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 ?
8751	(19*2^193114-1)/1186755	58129	Lelio R Paula	01/2014
8753	2^193091-1237	58127	Yves Minet	08/2012
8752	9*7^68780-2	58127	Lelio R Paula	09/2014
8754	2473^17130+17130^2473	58126	Norbert Schneider	10/2018
8755	2^193083-869688105	58124	Lelio R Paula	10/2012
8756	2^193058-45	58117	Lelio R Paula	04/2011
8757	(14016^14016+14017^14017)/(23710319913)	58115	David Broadhurst	09/2009
8758	11^55795-42	58105	Lelio R Paula	03/2013
8759	3^121779-16	58104	Lelio R Paula	10/2012
8760	(13*10^58103+191)/3	58104	Robert Price	08/2017
8761	2^192986+195	58095	Lelio R Paula	04/2011
8762	7^68740+2*3^68740	58093	Mike Oakes	07/2010
8763	(85*10^58091-1)/3	58093	Robert Price	07/2017
8764	(404*10^58087-53)/9	58089	Robert Price	11/2017
8765	12^53821+11	58083	Lelio R Paula	02/2013
8766	119^27979-118	58072	Norbert Schneider	10/2013
8767	(10223*2^192828+1)/243	58049	Lelio R Paula	05/2014
8768	2^192808-1127	58041	Yves Minet	05/2013
8769	(27*2^192803+1)/9827	58037	Lelio R Paula	07/2012
8771	(2^192781+lucasV(1,2,192781)+1)/4	58033	Mike Oakes	11/2016
8770	3*10^58032-23	58033	Robert Price	11/2017
8772	2^192678+72943	58002	Enzo Doria	04/2016
8773	(13*10^57997-37)/3	57998	Robert Price	08/2017
8774	2^192657-3189	57996	Yves Minet	10/2014
8775	6^74525-149	57992	Lelio R Paula	10/2012
8776	42^35723-41	57988	Norbert Schneider	06/2014
8777	(29*2^192625-1)/183	57986	Lelio R Paula	01/2014
8778	(3^121520-8)/3847	57977	Lelio R Paula	03/2012
8779	(2^192596-5)/139	57976	Lelio R Paula	02/2012
8780	10^57975+67833	57976	Patrick De Geest	09/2013
8781	10^57975-47693	57975	Patrick De Geest	09/2013
8782	(F(7707)^37-F(7706)^37)/F(7705)	57972	Wayne Halsdorf	03/2012
8783	(29*10^57967+673)/9	57968	Robert Price	10/2017
8784	(3^121492-5)/4	57966	Lelio R Paula	03/2012
8785	2^192549+35	57964	Lelio R Paula	04/2011
8786	28799!2+2	57962	Robert Price	10/2012
8787	(7*2^192534-1)/1347	57957	Lelio R Paula	01/2014
8788	7001^15069-100	57943	Enzo Doria	07/2012
8789	L(277273)/11090921	57940	Donovan Johnson	11/2005
8790	(2^192469-1017)/35	57938	Lelio R Paula	02/2012
8791	2^192457-1155*192457	57936	Henri Lifchitz	02/2005
8792	2^192443+1385	57932	Lelio R Paula	05/2011
8793	132^27317-131	57928	Norbert Schneider	03/2015
8794	41522!3-59049	57912	Robert Price	12/2015
8795	(3*2^192380-1)/169	57911	Lelio R Paula	01/2014
8796	2^192339-2515	57900	Yves Minet	07/2014
8797	2^192303+7695	57889	Lelio R Paula	10/2012
8798	2^192273-5955	57880	Lelio R Paula	05/2011
8799	2^192257+16095	57876	Lelio R Paula	05/2011
8800	109^28401-2	57865	Lelio R Paula	10/2017
8801	2^192218-111861	57864	Enzo Doria	05/2014
8802	2^192214-3941	57863	Yves Minet	04/2017
8803	(2^192212+3)/259	57860	Lelio R Paula	02/2012
8804	(3^121270+8)/155939753	57853	Lelio R Paula	03/2012
8805	80^30393-79	57841	Norbert Schneider	03/2015
8806	20^44455-3123	57838	Enzo Doria	03/2013
8808	2^192122-195	57835	Lelio R Paula	04/2011
8807	(29*10^57834+91)/3	57835	Robert Price	03/2016
8809	8*6^74306+5	57823	Lelio R Paula	09/2014
8810	(39^36341-1)/38	57820	Robert Price	04/2012
8811	2^192037-111805	57809	Enzo Doria	05/2014
