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 (> 30000)	Who ?	When ?
7751	(F(142164)^3-F(142163)^3)/F(142162)	59421	Wayne Halsdorf	03/2012
7752	2^197392-114629	59421	Enzo Doria	05/2015
7753	2^197355-157	59410	Lelio R Paula	04/2011
7754	5^84992-84	59407	Lelio R Paula	10/2012
7755	2*3^124504-5	59404	Lelio R Paula	04/2014
7756	2^197307-19165	59396	Enzo Doria	05/2013
7757	2^197303+32769	59395	Lelio R Paula	05/2011
7758	2*10^59394-69	59395	Robert Price	07/2017
7759	(53*10^59389+1)/9	59390	Serge Batalov	11/2010
7760	6^76316-35	59386	Lelio R Paula	10/2012
7761	2^197259-2929	59381	Yves Minet	09/2014
7762	lucasU(46,1,35715)-lucasU(46,1,35714)	59377	Mike Oakes	04/2009
7763	17^48253-6	59373	Lelio R Paula	03/2013
7764	2^197156-15837	59350	Enzo Doria	04/2013
7765	2^197149-18481	59348	Enzo Doria	05/2013
7766	2^197142-17157	59346	Enzo Doria	05/2013
7768	(F(6)^65707-F(5)^65707)/F(4)	59339	Wayne Halsdorf	04/2010
7767	(8^65707-5^65707)/3	59339	Robert Price	12/2012
7769	(2*14283^14283+1)/7925497975	59334	David Broadhurst	09/2010
7770	2^197012-111719	59307	Enzo Doria	05/2014
7771	2^196975+513	59296	Lelio R Paula	05/2011
7772	(61*10^59294+119)/9	59295	Robert Price	09/2017
7773	2^196960+97	59291	Lelio R Paula	04/2011
7774	9^62116+8^(62116-1)	59274	Robert Price	03/2016
7775	2^196900-97305	59273	Lelio R Paula	09/2011
7776	5*6^76155+7	59261	Lelio R Paula	09/2014
7777	15^50385-14	59258	Wojciech Florek	06/2006
7778	(136777#-1)/8823581477	59254	Donovan Johnson	05/2006
7779	(2^196744-3)*6-7	59227	Gilbert Mozzo	05/2016
7780	(67607*2^196696+1)/3	59216	Lelio R Paula	05/2014
7781	2^196696-112967	59212	Enzo Doria	06/2014
7782	20^45508-4223	59208	Enzo Doria	03/2013
7783	gcd(Phi(325820,10),(10^16291+1)^3(10^16291+1-10^8146)+(10^32582+10^16291)(10^8146+1)+10^48873)	59201	Serge Batalov	04/2015
7784	14^51651-81	59199	Lelio R Paula	03/2013
7785	2^196650-1451	59198	Yves Minet	08/2012
7786	2^196636-2797799	59194	Enzo Doria	04/2016
7787	1111*2^196610-555	59189	Henri Lifchitz	04/2005
7788	3^124041+658	59183	Lelio R Paula	10/2012
7789	2^196590-111797	59180	Enzo Doria	05/2014
7790	(10^59174-13)/3	59174	Robert Price	02/2017
7791	(2*10^59174-113)/3	59174	Robert Price	09/2017
7792	(9179*2^196533-1)/783	59164	Lelio R Paula	04/2015
7793	379*10^59152+9	59155	Arkadiusz Wesolowski	10/2011
7794	13^53095+40	59145	Lelio R Paula	03/2013
7795	2*F(282999)-1	59144	Henri Lifchitz	12/2009
7796	4*7^69984+3	59144	Lelio R Paula	09/2014
7797	(5*10^59142+1)/3	59143	Erik Branger	12/2013
7798	2^196463+5711	59142	Lelio R Paula	10/2011
7799	2^196453-97305	59139	Lelio R Paula	09/2011
7800	(28*10^59135+53)/9	59136	Serge Batalov	11/2008
7801	(28*10^59133+113)/3	59134	Robert Price	03/2016
7802	2^196434+7	59133	Lelio R Paula	04/2011
7803	(8*10^59127-29)/3	59128	Robert Price	05/2016
7804	2^196414+255	59127	Lelio R Paula	05/2011
7805	5^84586-92	59124	Lelio R Paula	10/2012
7806	2^196388-17177	59119	Enzo Doria	05/2013
7807	3^123890+20	59111	Lelio R Paula	10/2012
7808	2^196355-1021777	59109	Paul Bourdelais	11/2012
7809	11^56754-1410	59104	Enzo Doria	11/2012
7810	(7*2^196297-1)/1200407	59087	Lelio R Paula	01/2014
