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	10103^14577-114	58373	Enzo Doria	07/2012
7752	(22699*2^193883+1)/21	58368	Lelio R Paula	06/2014
7753	(31*2^193886+1)/140765	58362	Lelio R Paula	07/2012
7754	11^56041-1560	58361	Enzo Doria	11/2012
7755	(2^193881+9)/17699	58360	Lelio R Paula	02/2012
7756	3^122313+58	58359	Lelio R Paula	10/2012
7757	6^74996-119	58359	Lelio R Paula	10/2012
7758	(11*2^193859+1)/13	58358	Lelio R Paula	07/2012
7759	2^193861-112255	58358	Enzo Doria	06/2014
7760	(22699*2^193854+1)/4927	58357	Lelio R Paula	06/2014
7761	18^46487+37	58354	Lelio R Paula	03/2013
7762	17^47419+54	58347	Lelio R Paula	03/2013
7763	(31*2^193791+1)/3	58338	Lelio R Paula	02/2012
7764	(27*2^193805-1)/982249	58337	Lelio R Paula	01/2014
7765	3^122219-2^122219	58314	Mike Oakes	09/2003
7766	(199*10^58306+11)/3	58308	Robert Price	05/2017
7767	2^193674-18825	58302	Lelio R Paula	05/2011
7768	5*10^58275+3	58276	Dmitry Domanov	11/2010
7769	2^193578-112913	58273	Enzo Doria	06/2014
7770	2^193541+1299	58262	Lelio R Paula	05/2011
7771	10^58250+93	58251	Robert Price	01/2011
7772	10^58250-175607	58250	Patrick De Geest	12/2012
7773	2^193492+8415	58247	Lelio R Paula	10/2012
7774	2^193444+157	58233	Lelio R Paula	04/2011
7775	Phi(28754,28754)	58231	Henri Lifchitz	08/2013
7776	2^193430-111881	58229	Enzo Doria	05/2014
7777	10^58225+124579	58226	Patrick De Geest	12/2012
7778	10^58225-93	58225	Robert Price	05/2011
7779	2^193375-295	58212	Yves Minet	05/2013
7780	2^193345+77267	58203	Enzo Doria	05/2016
7781	21^44017-20^44017	58201	Robert Price	05/2012
7782	(17*2^193329-1)/9	58199	Lelio R Paula	01/2014
7783	17^47291+20	58190	Lelio R Paula	03/2013
7784	p(12528)#/2-128	58170	Robert Price	05/2017
7785	2^193214-135	58164	Lelio R Paula	04/2011
7786	19^45483-80	58162	Lelio R Paula	03/2013
7787	(4*10^58155+83)/3	58156	Robert Price	01/2017
7788	14^50739-13	58154	Lelio R Paula	03/2013
7789	(1017*2^193184-1)/4823	58154	Lelio R Paula	04/2015
7790	(2*10^58151+457)/9	58151	Robert Price	01/2017
7791	(9179*2^193183-1)/3999267879	58149	Lelio R Paula	04/2015
7792	(19*2^193114-1)/1186755	58129	Lelio R Paula	01/2014
7794	2^193091-1237	58127	Yves Minet	08/2012
7793	9*7^68780-2	58127	Lelio R Paula	09/2014
7795	2^193083-869688105	58124	Lelio R Paula	10/2012
7796	2^193058-45	58117	Lelio R Paula	04/2011
7797	(14016^14016+14017^14017)/(23710319913)	58115	David Broadhurst	09/2009
7798	11^55795-42	58105	Lelio R Paula	03/2013
7799	3^121779-16	58104	Lelio R Paula	10/2012
7800	(13*10^58103+191)/3	58104	Robert Price	08/2017
7801	2^192986+195	58095	Lelio R Paula	04/2011
7802	7^68740+2*3^68740	58093	Mike Oakes	07/2010
7803	(85*10^58091-1)/3	58093	Robert Price	07/2017
7804	12^53821+11	58083	Lelio R Paula	02/2013
7805	119^27979-118	58072	Norbert Schneider	10/2013
7806	(10223*2^192828+1)/243	58049	Lelio R Paula	05/2014
7807	2^192808-1127	58041	Yves Minet	05/2013
7808	(27*2^192803+1)/9827	58037	Lelio R Paula	07/2012
7809	(2^192781+lucasV(1,2,192781)+1)/4	58033	Mike Oakes	11/2016
7810	2^192678+72943	58002	Enzo Doria	04/2016
7811	(13*10^57997-37)/3	57998	Robert Price	08/2017