8812	2^192023-192023^2	57805	Henri Lifchitz	05/2005
8813	21^43717+2	57804	Ray Chandler	08/2011
8814	8*5^82687+7	57797	Lelio R Paula	09/2014
8815	5^82680-24	57791	Lelio R Paula	10/2012
8816	(2^191915+47)/95	57771	Lelio R Paula	02/2012
8817	(74*10^57763+133)/9	57764	Robert Price	10/2017
8818	6^74227-95	57760	Lelio R Paula	10/2012
8819	2^191861+29835	57756	Lelio R Paula	10/2012
8821	1908^17605+17605^1908	57755	Serge Batalov	05/2014
8820	5*10^57754+59	57755	Robert Price	09/2016
8822	(5*2^191821-1)/8924067	57738	Lelio R Paula	01/2014
8823	38^63917+5^63917-34^63917+3*2^63917	57724	Mike Oakes	11/2010
8824	41399!3-6561	57723	Robert Price	11/2015
8825	(44*10^57721-233)/9	57722	Robert Price	10/2017
8826	2^191745+17	57721	Lelio R Paula	04/2011
8827	2^191730-761	57717	Yves Minet	01/2012
8828	(2^191733-3)/2251	57715	Lelio R Paula	02/2012
8829	2^191698-111	57707	Lelio R Paula	04/2011
8830	(13*10^57691+23)/9	57692	Robert Price	02/2015
8831	20^44340-5423	57688	Enzo Doria	03/2013
8832	(27*2^191629+1)/125	57686	Lelio R Paula	07/2012
8833	410^57684+37^57684	57685	Mike Oakes	11/2010
8834	2*3^120898+5	57684	Lelio R Paula	04/2014
8835	(6883*2^191610-1)/7347	57681	Lelio R Paula	04/2015
8836	6^74117-49	57675	Lelio R Paula	10/2012
8837	2^191586-113201	57674	Enzo Doria	07/2014
8838	2^191580+193	57672	Lelio R Paula	04/2011
8839	(103*29^39433+10401)/4	57669	Curtis Bright	05/2015
8840	2^191560+255255	57666	Lelio R Paula	05/2011
8841	2^191515-85	57652	Lelio R Paula	04/2011
8842	2^191502-1127	57648	Yves Minet	05/2013
8843	2*5^82473-3^82473	57647	Mike Oakes	08/2010
8844	(13*10^57634-61)/3	57635	Robert Price	08/2017
8845	85^29868-29868^85	57628	Norbert Schneider	11/2017
8846	2^191430+103	57627	Lelio R Paula	04/2011
8847	3*2^191408+5	57621	Lelio R Paula	03/2014
8848	2^191382-1858931	57612	Enzo Doria	04/2016
8849	6*7^68163+5	57606	Lelio R Paula	09/2014
8850	91^29403-2	57602	Lelio R Paula	08/2013
8851	11^55308-7950	57598	Enzo Doria	02/2013
8852	2^191329+65	57596	Lelio R Paula	04/2011
8853	11^55302-240	57592	Enzo Doria	07/2012
8854	2^191299-1031467	57587	Paul Bourdelais	11/2012
8855	2^191295-111991	57586	Enzo Doria	05/2014
8856	2^191279-1297	57581	Yves Minet	08/2012
8857	3*6^73961+5	57554	Lelio R Paula	09/2014
8858	(3^120623+5)/52144	57548	Lelio R Paula	04/2012
8859	(17*10^57543-29)/3	57544	Robert Price	09/2017
8860	42^35445-41	57537	Norbert Schneider	06/2014
8861	(71^31079-1)/70	57534	Paul Bourdelais	08/2017
8862	2^191069-723403	57518	Paul Bourdelais	11/2012
8863	4*10^57506-3	57507	Serge Batalov	11/2010
8864	10^57501+67359	57502	Patrick De Geest	06/2016
8865	10^57501-1000000001	57501	Robert Price	05/2016
8866	10^57501-249861	57501	Patrick De Geest	06/2016
8867	(9^60251+4^60251)/13	57493	Robert Price	02/2013
8868	20^44184-6003	57485	Enzo Doria	03/2013
8869	2^190948+12705	57482	Lelio R Paula	10/2012
8870	2^190945+29	57481	Henri Lifchitz	06/2005
8871	2^190922-401	57474	Yves Minet	01/2012
8872	15^48860+46	57464	Lelio R Paula	02/2013
8873	3^120434+20	57462	Lelio R Paula	10/2012
8874	7^67964-38	57437	Lelio R Paula	10/2012
8875	2^190799-113065	57437	Enzo Doria	07/2014
8876	9*5^82159+2	57428	Lelio R Paula	09/2014