7811	(16*10^59062-19)/3	59063	Robert Price	03/2016
7812	35^38249-1228	59060	Enzo Doria	03/2013
7813	5^84475-18	59046	Lelio R Paula	10/2012
7814	2^196123-17701	59039	Enzo Doria	05/2013
7815	12^54702-31	59034	Lelio R Paula	03/2013
7816	2^196101-175	59033	Lelio R Paula	04/2011
7817	2^196085+5775	59028	Lelio R Paula	05/2011
7818	2^196034+11715	59013	Lelio R Paula	05/2011
7819	2^196018-18485	59008	Enzo Doria	05/2013
7820	2^195984-2163	58998	Yves Minet	08/2013
7821	3^123645-16	58994	Lelio R Paula	10/2012
7822	39^37078-38	58994	Norbert Schneider	05/2014
7823	2^195958-16853	58990	Enzo Doria	05/2013
7824	2^195930-3071	58981	Yves Minet	10/2014
7825	2^195924+513	58980	Lelio R Paula	05/2011
7826	2^195863+155	58961	Lelio R Paula	04/2011
7827	(28*10^58956+113)/3	58957	Robert Price	03/2016
7828	11^56612-9300	58956	Enzo Doria	02/2013
7829	2^195833-17173	58952	Enzo Doria	05/2013
7830	(27*2^195833-1)/53	58952	Lelio R Paula	01/2014
7831	(13*2^195821-1)/122425	58945	Lelio R Paula	01/2014
7832	139^27504-138	58942	Norbert Schneider	10/2015
7833	(418*10^58923+23)/9	58925	Robert Price	08/2017
7834	3^123495+44	58923	Lelio R Paula	10/2012
7835	2^195737-18565	58923	Enzo Doria	05/2013
7836	14^51407+47	58920	Lelio R Paula	03/2013
7837	2^195691-99	58909	Lelio R Paula	04/2011
7838	2^195667-1859827	58902	Enzo Doria	04/2016
7839	2^195642+75499	58895	Enzo Doria	04/2016
7840	8*6^75678+5	58890	Lelio R Paula	09/2014
7842	2^195618+73189	58887	Enzo Doria	04/2016
7841	(3928^20480+1)/(3928^4096+1)	58887	Serge Batalov	01/2017
7843	t(197953)	58881	Robert Price	12/2014
7844	2^195581-16105	58876	Enzo Doria	04/2013
7845	(8*10^58872+67)/3	58873	Robert Price	01/2017
7846	7*2^195542-5	58865	Lelio R Paula	03/2014
7847	2*10^58861+9^58861	58862	Mike Oakes	04/2011
7848	11^56513-1620	58853	Enzo Doria	11/2012
7849	2^195496+165	58851	Lelio R Paula	04/2011
7850	5^84187+66	58845	Lelio R Paula	10/2012
7851	(28*10^58843-43)/3	58844	Robert Price	04/2016
7852	2^195462-17565	58840	Enzo Doria	05/2013
7853	2^195435+59273	58832	Yves Minet	01/2011
7854	2^195424-18605	58829	Enzo Doria	05/2013
7855	2^195385-111	58817	Lelio R Paula	04/2011
7856	7*10^58815-83	58816	Robert Price	09/2017
7857	(47*2^195254+1)/268821	58774	Lelio R Paula	03/2015
7858	2^195207-18109	58764	Enzo Doria	05/2013
7859	2^195199-1567	58761	Yves Minet	08/2012
7860	2^195190+73759	58759	Enzo Doria	04/2016
7861	9*7^69525-4	58757	Lelio R Paula	09/2014
7862	2^195170-18045	58753	Enzo Doria	05/2013
7863	2^195166-165	58751	Lelio R Paula	04/2011
7864	(22699*2^195140+1)/175	58746	Lelio R Paula	05/2014
7865	7*3^123109-2	58739	Lelio R Paula	04/2014
7866	18^46790+77	58735	Lelio R Paula	03/2013
7868	2^195095-337297	58730	Gary Barnes	09/2009
7867	(14*10^58729+31)/9	58730	Robert Price	02/2015
7869	99^29424+98	58720	Norbert Schneider	07/2013
7870	(15185*2^195039-1)/219	58715	Lelio R Paula	04/2015
7871	2^195001-69	58702	Lelio R Paula	04/2011
7872	2^194978-487811	58695	Gary Barnes	09/2009
7873	163^26530+26530^163	58690	Serge Batalov	05/2014
7874	2^194940-194940+1	58683	Robert Price	10/2014
7875	(76*10^58669+41)/9	58670	Robert Price	10/2015
7876	14^51186+87	58666	Lelio R Paula	03/2013
