	03/2020
7769	11^79701-3150	83001	Enzo Doria	12/2012
7770	(2^275721+1554)/2	83000	Stefano Morozzi	01/2020
7771	(2^275704+1858)/2	82995	Stefano Morozzi	01/2020
7772	(2^275696+1726)/2	82993	Stefano Morozzi	01/2020
7773	(55459*2^275657+1)/21	82985	Lelio R Paula	06/2014
7774	(7*10^82960-457)/9	82960	Robert Price	09/2017
7775	2^275535-6855	82945	Lelio R Paula	08/2013
7776	3^173828-14	82938	Robert Price	08/2013
7777	2^275512-109677	82938	Enzo Doria	04/2014
7778	(2^275450+1698)/2	82919	Stefano Morozzi	01/2020
7779	2^275446-110045	82918	Enzo Doria	04/2014
7780	(2^275473+47)/29526097447	82916	Lelio R Paula	12/2012
7781	3^173755-14	82903	Robert Price	08/2013
7782	(182*10^82898+43)/9	82900	Robert Price	11/2017
7783	2^275363-112309	82893	Enzo Doria	06/2014
7784	61^46427-60	82888	Norbert Schneider	10/2014
7785	3*10^82880-7^82880	82881	Mike Oakes	02/2010
7786	2^275290+90195	82871	Lelio R Paula	07/2013
7787	(35*10^82870-71)/9	82871	Robert Price	05/2015
7788	2^275270-1859621	82865	Enzo Doria	03/2016
7789	2^275259+81	82862	Henri Lifchitz	01/2007
7790	21436^7335+7335^21436	82859	Hans Havermann	05/2020
7791	(2^275247+1590)/2	82858	Stefano Morozzi	01/2020
7792	22515^4784+4784^22515	82851	Hans Havermann	05/2020
7793	6*10^82842-31	82843	Robert Price	07/2020
7794	(10013^20707-1)/10012	82836	Serge Batalov	08/2020
7795	(113703^16384+1)/2	82834	Richard Fischer	04/2018
7796	(2^275146+954)/2	82827	Stefano Morozzi	01/2020
7797	7^98003+98003^7+1	82823	Robert Price	05/2014
7798	(2^275101+3566)/2	82814	Stefano Morozzi	01/2020
7799	(2^275050+3150)/2	82798	Stefano Morozzi	01/2020
7800	(2^275044+2482)/2	82797	Stefano Morozzi	01/2020
7801	10^82790+126043	82791	Patrick De Geest	07/2013
7802	10^82790-47	82790	Robert Price	05/2011
7803	20762^9711+9711^20762	82784	Hans Havermann	05/2020
7804	2^274985-112663	82779	Enzo Doria	06/2014
7805	2^274935+15015	82764	Lelio R Paula	07/2013
7806	(17*2^274922+1)/3	82761	Lelio R Paula	12/2012
7807	[(55^5)^9511-(22434^2)^9511]/19	82759	Richard Fischer	11/2019
7808	(43*10^82752-61)/9	82753	Robert Price	06/2015
7809	(3*2^274862+1)/1027	82740	Lelio R Paula	12/2012
7810	(2^274851+3126)/2	82739	Stefano Morozzi	01/2020
7811	(31*2^274848-1)/4065	82736	Lelio R Paula	02/2014
7812	(4^137405+23)/3	82726	Robert Price	02/2017
7813	(2^274798+414)/2	82723	Stefano Morozzi	01/2020
7814	2^274791-110491	82721	Enzo Doria	05/2014
7815	(11*2^274776-1)/95	82715	Lelio R Paula	02/2014
7816	(47*10^82706-119)/9	82707	Robert Price	09/2017
7817	2^274704-111395	82695	Enzo Doria	05/2014
7818	2^274686-3911	82689	Yves Minet	04/2017
7819	(1629^25741-1)/1628	82675	Serge Batalov	08/2020
7820	21474^7075+7075^21474	82670	Hans Havermann	06/2020
7821	(2^274663-1017)/48871318292279	82669	Lelio R Paula	12/2012
7822	(3^173263-5)/14498	82664	Lelio R Paula	12/2012
7823	20488^10815+10815^20488	82650	Hans Havermann	07/2020
7824	(2^274554+894)/2	82649	Stefano Morozzi	01/2020
7826	2^274511-64875	82637	Lelio R Paula	08/2013
7825	(2^274512+1222)/2	82637	Stefano Morozzi	01/2020