8877	(F(22898)^13-F(22897)^13)/F(22896)	57422	Wayne Halsdorf	03/2012
8880	lucasU(432,25,21787)-5*lucasU(432,25,21786)	57416	Mike Oakes	05/2009
8879	(103*10^57414-1)/3	57416	Serge Batalov	12/2014
8878	(1654*30^38869-1)/29	57416	Karsten Bonath	05/2017
8881	2*10^57410+9^57410	57411	Mike Oakes	04/2011
8882	2^190704-1595	57408	Lelio R Paula	05/2011
8883	11^55121-1740	57403	Enzo Doria	11/2012
8884	2^190644-185	57390	Lelio R Paula	04/2011
8885	41182!3-3^41182	57389	Robert Price	08/2015
8886	2^190629-112255	57386	Enzo Doria	06/2014
8887	(2*10^57384-71)/3	57384	Robert Price	01/2017
8888	2*6^73735+5^73735	57378	Mike Oakes	11/2009
8889	2^190605+59	57378	Lelio R Paula	04/2011
8890	6^73727-7	57371	Lelio R Paula	10/2012
8891	2^190561-112225	57365	Enzo Doria	06/2014
8892	10^57358+170899	57359	Patrick De Geest	06/2016
8893	10^57358-8001	57358	Robert Price	03/2016
8894	18^45687-11	57350	Lelio R Paula	02/2013
8895	11^55069-210	57349	Enzo Doria	07/2012
8896	11^55068-12	57348	Lelio R Paula	02/2013
8897	19^44839+54	57339	Lelio R Paula	02/2013
8898	(7*2^190468-1)/8511	57334	Lelio R Paula	01/2014
8899	(23*10^57333-59)/9	57334	Robert Price	03/2017
8900	2^190455-1155*190455	57333	Henri Lifchitz	02/2005
8901	65^31620+28	57325	Lelio R Paula	01/2016
8902	2^190403+16095	57318	Lelio R Paula	05/2011
8903	(19*10^57316+119)/3	57317	Robert Price	02/2017
8904	(21*2^190393+1)/211	57314	Lelio R Paula	07/2012
8906	2^190392-112025	57314	Enzo Doria	05/2014
8905	13173^13912-13912^13173	57314	Norbert Schneider	08/2018
8907	(24737*2^190234+1)/9	57270	Lelio R Paula	05/2014
8908	(7*2^190230+1)/23	57265	Lelio R Paula	07/2012
8909	(10223*2^190197+1)/3211	57256	Lelio R Paula	05/2014
8910	18^45590-97	57228	Lelio R Paula	02/2013
8911	(3*2^190105-1)/19205	57224	Lelio R Paula	01/2014
8912	(16*10^57219-31)/3	57220	Robert Price	03/2016
8913	(2^190074+47)/51	57217	Lelio R Paula	02/2012
8914	3^119894-140	57204	Lelio R Paula	10/2012
8916	(37^36473-1)/36	57196	Robert Price	03/2012
8915	2^190000-2163	57196	Yves Minet	08/2013
8917	2^189987-2798107	57192	Enzo Doria	04/2016
8918	2^189935-112117	57177	Enzo Doria	05/2014
8919	2^189909-112231	57169	Enzo Doria	06/2014
8920	132049#+149053	57161	Makoto Morimoto	12/2015
8921	41032!3-27	57158	Robert Price	09/2014
8922	19^44694+22	57153	Lelio R Paula	02/2013
8923	12^52956-17	57150	Lelio R Paula	02/2013
8924	2^189823-967	57143	Yves Minet	01/2012
8925	(25*10^57138-61)/9	57139	Robert Price	02/2015
8926	5^81743-4^(81743+1)	57136	Robert Price	04/2016
8927	7^67593-54	57123	Lelio R Paula	10/2012
8928	7*3^119712+2	57118	Lelio R Paula	03/2014
8930	5^81700+16	57106	Lelio R Paula	10/2012
8929	2^189700+76561	57106	Enzo Doria	05/2016
8932	2^189671+131	57097	Lelio R Paula	04/2011
8931	4*6^73374+5	57097	Lelio R Paula	09/2014
8933	(67607*2^189651+1)/43727	57091	Lelio R Paula	05/2014
8934	(29*2^189619-1)/393	57080	Lelio R Paula	01/2014
8935	3^119587+80	57058	Lelio R Paula	10/2012
8936	2^189502-113453	57046	Enzo Doria	07/2014
8937	2^189455+153	57032	Lelio R Paula	04/2011
8938	24^41317-41317^24	57027	Norbert Schneider	07/2016
8939	2^189414-17	57020	Lelio R Paula	03/2011