7877	2^194878-97305	58665	Lelio R Paula	09/2011
7878	5^83927-18136	58663	Enzo Doria	05/2014
7879	(24737*2^194865+1)/1085	58662	Lelio R Paula	06/2014
7880	7^69411+40	58660	Lelio R Paula	10/2012
7881	6^75382-79	58659	Lelio R Paula	10/2012
7882	2^194854+27	58657	Lelio R Paula	04/2011
7883	2^194801+29835	58641	Lelio R Paula	10/2012
7884	2^194752+195	58627	Lelio R Paula	04/2011
7885	7^69371-6^69371	58626	Predrag Minovic	08/2004
7886	2^194747-112519	58625	Enzo Doria	06/2014
7887	(15*2^194737+1)/59	58622	Lelio R Paula	07/2012
7888	(23*2^194700+1)/3	58612	Lelio R Paula	02/2012
7889	10^58608+55273	58609	Patrick De Geest	07/2017
7890	10^58608-800001	58608	Robert Price	06/2017
7891	10^58608-60119	58608	Patrick De Geest	07/2017
7892	5^83836+76	58599	Lelio R Paula	10/2012
7893	18^46664+31	58577	Lelio R Paula	03/2013
7894	(34*10^58577-7)/9/19/463	58574	Makoto Morimoto	04/2016
7895	2^194574+165	58573	Lelio R Paula	04/2011
7898	2^194569-12211	58572	Enzo Doria	06/2014
7896	10^58571+5^58571+2^58571	58572	Robert Price	12/2016
7897	10^58571+202837	58572	Patrick De Geest	02/2017
7899	(10^58571+41)/3	58571	Robert Price	01/2017
7900	10^58571-343629	58571	Patrick De Geest	02/2017
7901	(43*10^58563-403)/9	58564	Robert Price	04/2017
7902	11^56235-7950	58563	Enzo Doria	02/2013
7903	2^194479-113239	58545	Enzo Doria	07/2014
7904	2^194455-112249	58537	Enzo Doria	06/2014
7905	2^194405-111919	58522	Enzo Doria	05/2014
7906	(4*10^58521-19)/3	58522	Robert Price	06/2017
7908	(7^69247-4^69247)/3	58521	Robert Price	06/2012
7907	5*7^69246+8	58521	Lelio R Paula	09/2014
7909	2^194358-1167	58508	Lelio R Paula	05/2011
7910	(2^194366+7)/1373	58507	Lelio R Paula	02/2012
7911	(493*10^58486-7)/9	58488	Robert Price	07/2016
7912	3^122579-340	58486	Lelio R Paula	10/2012
7913	(11*10^58458-149)/3	58459	Robert Price	01/2017
7914	(47*10^58456+133)/9	58457	Robert Price	04/2017
7915	2^194186+85	58456	Lelio R Paula	04/2011
7916	3^122506-2^(122506-1)	58451	Robert Price	01/2016
7917	(74^31267-1)/73	58444	Paul Bourdelais	08/2017
7918	177^25998-2	58443	Lelio R Paula	10/2017
7919	15^49690-26	58440	Lelio R Paula	03/2013
7920	10^58437+110721	58438	Patrick De Geest	12/2012
7921	10^58437-11	58437	Robert Price	05/2011
7922	2^194095+69	58429	Lelio R Paula	04/2011
7923	(29*10^58417-77)/3	58418	Robert Price	01/2017
7924	2^194034+177	58411	Lelio R Paula	04/2011
7925	789^20158+20158^789	58400	Norbert Schneider	06/2016
7926	14^50949+75	58395	Lelio R Paula	03/2013
7927	2^193974-114761	58392	Enzo Doria	05/2015
7928	2^193965+5	58390	Henri Lifchitz	12/2002
7929	(5*10^58384-29)/3	58385	Robert Price	02/2017
7930	3^122360+80	58381	Lelio R Paula	10/2012
7931	10103^14577-114	58373	Enzo Doria	07/2012
7932	(22699*2^193883+1)/21	58368	Lelio R Paula	06/2014
7933	(31*2^193886+1)/140765	58362	Lelio R Paula	07/2012
7934	11^56041-1560	58361	Enzo Doria	11/2012
7935	(2^193881+9)/17699	58360	Lelio R Paula	02/2012
7936	3^122313+58	58359	Lelio R Paula	10/2012
7937	6^74996-119	58359	Lelio R Paula	10/2012
7938	(11*2^193859+1)/13	58358	Lelio R Paula	07/2012
7939	2^193861-112255	58358	Enzo Doria	06/2014
7940	(22699*2^193854+1)/4927	58357	Lelio R Paula	06/2014
