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 ?
8751	Phi(28754,28754)	58231	Henri Lifchitz	08/2013
8752	2^193430-111881	58229	Enzo Doria	05/2014
8753	10^58225+124579	58226	Patrick De Geest	12/2012
8754	10^58225-93	58225	Robert Price	05/2011
8755	2^193375-295	58212	Yves Minet	05/2013
8756	14018^14037-14037^14018	58208	Norbert Schneider	10/2018
8757	2^193345+77267	58203	Enzo Doria	05/2016
8758	21^44017-20^44017	58201	Robert Price	05/2012
8759	(17*2^193329-1)/9	58199	Lelio R Paula	01/2014
8760	17^47291+20	58190	Lelio R Paula	03/2013
8761	p(12528)#/2-128	58170	Robert Price	05/2017
8762	2^193214-135	58164	Lelio R Paula	04/2011
8763	19^45483-80	58162	Lelio R Paula	03/2013
8764	(4*10^58155+83)/3	58156	Robert Price	01/2017
8766	14^50739-13	58154	Lelio R Paula	03/2013
8765	(1017*2^193184-1)/4823	58154	Lelio R Paula	04/2015
8767	(2*10^58151+457)/9	58151	Robert Price	01/2017
8768	(9179*2^193183-1)/3999267879	58149	Lelio R Paula	04/2015
8769	(19*2^193114-1)/1186755	58129	Lelio R Paula	01/2014
8771	2^193091-1237	58127	Yves Minet	08/2012
8770	9*7^68780-2	58127	Lelio R Paula	09/2014
8772	2473^17130+17130^2473	58126	Norbert Schneider	10/2018
8773	2^193083-869688105	58124	Lelio R Paula	10/2012
8774	2^193058-45	58117	Lelio R Paula	04/2011
8775	(14016^14016+14017^14017)/(23710319913)	58115	David Broadhurst	09/2009
8776	11^55795-42	58105	Lelio R Paula	03/2013
8777	3^121779-16	58104	Lelio R Paula	10/2012
8778	(13*10^58103+191)/3	58104	Robert Price	08/2017
8779	2^192986+195	58095	Lelio R Paula	04/2011
8780	7^68740+2*3^68740	58093	Mike Oakes	07/2010
8781	(85*10^58091-1)/3	58093	Robert Price	07/2017
8782	(404*10^58087-53)/9	58089	Robert Price	11/2017
8783	12^53821+11	58083	Lelio R Paula	02/2013
8784	119^27979-118	58072	Norbert Schneider	10/2013
8785	(10223*2^192828+1)/243	58049	Lelio R Paula	05/2014
8786	2^192808-1127	58041	Yves Minet	05/2013
8787	(27*2^192803+1)/9827	58037	Lelio R Paula	07/2012
8789	(2^192781+lucasV(1,2,192781)+1)/4	58033	Mike Oakes	11/2016
8788	3*10^58032-23	58033	Robert Price	11/2017
8790	2^192678+72943	58002	Enzo Doria	04/2016
8791	(13*10^57997-37)/3	57998	Robert Price	08/2017
8792	2^192657-3189	57996	Yves Minet	10/2014
8793	6^74525-149	57992	Lelio R Paula	10/2012
8794	42^35723-41	57988	Norbert Schneider	06/2014
8795	(29*2^192625-1)/183	57986	Lelio R Paula	01/2014
8796	(3^121520-8)/3847	57977	Lelio R Paula	03/2012
8797	(2^192596-5)/139	57976	Lelio R Paula	02/2012
8798	10^57975+67833	57976	Patrick De Geest	09/2013
8799	10^57975-47693	57975	Patrick De Geest	09/2013
8800	(F(7707)^37-F(7706)^37)/F(7705)	57972	Wayne Halsdorf	03/2012
8801	(29*10^57967+673)/9	57968	Robert Price	10/2017
8802	(3^121492-5)/4	57966	Lelio R Paula	03/2012
8803	2^192549+35	57964	Lelio R Paula	04/2011
8804	28799!2+2	57962	Robert Price	10/2012
8805	(7*2^192534-1)/1347	57957	Lelio R Paula	01/2014
8806	7001^15069-100	57943	Enzo Doria	07/2012
8807	L(277273)/11090921	57940	Donovan Johnson	11/2005
8808	(2^192469-1017)/35	57938	Lelio R Paula	02/2012
8809	2^192457-1155*192457	57936	Henri Lifchitz	02/2005
8810	2^192443+1385	57932	Lelio R Paula	05/2011