7812	2^192657-3189	57996	Yves Minet	10/2014
7813	6^74525-149	57992	Lelio R Paula	10/2012
7814	42^35723-41	57988	Norbert Schneider	06/2014
7815	(29*2^192625-1)/183	57986	Lelio R Paula	01/2014
7816	(3^121520-8)/3847	57977	Lelio R Paula	03/2012
7817	(2^192596-5)/139	57976	Lelio R Paula	02/2012
7818	10^57975+67833	57976	Patrick De Geest	09/2013
7819	10^57975-47693	57975	Patrick De Geest	09/2013
7820	(F(7707)^37-F(7706)^37)/F(7705)	57972	Wayne Halsdorf	03/2012
7821	(3^121492-5)/4	57966	Lelio R Paula	03/2012
7822	2^192549+35	57964	Lelio R Paula	04/2011
7823	28799!2+2	57962	Robert Price	10/2012
7824	(7*2^192534-1)/1347	57957	Lelio R Paula	01/2014
7825	7001^15069-100	57943	Enzo Doria	07/2012
7826	L(277273)/11090921	57940	Donovan Johnson	11/2005
7827	(2^192469-1017)/35	57938	Lelio R Paula	02/2012
7828	2^192457-1155*192457	57936	Henri Lifchitz	02/2005
7829	2^192443+1385	57932	Lelio R Paula	05/2011
7830	132^27317-131	57928	Norbert Schneider	03/2015
7831	41522!3-59049	57912	Robert Price	12/2015
7832	(3*2^192380-1)/169	57911	Lelio R Paula	01/2014
7833	2^192339-2515	57900	Yves Minet	07/2014
7834	2^192303+7695	57889	Lelio R Paula	10/2012
7835	2^192273-5955	57880	Lelio R Paula	05/2011
7836	2^192257+16095	57876	Lelio R Paula	05/2011
7837	2^192218-111861	57864	Enzo Doria	05/2014
7838	2^192214-3941	57863	Yves Minet	04/2017
7839	(2^192212+3)/259	57860	Lelio R Paula	02/2012
7840	(3^121270+8)/155939753	57853	Lelio R Paula	03/2012
7841	80^30393-79	57841	Norbert Schneider	03/2015
7842	20^44455-3123	57838	Enzo Doria	03/2013
7843	2^192122-195	57835	Lelio R Paula	04/2011
7844	(29*10^57834+91)/3	57835	Robert Price	03/2016
7845	8*6^74306+5	57823	Lelio R Paula	09/2014
7846	(39^36341-1)/38	57820	Robert Price	04/2012
7847	2^192037-111805	57809	Enzo Doria	05/2014
7848	2^192023-192023^2	57805	Henri Lifchitz	05/2005
7849	21^43717+2	57804	Ray Chandler	08/2011
7850	8*5^82687+7	57797	Lelio R Paula	09/2014
7851	5^82680-24	57791	Lelio R Paula	10/2012
7852	(2^191915+47)/95	57771	Lelio R Paula	02/2012
7853	6^74227-95	57760	Lelio R Paula	10/2012
7854	2^191861+29835	57756	Lelio R Paula	10/2012
7855	1908^17605+17605^1908	57755	Serge Batalov	05/2014
7856	5*10^57754+59	57755	Robert Price	09/2016
7857	(5*2^191821-1)/8924067	57738	Lelio R Paula	01/2014
7858	38^63917+5^63917-34^63917+3*2^63917	57724	Mike Oakes	11/2010
7859	41399!3-6561	57723	Robert Price	11/2015
7860	2^191745+17	57721	Lelio R Paula	04/2011
7861	2^191730-761	57717	Yves Minet	01/2012
7862	(2^191733-3)/2251	57715	Lelio R Paula	02/2012
7863	2^191698-111	57707	Lelio R Paula	04/2011
7864	(13*10^57691+23)/9	57692	Robert Price	02/2015
7865	20^44340-5423	57688	Enzo Doria	03/2013
7866	(27*2^191629+1)/125	57686	Lelio R Paula	07/2012
7867	410^57684+37^57684	57685	Mike Oakes	11/2010
7868	2*3^120898+5	57684	Lelio R Paula	04/2014
7869	(6883*2^191610-1)/7347	57681	Lelio R Paula	04/2015
7870	6^74117-49	57675	Lelio R Paula	10/2012
7871	2^191586-113201	57674	Enzo Doria	07/2014
7872	2^191580+193	57672	Lelio R Paula	04/2011
7873	(103*29^39433+10401)/4	57669	Curtis Bright	05/2015
7874	2^191560+255255	57666	Lelio R Paula	05/2011