7827	12^76572-83	82636	Lelio R Paula	11/2015
7828	3^173191-2^173191	82634	Mike Oakes	02/2004
7829	(2^274500+2970)/2	82633	Stefano Morozzi	01/2020
7830	20507^10698+10698^20507	82629	Hans Havermann	07/2020
7831	(2^274429+3726)/2	82612	Stefano Morozzi	01/2020
7832	14^72072-15	82604	Lelio R Paula	11/2015
7833	(2^274374+2950)/2	82595	Stefano Morozzi	01/2020
7834	(55459*2^274339+1)/3	82589	Lelio R Paula	06/2014
7835	2^274351+123	82588	Lelio R Paula	06/2012
7836	(1017*2^274339-1)/3515	82584	Lelio R Paula	04/2015
7837	21208^7833+7833^21208	82583	Hans Havermann	07/2020
7838	(2^274248+750)/2	82557	Stefano Morozzi	01/2020
7839	(2^274240+822)/2	82555	Stefano Morozzi	01/2020
7840	6^106086+113	82551	Lelio R Paula	12/2015
7841	(17*10^82540-377)/9	82541	Robert Price	11/2017
7842	(3470^23311-1)/3469	82526	Serge Batalov	08/2020
7843	2^274093-58695	82511	Lelio R Paula	07/2013
7844	7*10^82509-47	82510	Robert Price	02/2017
7845	2^274081-6555	82507	Lelio R Paula	07/2013
7847	2^274074-274074+1	82505	Robert Price	10/2014
7848	14^71985+47	82505	Lelio R Paula	11/2015
7846	5*10^82504+21	82505	Robert Price	01/2017
7849	(2^274062+498)/2	82501	Stefano Morozzi	01/2020
7850	6^106014-139	82495	Lelio R Paula	12/2015
7851	(2^274046+47)/753	82494	Lelio R Paula	12/2012
7852	2^274008-1838099	82485	Enzo Doria	05/2015
7853	2^273981-110029	82477	Enzo Doria	04/2014
7854	19^64490-30	82467	Lelio R Paula	12/2015
7855	(2^273864+3150)/2	82441	Stefano Morozzi	01/2020
7856	21328^7333+7333^21328	82439	Hans Havermann	07/2020
7857	20829^9070+9070^20829	82434	Hans Havermann	07/2020
7860	2^273785+11715	82418	Lelio R Paula	07/2013
7859	8*10^82417+51	82418	Robert Price	05/2017
7858	(2^273786+2242)/2	82418	Stefano Morozzi	01/2020
7861	11^79133-10	82409	Theodore Burton	11/2005
7862	(2^273752+1882)/2	82408	Stefano Morozzi	01/2020
7863	91^42063+90	82404	Norbert Schneider	01/2016
7865	2^273662-63	82381	Lelio R Paula	06/2012
7864	2^273661+255	82381	Lelio R Paula	07/2013
7866	(62*10^82377-17)/9	82378	Robert Price	09/2015
7867	2^273608+524287	82365	Paul Underwood	08/2018
7868	8*10^82360-51	82361	Robert Price	10/2017
7869	(79*10^82347-1)/3	82349	Robert Price	11/2017
7870	(11*10^82323+91)/3	82323	Robert Price	02/2017
7871	(189977#+19081)/(19081*17260483)	82317	Makoto Morimoto	10/2017
7872	(189977#+196924)/(271354128874441)	82316	Makoto Morimoto	10/2017
7873	15^69984+32	82308	Lelio R Paula	11/2015
7874	9*6^105746+7	82288	Lelio R Paula	10/2014
7875	89^42211-88	82286	Norbert Schneider	01/2016
7876	gcd(V(1476435),5F(295287)(F(295287)+1)+1)	82281	Serge Batalov	04/2015
7877	20596^9883+9883^20596	82279	Hans Havermann	06/2020
7878	(19*10^82270-43)/3	82271	Robert Price	10/2017
7879	2^273282-110241	82267	Enzo Doria	05/2014
7880	(2^273277+3746)/2	82265	Stefano Morozzi	01/2020
7881	(13^73849+4^73849)/17	82263	Robert Price	05/2013
7883	10^82254+9^(82254+1)	82255	Robert Price	08/2016
7882	10^82254+457773	82255	Patrick De Geest	12/2016
7884	10^82254-99609	82254	Patrick De Geest	12/2016