8811	132^27317-131	57928	Norbert Schneider	03/2015
8812	41522!3-59049	57912	Robert Price	12/2015
8813	(3*2^192380-1)/169	57911	Lelio R Paula	01/2014
8814	2^192339-2515	57900	Yves Minet	07/2014
8815	2^192303+7695	57889	Lelio R Paula	10/2012
8816	2^192273-5955	57880	Lelio R Paula	05/2011
8817	2^192257+16095	57876	Lelio R Paula	05/2011
8818	109^28401-2	57865	Lelio R Paula	10/2017
8819	2^192218-111861	57864	Enzo Doria	05/2014
8820	2^192214-3941	57863	Yves Minet	04/2017
8821	(2^192212+3)/259	57860	Lelio R Paula	02/2012
8822	(3^121270+8)/155939753	57853	Lelio R Paula	03/2012
8823	80^30393-79	57841	Norbert Schneider	03/2015
8824	20^44455-3123	57838	Enzo Doria	03/2013
8826	2^192122-195	57835	Lelio R Paula	04/2011
8825	(29*10^57834+91)/3	57835	Robert Price	03/2016
8827	8*6^74306+5	57823	Lelio R Paula	09/2014
8828	(39^36341-1)/38	57820	Robert Price	04/2012
8829	2^192037-111805	57809	Enzo Doria	05/2014
8830	2^192023-192023^2	57805	Henri Lifchitz	05/2005
8831	21^43717+2	57804	Ray Chandler	08/2011
8832	8*5^82687+7	57797	Lelio R Paula	09/2014
8833	5^82680-24	57791	Lelio R Paula	10/2012
8834	(2^191915+47)/95	57771	Lelio R Paula	02/2012
8835	(74*10^57763+133)/9	57764	Robert Price	10/2017
8836	6^74227-95	57760	Lelio R Paula	10/2012
8837	2^191861+29835	57756	Lelio R Paula	10/2012
8838	1908^17605+17605^1908	57755	Serge Batalov	05/2014
8839	5*10^57754+59	57755	Robert Price	09/2016
8840	(5*2^191821-1)/8924067	57738	Lelio R Paula	01/2014
8841	38^63917+5^63917-34^63917+3*2^63917	57724	Mike Oakes	11/2010
8842	41399!3-6561	57723	Robert Price	11/2015
8843	(44*10^57721-233)/9	57722	Robert Price	10/2017
8844	2^191745+17	57721	Lelio R Paula	04/2011
8845	2^191730-761	57717	Yves Minet	01/2012
8846	(2^191733-3)/2251	57715	Lelio R Paula	02/2012
8847	2^191698-111	57707	Lelio R Paula	04/2011
8848	(13*10^57691+23)/9	57692	Robert Price	02/2015
8849	20^44340-5423	57688	Enzo Doria	03/2013
8850	(27*2^191629+1)/125	57686	Lelio R Paula	07/2012
8851	410^57684+37^57684	57685	Mike Oakes	11/2010
8852	2*3^120898+5	57684	Lelio R Paula	04/2014
8853	(6883*2^191610-1)/7347	57681	Lelio R Paula	04/2015
8854	6^74117-49	57675	Lelio R Paula	10/2012
8855	2^191586-113201	57674	Enzo Doria	07/2014
8856	2^191580+193	57672	Lelio R Paula	04/2011
8857	(103*29^39433+10401)/4	57669	Curtis Bright	05/2015
8858	2^191560+255255	57666	Lelio R Paula	05/2011
8859	2^191515-85	57652	Lelio R Paula	04/2011
8860	2^191502-1127	57648	Yves Minet	05/2013
8861	2*5^82473-3^82473	57647	Mike Oakes	08/2010
8862	(13*10^57634-61)/3	57635	Robert Price	08/2017
8863	85^29868-29868^85	57628	Norbert Schneider	11/2017
8864	2^191430+103	57627	Lelio R Paula	04/2011
8865	3*2^191408+5	57621	Lelio R Paula	03/2014
8866	2^191382-1858931	57612	Enzo Doria	04/2016
8867	6*7^68163+5	57606	Lelio R Paula	09/2014
8868	91^29403-2	57602	Lelio R Paula	08/2013
8869	11^55308-7950	57598	Enzo Doria	02/2013
8870	2^191329+65	57596	Lelio R Paula	04/2011
8871	11^55302-240	57592	Enzo Doria	07/2012
8872	2^191299-1031467	57587	Paul Bourdelais	11/2012
8873	2^191295-111991	57586	Enzo Doria	05/2014
8874	2^191279-1297	57581	Yves Minet	08/2012
8875	3*6^73961+5	57554	Lelio R Paula	09/2014