7875	2^191515-85	57652	Lelio R Paula	04/2011
7876	2^191502-1127	57648	Yves Minet	05/2013
7877	2*5^82473-3^82473	57647	Mike Oakes	08/2010
7878	2^191430+103	57627	Lelio R Paula	04/2011
7879	3*2^191408+5	57621	Lelio R Paula	03/2014
7880	2^191382-1858931	57612	Enzo Doria	04/2016
7881	6*7^68163+5	57606	Lelio R Paula	09/2014
7882	91^29403-2	57602	Lelio R Paula	08/2013
7883	11^55308-7950	57598	Enzo Doria	02/2013
7884	2^191329+65	57596	Lelio R Paula	04/2011
7885	11^55302-240	57592	Enzo Doria	07/2012
7886	2^191299-1031467	57587	Paul Bourdelais	11/2012
7887	2^191295-111991	57586	Enzo Doria	05/2014
7888	2^191279-1297	57581	Yves Minet	08/2012
7889	3*6^73961+5	57554	Lelio R Paula	09/2014
7890	(3^120623+5)/52144	57548	Lelio R Paula	04/2012
7891	42^35445-41	57537	Norbert Schneider	06/2014
7892	2^191069-723403	57518	Paul Bourdelais	11/2012
7893	4*10^57506-3	57507	Serge Batalov	11/2010
7894	10^57501+67359	57502	Patrick De Geest	06/2016
7895	10^57501-1000000001	57501	Robert Price	05/2016
7896	10^57501-249861	57501	Patrick De Geest	06/2016
7897	(9^60251+4^60251)/13	57493	Robert Price	02/2013
7898	20^44184-6003	57485	Enzo Doria	03/2013
7899	2^190948+12705	57482	Lelio R Paula	10/2012
7900	2^190945+29	57481	Henri Lifchitz	06/2005
7901	2^190922-401	57474	Yves Minet	01/2012
7902	15^48860+46	57464	Lelio R Paula	02/2013
7903	3^120434+20	57462	Lelio R Paula	10/2012
7904	7^67964-38	57437	Lelio R Paula	10/2012
7905	2^190799-113065	57437	Enzo Doria	07/2014
7906	9*5^82159+2	57428	Lelio R Paula	09/2014
7907	(F(22898)^13-F(22897)^13)/F(22896)	57422	Wayne Halsdorf	03/2012
7910	lucasU(432,25,21787)-5*lucasU(432,25,21786)	57416	Mike Oakes	05/2009
7908	(103*10^57414-1)/3	57416	Serge Batalov	12/2014
7909	(1654*30^38869-1)/29	57416	Karsten Bonath	05/2017
7911	2*10^57410+9^57410	57411	Mike Oakes	04/2011
7912	2^190704-1595	57408	Lelio R Paula	05/2011
7913	11^55121-1740	57403	Enzo Doria	11/2012
7914	2^190644-185	57390	Lelio R Paula	04/2011
7915	41182!3-3^41182	57389	Robert Price	08/2015
7916	2^190629-112255	57386	Enzo Doria	06/2014
7917	(2*10^57384-71)/3	57384	Robert Price	01/2017
7919	2*6^73735+5^73735	57378	Mike Oakes	11/2009
7918	2^190605+59	57378	Lelio R Paula	04/2011
7920	6^73727-7	57371	Lelio R Paula	10/2012
7921	2^190561-112225	57365	Enzo Doria	06/2014
7922	10^57358+170899	57359	Patrick De Geest	06/2016
7923	10^57358-8001	57358	Robert Price	03/2016
7924	18^45687-11	57350	Lelio R Paula	02/2013
7925	11^55069-210	57349	Enzo Doria	07/2012
7926	11^55068-12	57348	Lelio R Paula	02/2013
7927	19^44839+54	57339	Lelio R Paula	02/2013
7929	(7*2^190468-1)/8511	57334	Lelio R Paula	01/2014
7928	(23*10^57333-59)/9	57334	Robert Price	03/2017
7930	2^190455-1155*190455	57333	Henri Lifchitz	02/2005
7931	65^31620+28	57325	Lelio R Paula	01/2016
7932	2^190403+16095	57318	Lelio R Paula	05/2011
7933	(19*10^57316+119)/3	57317	Robert Price	02/2017
7935	(21*2^190393+1)/211	57314	Lelio R Paula	07/2012
7934	2^190392-112025	57314	Enzo Doria	05/2014
7936	(24737*2^190234+1)/9	57270	Lelio R Paula	05/2014
7937	(7*2^190230+1)/23	57265	Lelio R Paula	07/2012
7938	(10223*2^190197+1)/3211	57256	Lelio R Paula	05/2014