8940	24^41311+23	57018	Norbert Schneider	12/2013
8941	norm(Mod(x,x^4+x^3-x+1)^207341-1)/2	56998	Paul Vanderveen	05/2018
8942	(4*10^56989-31)/9	56989	Erik Branger	05/2011
8943	11^54712-1620	56977	Enzo Doria	11/2012
8944	2^189237-112231	56967	Enzo Doria	06/2014
8945	17^46285-48	56952	Lelio R Paula	02/2013
8946	2^189188+75241	56952	Enzo Doria	04/2016
8947	2^189181+94395	56950	Henri Lifchitz	01/2005
8948	7001^14808-108	56940	Enzo Doria	07/2012
8949	2^189147-112639	56939	Enzo Doria	06/2014
8950	(19*10^56933-43)/3	56934	Robert Price	10/2017
8951	2^189110-3	56928	M. Frind & P. Underwood	11/2002
8952	2^189069+12909	56916	Lelio R Paula	04/2011
8953	(13*10^56909+191)/3	56910	Robert Price	08/2017
8954	(35*10^56898-17)/9	56899	Serge Batalov	02/2009
8955	2^189011-5955	56898	Lelio R Paula	04/2011
8956	6^73119-5	56898	Lelio R Paula	10/2012
8957	13^51076-90	56896	Lelio R Paula	02/2013
8958	2^188997+56897	56894	Yves Minet	02/2010
8959	5^81388-13766	56888	Enzo Doria	02/2013
8960	(104^28201+1)/105	56881	Richard Fischer	04/2018
8961	(156^25933+1)/157	56873	Eric Chen	12/2017
8962	20^43713-6403	56872	Enzo Doria	03/2013
8963	(71*10^56858-287)/9	56859	Robert Price	05/2017
8964	2^188857-254233	56852	Gary Barnes	09/2009
8965	15^48338-88	56850	Lelio R Paula	02/2013
8966	10^56849+136437	56850	Patrick De Geest	07/2017
8967	10^56849-701	56849	Robert Price	06/2017
8968	(2^188788+78557)/3	56831	Lelio R Paula	05/2012
8969	2^188771+16095	56826	Lelio R Paula	04/2011
8970	7*2^188742-9	56818	Lelio R Paula	03/2014
8971	12^52646-65	56815	Lelio R Paula	02/2013
8972	5003^15358-158	56813	Enzo Doria	07/2012
8973	2^188713+577294575	56809	Lelio R Paula	03/2013
8974	2^188693-112099	56803	Enzo Doria	05/2014
8975	(7^67211+4^67211)/11	56799	Robert Price	10/2012
8976	2^188678-94395	56798	Lelio R Paula	09/2011
8977	20^43651-8503	56792	Enzo Doria	03/2013
8979	2^188657-2371	56792	Yves Minet	10/2013
8978	152^26029-151^26029	56792	Eric Chen	04/2018
8980	(14^49549+5^49549)/19	56789	Robert Price	05/2013
8981	(45^34351-1)/44	56788	Robert Price	05/2014
8982	7*10^56785-23	56786	Robert Price	04/2016
8983	(10^56781-31)/3	56781	Serge Batalov	12/2014
8984	7*10^56779+3	56780	Erik Branger	11/2009
8985	12858^13817-13817^12858	56777	Norbert Schneider	11/2018
8986	10^56765+259179	56766	Patrick De Geest	09/2013
8987	10^56765-249497	56765	Patrick De Geest	09/2013
8988	t(188706)	56764	Robert Price	04/2015
8989	2^188551-904327	56760	Paul Bourdelais	11/2012
8991	(64*10^56756+17)/9	56757	Robert Price	09/2015
8990	131101#+146291	56757	Makoto Morimoto	02/2016
8992	2^188539-112519	56756	Enzo Doria	06/2014
8993	6^72927+101	56749	Lelio R Paula	10/2012
8994	20^43617-1603	56748	Enzo Doria	03/2013
8995	(3^118892-8)/91358929	56718	Lelio R Paula	03/2012
8996	13339^13748-13748^13339	56713	Norbert Schneider	09/2018
8997	(509203*2^188338-1)/3	56701	Lelio R Paula	03/2015
8998	20^43567-5623	56682	Enzo Doria	03/2013
8999	2^188234-113183	56665	Enzo Doria	07/2014
9000	(139^26437+1)/140	56653	Richard Fischer	03/2018

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PRP Records

Probable Primes Top 10000

(247113 PRPs in the top)