8876	(3^120623+5)/52144	57548	Lelio R Paula	04/2012
8877	(17*10^57543-29)/3	57544	Robert Price	09/2017
8878	42^35445-41	57537	Norbert Schneider	06/2014
8879	(71^31079-1)/70	57534	Paul Bourdelais	08/2017
8880	2^191069-723403	57518	Paul Bourdelais	11/2012
8881	4*10^57506-3	57507	Serge Batalov	11/2010
8882	10^57501+67359	57502	Patrick De Geest	06/2016
8883	10^57501-1000000001	57501	Robert Price	05/2016
8884	10^57501-249861	57501	Patrick De Geest	06/2016
8885	(9^60251+4^60251)/13	57493	Robert Price	02/2013
8886	20^44184-6003	57485	Enzo Doria	03/2013
8887	2^190948+12705	57482	Lelio R Paula	10/2012
8888	2^190945+29	57481	Henri Lifchitz	06/2005
8889	2^190922-401	57474	Yves Minet	01/2012
8890	15^48860+46	57464	Lelio R Paula	02/2013
8891	3^120434+20	57462	Lelio R Paula	10/2012
8892	7^67964-38	57437	Lelio R Paula	10/2012
8893	2^190799-113065	57437	Enzo Doria	07/2014
8894	9*5^82159+2	57428	Lelio R Paula	09/2014
8895	(F(22898)^13-F(22897)^13)/F(22896)	57422	Wayne Halsdorf	03/2012
8898	lucasU(432,25,21787)-5*lucasU(432,25,21786)	57416	Mike Oakes	05/2009
8896	(103*10^57414-1)/3	57416	Serge Batalov	12/2014
8897	(1654*30^38869-1)/29	57416	Karsten Bonath	05/2017
8899	2*10^57410+9^57410	57411	Mike Oakes	04/2011
8900	2^190704-1595	57408	Lelio R Paula	05/2011
8901	11^55121-1740	57403	Enzo Doria	11/2012
8902	2^190644-185	57390	Lelio R Paula	04/2011
8903	41182!3-3^41182	57389	Robert Price	08/2015
8904	2^190629-112255	57386	Enzo Doria	06/2014
8905	(2*10^57384-71)/3	57384	Robert Price	01/2017
8907	2*6^73735+5^73735	57378	Mike Oakes	11/2009
8906	2^190605+59	57378	Lelio R Paula	04/2011
8908	6^73727-7	57371	Lelio R Paula	10/2012
8909	2^190561-112225	57365	Enzo Doria	06/2014
8910	10^57358+170899	57359	Patrick De Geest	06/2016
8911	10^57358-8001	57358	Robert Price	03/2016
8912	18^45687-11	57350	Lelio R Paula	02/2013
8913	11^55069-210	57349	Enzo Doria	07/2012
8914	11^55068-12	57348	Lelio R Paula	02/2013
8915	19^44839+54	57339	Lelio R Paula	02/2013
8917	(7*2^190468-1)/8511	57334	Lelio R Paula	01/2014
8916	(23*10^57333-59)/9	57334	Robert Price	03/2017
8918	2^190455-1155*190455	57333	Henri Lifchitz	02/2005
8919	65^31620+28	57325	Lelio R Paula	01/2016
8920	2^190403+16095	57318	Lelio R Paula	05/2011
8921	(19*10^57316+119)/3	57317	Robert Price	02/2017
8922	(21*2^190393+1)/211	57314	Lelio R Paula	07/2012
8923	2^190392-112025	57314	Enzo Doria	05/2014
8924	13173^13912-13912^13173	57314	Norbert Schneider	08/2018
8925	(24737*2^190234+1)/9	57270	Lelio R Paula	05/2014
8926	(7*2^190230+1)/23	57265	Lelio R Paula	07/2012
8927	(10223*2^190197+1)/3211	57256	Lelio R Paula	05/2014
8928	18^45590-97	57228	Lelio R Paula	02/2013
8929	(3*2^190105-1)/19205	57224	Lelio R Paula	01/2014
8930	(16*10^57219-31)/3	57220	Robert Price	03/2016
8931	(2^190074+47)/51	57217	Lelio R Paula	02/2012
8932	3^119894-140	57204	Lelio R Paula	10/2012
8934	(37^36473-1)/36	57196	Robert Price	03/2012
8933	2^190000-2163	57196	Yves Minet	08/2013
8935	2^189987-2798107	57192	Enzo Doria	04/2016
8936	2^189935-112117	57177	Enzo Doria	05/2014
8937	2^189909-112231	57169	Enzo Doria	06/2014
8938	132049#+149053	57161	Makoto Morimoto	12/2015