7885	(754*10^82250-7)/9	82252	Robert Price	11/2017
7886	18^65524+13	82251	Lelio R Paula	11/2015
7887	2^273206-107	82244	Lelio R Paula	06/2012
7888	2^273193-459145	82240	Enzo Doria	05/2015
7890	2^273126+36937	82220	Yves Minet	06/2010
7889	39505!2+128	82220	Robert Price	03/2015
7891	(2^273090+2214)/2	82208	Stefano Morozzi	01/2020
7892	2^273053-112111	82198	Enzo Doria	06/2014
7893	(2^273052+3138)/2	82197	Stefano Morozzi	01/2020
7894	2^273016+1185	82187	Lelio R Paula	07/2013
7895	(2^273008+3)/7	82183	Lelio R Paula	12/2012
7896	(2^272992+2230)/2	82179	Stefano Morozzi	01/2020
7898	5^117554-15386	82167	Enzo Doria	02/2013
7897	21158^7647+7647^21158	82167	Hans Havermann	06/2020
7899	20194^11715+11715^20194	82165	Hans Havermann	06/2020
7900	(38*10^82161+403)/9	82162	Robert Price	11/2017
7901	2^272907-111439	82154	Enzo Doria	05/2014
7902	(67607*2^272901+1)/50790115	82149	Lelio R Paula	06/2014
7903	2^272875-69	82144	Lelio R Paula	06/2012
7904	(3997^22807-1)/3996	82142	Serge Batalov	08/2020
7905	7^97197+4	82141	Robert Price	01/2014
7906	(4*6^105554+1)/5	82137	Serge Batalov	10/2014
7907	2^272826-4433	82129	Yves Minet	03/2019
7908	6^105531-109	82120	Lelio R Paula	12/2015
7909	2^272766-65	82111	Lelio R Paula	06/2012
7910	19^64205-78	82103	Lelio R Paula	12/2015
7911	2^272702+1869979	82092	Enzo Doria	05/2016
7912	(29*2^272687-1)/9	82088	Lelio R Paula	02/2014
7913	(5*10^82085-119)/3	82086	Robert Price	04/2016
7914	(2^272665+1334)/2	82081	Stefano Morozzi	01/2020
7915	2^272660-110049	82079	Enzo Doria	04/2014
7916	6^105474+67	82075	Lelio R Paula	12/2015
7917	2^272637+82875	82072	Lelio R Paula	07/2013
7918	(6330^21589-1)/6329	82065	Serge Batalov	08/2020
7919	2^272587-31	82057	Lelio R Paula	06/2012
7920	(1969^24907-1)/1968	82047	Serge Batalov	08/2020
7921	(41*10^82044-59)/9	82045	Robert Price	10/2017
7922	8*5^117368+9	82038	Lelio R Paula	10/2014
7923	(101525^16384+1)/131074	82023	Lelio R Paula	11/2011
7924	4*5^117343-7	82020	Lelio R Paula	10/2014
7925	(2^272381+506)/2	81995	Stefano Morozzi	01/2020
7926	(265*10^81990+17)/3	81992	Robert Price	05/2016
7927	3^171843+10	81990	Robert Price	10/2013
7928	(2^272361+3762)/2	81989	Stefano Morozzi	01/2020
7929	(7*10^81985+107)/3	81986	Robert Price	02/2017
7930	(3*2^272356+1)/177163	81983	Lelio R Paula	12/2012
7931	2^272296-111149	81970	Enzo Doria	05/2014
7932	(2^272293+2810)/2	81969	Stefano Morozzi	01/2020
7933	(2^272278+2118)/2	81964	Stefano Morozzi	01/2020
7934	(9*2^272243-1)/7	81954	Lelio R Paula	02/2014
7935	2^272177-111223	81934	Enzo Doria	05/2014
7936	(2^272127+3878)/2	81919	Stefano Morozzi	01/2020
7938	(151009^15817+1)/151010	81912	Faysal YAtim	06/2017
7937	(2^272104+1950)/2	81912	Stefano Morozzi	01/2020
7939	23160^3437+3437^23160	81898	Hans Havermann	05/2020
7940	(16*10^81896-19)/3	81897	Robert Price	03/2016
7941	(16*10^81872-73)/3	81873	Robert Price	07/2020
7942	(2^271922+78557)/63	81855	Lelio R Paula	12/2012
7943	(10^81848+77)/3	81848	Robert Price	01/2017