7941	18^46487+37	58354	Lelio R Paula	03/2013
7942	17^47419+54	58347	Lelio R Paula	03/2013
7943	(31*2^193791+1)/3	58338	Lelio R Paula	02/2012
7944	(27*2^193805-1)/982249	58337	Lelio R Paula	01/2014
7945	3^122219-2^122219	58314	Mike Oakes	09/2003
7946	(199*10^58306+11)/3	58308	Robert Price	05/2017
7947	2^193674-18825	58302	Lelio R Paula	05/2011
7948	5*10^58275+3	58276	Dmitry Domanov	11/2010
7949	2^193578-112913	58273	Enzo Doria	06/2014
7950	2^193541+1299	58262	Lelio R Paula	05/2011
7951	10^58250+93	58251	Robert Price	01/2011
7952	10^58250-175607	58250	Patrick De Geest	12/2012
7953	2^193492+8415	58247	Lelio R Paula	10/2012
7954	2^193444+157	58233	Lelio R Paula	04/2011
7955	Phi(28754,28754)	58231	Henri Lifchitz	08/2013
7956	2^193430-111881	58229	Enzo Doria	05/2014
7957	10^58225+124579	58226	Patrick De Geest	12/2012
7958	10^58225-93	58225	Robert Price	05/2011
7959	2^193375-295	58212	Yves Minet	05/2013
7960	2^193345+77267	58203	Enzo Doria	05/2016
7961	21^44017-20^44017	58201	Robert Price	05/2012
7962	(17*2^193329-1)/9	58199	Lelio R Paula	01/2014
7963	17^47291+20	58190	Lelio R Paula	03/2013
7964	p(12528)#/2-128	58170	Robert Price	05/2017
7965	2^193214-135	58164	Lelio R Paula	04/2011
7966	19^45483-80	58162	Lelio R Paula	03/2013
7967	(4*10^58155+83)/3	58156	Robert Price	01/2017
7968	14^50739-13	58154	Lelio R Paula	03/2013
7969	(1017*2^193184-1)/4823	58154	Lelio R Paula	04/2015
7970	(2*10^58151+457)/9	58151	Robert Price	01/2017
7971	(9179*2^193183-1)/3999267879	58149	Lelio R Paula	04/2015
7972	(19*2^193114-1)/1186755	58129	Lelio R Paula	01/2014
7974	2^193091-1237	58127	Yves Minet	08/2012
7973	9*7^68780-2	58127	Lelio R Paula	09/2014
7975	2^193083-869688105	58124	Lelio R Paula	10/2012
7976	2^193058-45	58117	Lelio R Paula	04/2011
7977	(14016^14016+14017^14017)/(23710319913)	58115	David Broadhurst	09/2009
7978	11^55795-42	58105	Lelio R Paula	03/2013
7979	3^121779-16	58104	Lelio R Paula	10/2012
7980	(13*10^58103+191)/3	58104	Robert Price	08/2017
7981	2^192986+195	58095	Lelio R Paula	04/2011
7982	7^68740+2*3^68740	58093	Mike Oakes	07/2010
7983	(85*10^58091-1)/3	58093	Robert Price	07/2017
7984	12^53821+11	58083	Lelio R Paula	02/2013
7985	119^27979-118	58072	Norbert Schneider	10/2013
7986	(10223*2^192828+1)/243	58049	Lelio R Paula	05/2014
7987	2^192808-1127	58041	Yves Minet	05/2013
7988	(27*2^192803+1)/9827	58037	Lelio R Paula	07/2012
7989	(2^192781+lucasV(1,2,192781)+1)/4	58033	Mike Oakes	11/2016
7990	2^192678+72943	58002	Enzo Doria	04/2016
7991	(13*10^57997-37)/3	57998	Robert Price	08/2017
7992	2^192657-3189	57996	Yves Minet	10/2014
7993	6^74525-149	57992	Lelio R Paula	10/2012
7994	42^35723-41	57988	Norbert Schneider	06/2014
7995	(29*2^192625-1)/183	57986	Lelio R Paula	01/2014
7996	(3^121520-8)/3847	57977	Lelio R Paula	03/2012
7997	(2^192596-5)/139	57976	Lelio R Paula	02/2012
7998	10^57975+67833	57976	Patrick De Geest	09/2013
7999	10^57975-47693	57975	Patrick De Geest	09/2013
8000	(F(7707)^37-F(7706)^37)/F(7705)	57972	Wayne Halsdorf	03/2012

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PRP Records

Probable Primes Top 10000

(183432 PRPs in the top)