8939	41032!3-27	57158	Robert Price	09/2014
8940	19^44694+22	57153	Lelio R Paula	02/2013
8941	12^52956-17	57150	Lelio R Paula	02/2013
8942	2^189823-967	57143	Yves Minet	01/2012
8943	(25*10^57138-61)/9	57139	Robert Price	02/2015
8944	5^81743-4^(81743+1)	57136	Robert Price	04/2016
8945	7^67593-54	57123	Lelio R Paula	10/2012
8946	7*3^119712+2	57118	Lelio R Paula	03/2014
8947	5^81700+16	57106	Lelio R Paula	10/2012
8948	2^189700+76561	57106	Enzo Doria	05/2016
8949	2^189671+131	57097	Lelio R Paula	04/2011
8950	4*6^73374+5	57097	Lelio R Paula	09/2014
8951	(67607*2^189651+1)/43727	57091	Lelio R Paula	05/2014
8952	(29*2^189619-1)/393	57080	Lelio R Paula	01/2014
8953	3^119587+80	57058	Lelio R Paula	10/2012
8954	2^189502-113453	57046	Enzo Doria	07/2014
8955	2^189455+153	57032	Lelio R Paula	04/2011
8956	24^41317-41317^24	57027	Norbert Schneider	07/2016
8957	2^189414-17	57020	Lelio R Paula	03/2011
8958	24^41311+23	57018	Norbert Schneider	12/2013
8959	norm(Mod(x,x^4+x^3-x+1)^207341-1)/2	56998	Paul Vanderveen	05/2018
8960	(4*10^56989-31)/9	56989	Erik Branger	05/2011
8961	11^54712-1620	56977	Enzo Doria	11/2012
8962	2^189237-112231	56967	Enzo Doria	06/2014
8963	17^46285-48	56952	Lelio R Paula	02/2013
8964	2^189188+75241	56952	Enzo Doria	04/2016
8965	2^189181+94395	56950	Henri Lifchitz	01/2005
8966	7001^14808-108	56940	Enzo Doria	07/2012
8967	2^189147-112639	56939	Enzo Doria	06/2014
8968	(19*10^56933-43)/3	56934	Robert Price	10/2017
8969	2^189110-3	56928	M. Frind & P. Underwood	11/2002
8970	2^189069+12909	56916	Lelio R Paula	04/2011
8971	(13*10^56909+191)/3	56910	Robert Price	08/2017
8972	(35*10^56898-17)/9	56899	Serge Batalov	02/2009
8973	2^189011-5955	56898	Lelio R Paula	04/2011
8974	6^73119-5	56898	Lelio R Paula	10/2012
8975	13^51076-90	56896	Lelio R Paula	02/2013
8976	2^188997+56897	56894	Yves Minet	02/2010
8977	5^81388-13766	56888	Enzo Doria	02/2013
8978	(104^28201+1)/105	56881	Richard Fischer	04/2018
8979	(156^25933+1)/157	56873	Eric Chen	12/2017
8980	20^43713-6403	56872	Enzo Doria	03/2013
8981	(71*10^56858-287)/9	56859	Robert Price	05/2017
8982	2^188857-254233	56852	Gary Barnes	09/2009
8984	15^48338-88	56850	Lelio R Paula	02/2013
8983	10^56849+136437	56850	Patrick De Geest	07/2017
8985	10^56849-701	56849	Robert Price	06/2017
8986	(2^188788+78557)/3	56831	Lelio R Paula	05/2012
8987	2^188771+16095	56826	Lelio R Paula	04/2011
8988	7*2^188742-9	56818	Lelio R Paula	03/2014
8989	12^52646-65	56815	Lelio R Paula	02/2013
8990	5003^15358-158	56813	Enzo Doria	07/2012
8991	2^188713+577294575	56809	Lelio R Paula	03/2013
8992	2^188693-112099	56803	Enzo Doria	05/2014
8993	(7^67211+4^67211)/11	56799	Robert Price	10/2012
8994	2^188678-94395	56798	Lelio R Paula	09/2011
8995	20^43651-8503	56792	Enzo Doria	03/2013
8997	2^188657-2371	56792	Yves Minet	10/2013
8996	152^26029-151^26029	56792	Eric Chen	04/2018
8998	(14^49549+5^49549)/19	56789	Robert Price	05/2013
8999	(45^34351-1)/44	56788	Robert Price	05/2014
9000	7*10^56785-23	56786	Robert Price	04/2016

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Probable Primes Top 10000

(252402 PRPs in the top)