7939	18^45590-97	57228	Lelio R Paula	02/2013
7940	(3*2^190105-1)/19205	57224	Lelio R Paula	01/2014
7941	(16*10^57219-31)/3	57220	Robert Price	03/2016
7942	(2^190074+47)/51	57217	Lelio R Paula	02/2012
7943	3^119894-140	57204	Lelio R Paula	10/2012
7945	(37^36473-1)/36	57196	Robert Price	03/2012
7944	2^190000-2163	57196	Yves Minet	08/2013
7946	2^189987-2798107	57192	Enzo Doria	04/2016
7947	2^189935-112117	57177	Enzo Doria	05/2014
7948	2^189909-112231	57169	Enzo Doria	06/2014
7949	132049#+149053	57161	Makoto Morimoto	12/2015
7950	41032!3-27	57158	Robert Price	09/2014
7951	19^44694+22	57153	Lelio R Paula	02/2013
7952	12^52956-17	57150	Lelio R Paula	02/2013
7953	2^189823-967	57143	Yves Minet	01/2012
7954	(25*10^57138-61)/9	57139	Robert Price	02/2015
7955	5^81743-4^(81743+1)	57136	Robert Price	04/2016
7956	7^67593-54	57123	Lelio R Paula	10/2012
7957	7*3^119712+2	57118	Lelio R Paula	03/2014
7959	5^81700+16	57106	Lelio R Paula	10/2012
7958	2^189700+76561	57106	Enzo Doria	05/2016
7961	2^189671+131	57097	Lelio R Paula	04/2011
7960	4*6^73374+5	57097	Lelio R Paula	09/2014
7962	(67607*2^189651+1)/43727	57091	Lelio R Paula	05/2014
7963	(29*2^189619-1)/393	57080	Lelio R Paula	01/2014
7964	3^119587+80	57058	Lelio R Paula	10/2012
7965	2^189502-113453	57046	Enzo Doria	07/2014
7966	2^189455+153	57032	Lelio R Paula	04/2011
7967	24^41317-41317^24	57027	Norbert Schneider	07/2016
7968	2^189414-17	57020	Lelio R Paula	03/2011
7969	24^41311+23	57018	Norbert Schneider	12/2013
7970	(4*10^56989-31)/9	56989	Erik Branger	05/2011
7971	11^54712-1620	56977	Enzo Doria	11/2012
7972	2^189237-112231	56967	Enzo Doria	06/2014
7973	17^46285-48	56952	Lelio R Paula	02/2013
7974	2^189188+75241	56952	Enzo Doria	04/2016
7975	2^189181+94395	56950	Henri Lifchitz	01/2005
7976	7001^14808-108	56940	Enzo Doria	07/2012
7977	2^189147-112639	56939	Enzo Doria	06/2014
7978	2^189110-3	56928	M. Frind & P. Underwood	11/2002
7979	2^189069+12909	56916	Lelio R Paula	04/2011
7980	(13*10^56909+191)/3	56910	Robert Price	08/2017
7981	(35*10^56898-17)/9	56899	Serge Batalov	02/2009
7982	2^189011-5955	56898	Lelio R Paula	04/2011
7983	6^73119-5	56898	Lelio R Paula	10/2012
7984	13^51076-90	56896	Lelio R Paula	02/2013
7985	2^188997+56897	56894	Yves Minet	02/2010
7986	5^81388-13766	56888	Enzo Doria	02/2013
7987	20^43713-6403	56872	Enzo Doria	03/2013
7988	(71*10^56858-287)/9	56859	Robert Price	05/2017
7989	2^188857-254233	56852	Gary Barnes	09/2009
7990	15^48338-88	56850	Lelio R Paula	02/2013
7991	10^56849+136437	56850	Patrick De Geest	07/2017
7992	10^56849-701	56849	Robert Price	06/2017
7993	(2^188788+78557)/3	56831	Lelio R Paula	05/2012
7994	2^188771+16095	56826	Lelio R Paula	04/2011
7995	7*2^188742-9	56818	Lelio R Paula	03/2014
7996	12^52646-65	56815	Lelio R Paula	02/2013
7997	5003^15358-158	56813	Enzo Doria	07/2012
7998	2^188713+577294575	56809	Lelio R Paula	03/2013
7999	2^188693-112099	56803	Enzo Doria	05/2014
8000	(7^67211+4^67211)/11	56799	Robert Price	10/2012

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Probable Primes Top 10000

(180278 PRPs in the top)