7944	(24737*2^271883+1)/3757	81846	Lelio R Paula	06/2014
7945	(2^271885+1670)/2	81846	Stefano Morozzi	01/2020
7946	18813^19144-19144^18813	81831	Norbert Schneider	02/2020
7947	(14*10^81818-89)/3	81819	Robert Price	05/2020
7948	19492^15731+15731^19492	81804	Hans Havermann	07/2020
7949	20420^10137+10137^20420	81801	Hans Havermann	06/2020
7950	(2^271734+3942)/2	81800	Stefano Morozzi	01/2020
7951	(15429^19531-1)/15428	81799	Serge Batalov	08/2020
7952	10^81778+39	81779	Robert Price	03/2011
7953	10^81778-171999	81778	Patrick De Geest	07/2013
7954	(2^271652+2886)/2	81776	Stefano Morozzi	01/2020
7955	(14*10^81767-11)/3	81768	Erik Branger	09/2014
7956	(2^271546+610)/2	81744	Stefano Morozzi	01/2020
7957	2^271541+1868417	81742	Enzo Doria	04/2016
7958	(2^271549-1)/238749682487	81734	Jens K. Andersen	02/2009
7959	19339^16836+16836^19339	81732	Hans Havermann	06/2020
7960	2^271484-167	81725	Lelio R Paula	06/2012
7962	(8*10^81709-611)/9	81709	Robert Price	11/2017
7961	(2^271431+1790)/2	81709	Stefano Morozzi	01/2020
7963	19648^14399+14399^19648	81703	Hans Havermann	05/2020
7964	2^271382+12909	81695	Lelio R Paula	07/2013
7965	49^48334+48	81694	Norbert Schneider	07/2014
7966	7^96668+48	81694	Lelio R Paula	10/2015
7967	11^78435-1410	81682	Enzo Doria	12/2012
7968	19575^14882+14882^19575	81680	Hans Havermann	04/2020
7969	5*10^81653+9	81654	Dmitry Domanov	11/2010
7970	(2^271224+1230)/2	81647	Stefano Morozzi	01/2020
7971	(2^271211-1)/613961495159	81631	Jens K. Andersen	02/2009
7972	(2^271168+1806)/2	81630	Stefano Morozzi	01/2020
7973	3^171068+52	81621	Lelio R Paula	12/2015
7974	2^271115-110407	81614	Enzo Doria	05/2014
7975	2^271111-110635	81613	Enzo Doria	05/2014
7976	2^271098-111	81609	Lelio R Paula	06/2012
7977	(77*10^81606+13)/9	81607	Robert Price	10/2015
7978	2^271064-2790209	81599	Enzo Doria	03/2016
7979	(13*2^271053-1)/3095	81593	Lelio R Paula	02/2014
7980	2^271040-57	81592	Lelio R Paula	06/2012
7981	(14*10^81585+73)/3	81586	Robert Price	04/2016
7982	127^38779+126	81584	Norbert Schneider	02/2015
7983	18^64966-43	81551	Lelio R Paula	11/2015
7984	19406^15909+15909^19406	81538	Hans Havermann	06/2020
7985	(2^270843+1074)/2	81532	Stefano Morozzi	01/2020
7986	(2^270840+47)/591	81529	Lelio R Paula	12/2012
7987	20^62654+87	81515	Lelio R Paula	01/2016
7988	20120^11241+11241^20120	81503	Hans Havermann	05/2020
7989	(19*10^81488+191)/3	81489	Robert Price	01/2017
7990	8*10^81487+21	81488	Robert Price	02/2017
7991	(73*10^81485+107)/9	81486	Robert Price	08/2016
7992	536^29847+29847^536	81458	Norbert Schneider	03/2017
7993	8*7^96378+9	81450	Lelio R Paula	10/2014
7994	(2^270560+3862)/2	81447	Stefano Morozzi	01/2020
7995	(5728^21673-1)/5727	81444	Serge Batalov	08/2020
7996	2^270546-110345	81443	Enzo Doria	05/2014
7997	13^73105-60	81435	Lelio R Paula	11/2015
7998	(2^270502+1518)/2	81429	Stefano Morozzi	01/2020
7999	(2^270479+2114)/2	81422	Stefano Morozzi	01/2020
8000	(2^270384+1218)/2	81394	Stefano Morozzi	01/2020

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