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	79185!6-16	58921	Robert Price	08/2018
8752	14^51407+47	58920	Lelio R Paula	03/2013
8753	2^195691-99	58909	Lelio R Paula	04/2011
8754	2^195667-1859827	58902	Enzo Doria	04/2016
8755	2^195642+75499	58895	Enzo Doria	04/2016
8756	(299*10^58893+1)/3	58895	Robert Price	11/2017
8757	8*6^75678+5	58890	Lelio R Paula	09/2014
8759	2^195618+73189	58887	Enzo Doria	04/2016
8758	(3928^20480+1)/(3928^4096+1)	58887	Serge Batalov	01/2017
8760	t(197953)	58881	Robert Price	12/2014
8761	2^195581-16105	58876	Enzo Doria	04/2013
8762	(8*10^58872+67)/3	58873	Robert Price	01/2017
8763	7*2^195542-5	58865	Lelio R Paula	03/2014
8764	2*10^58861+9^58861	58862	Mike Oakes	04/2011
8765	11^56513-1620	58853	Enzo Doria	11/2012
8766	2^195496+165	58851	Lelio R Paula	04/2011
8767	5^84187+66	58845	Lelio R Paula	10/2012
8768	(28*10^58843-43)/3	58844	Robert Price	04/2016
8769	2^195462-17565	58840	Enzo Doria	05/2013
8770	2^195449-4171	58837	Yves Minet	02/2018
8771	2^195435+59273	58832	Yves Minet	01/2011
8772	2^195424-18605	58829	Enzo Doria	05/2013
8773	2^195385-111	58817	Lelio R Paula	04/2011
8774	7*10^58815-83	58816	Robert Price	09/2017
8775	2^195357-4303	58809	Yves Minet	08/2018
8776	(47*2^195254+1)/268821	58774	Lelio R Paula	03/2015
8777	2^195207-18109	58764	Enzo Doria	05/2013
8778	2^195199-1567	58761	Yves Minet	08/2012
8779	2^195190+73759	58759	Enzo Doria	04/2016
8780	9*7^69525-4	58757	Lelio R Paula	09/2014
8781	2^195170-18045	58753	Enzo Doria	05/2013
8782	2^195166-165	58751	Lelio R Paula	04/2011
8783	(754*10^58748-7)/9	58750	Robert Price	11/2017
8784	(22699*2^195140+1)/175	58746	Lelio R Paula	05/2014
8785	7*3^123109-2	58739	Lelio R Paula	04/2014
8786	(8*10^58738-611)/9	58738	Robert Price	11/2017
8787	18^46790+77	58735	Lelio R Paula	03/2013
8789	2^195095-337297	58730	Gary Barnes	09/2009
8788	(14*10^58729+31)/9	58730	Robert Price	02/2015
8790	99^29424+98	58720	Norbert Schneider	07/2013
8791	(15185*2^195039-1)/219	58715	Lelio R Paula	04/2015
8792	2^195001-69	58702	Lelio R Paula	04/2011
8793	2^194978-487811	58695	Gary Barnes	09/2009
8794	163^26530+26530^163	58690	Serge Batalov	05/2014
8795	2^194940-194940+1	58683	Robert Price	10/2014
8796	(76*10^58669+41)/9	58670	Robert Price	10/2015
8797	14^51186+87	58666	Lelio R Paula	03/2013
8798	2^194878-97305	58665	Lelio R Paula	09/2011
8799	5^83927-18136	58663	Enzo Doria	05/2014
8800	(24737*2^194865+1)/1085	58662	Lelio R Paula	06/2014
8801	7^69411+40	58660	Lelio R Paula	10/2012
8802	6^75382-79	58659	Lelio R Paula	10/2012
8803	2^194854+27	58657	Lelio R Paula	04/2011
8804	2^194801+29835	58641	Lelio R Paula	10/2012
8805	2^194752+195	58627	Lelio R Paula	04/2011
8806	7^69371-6^69371	58626	Predrag Minovic	08/2004
8807	2^194747-112519	58625	Enzo Doria	06/2014
8808	(15*2^194737+1)/59	58622	Lelio R Paula	07/2012
8809	(23*2^194700+1)/3	58612	Lelio R Paula	02/2012
8810	10^58608+55273	58609	Patrick De Geest	07/2017
8811	10^58608-800001	58608	Robert Price	06/2017
8812	10^58608-60119	58608	Patrick De Geest	07/2017
8813	5^83836+76	58599	Lelio R Paula	10/2012
8814	18^46664+31	58577	Lelio R Paula	03/2013
8815	(34*10^58577-7)/9/19/463	58574	Makoto Morimoto	04/2016
8816	2^194574+165	58573	Lelio R Paula	04/2011
8819	2^194569-12211	58572	Enzo Doria	06/2014
8817	10^58571+5^58571+2^58571	58572	Robert Price	12/2016
8818	10^58571+202837	58572	Patrick De Geest	02/2017
8820	(10^58571+41)/3	58571	Robert Price	01/2017
8821	10^58571-343629	58571	Patrick De Geest	02/2017
8822	(43*10^58563-403)/9	58564	Robert Price	04/2017
8823	11^56235-7950	58563	Enzo Doria	02/2013
8824	145^27095-144	58563	Norbert Schneider	11/2018
8825	(14*10^58550+211)/9	58551	Robert Price	11/2017
8826	2^194479-113239	58545	Enzo Doria	07/2014
8827	2^194455-112249	58537	Enzo Doria	06/2014
8828	2^194405-111919	58522	Enzo Doria	05/2014
8829	(4*10^58521-19)/3	58522	Robert Price	06/2017
8831	(7^69247-4^69247)/3	58521	Robert Price	06/2012
8830	5*7^69246+8	58521	Lelio R Paula	09/2014
8832	2^194358-1167	58508	Lelio R Paula	05/2011
8833	(2^194366+7)/1373	58507	Lelio R Paula	02/2012
8834	(493*10^58486-7)/9	58488	Robert Price	07/2016
8835	3^122579-340	58486	Lelio R Paula	10/2012
8836	(11*10^58458-149)/3	58459	Robert Price	01/2017
8837	(47*10^58456+133)/9	58457	Robert Price	04/2017
8838	2^194186+85	58456	Lelio R Paula	04/2011
8839	3^122506-2^(122506-1)	58451	Robert Price	01/2016
8840	(74^31267-1)/73	58444	Paul Bourdelais	08/2017
8841	177^25998-2	58443	Lelio R Paula	10/2017
8842	15^49690-26	58440	Lelio R Paula	03/2013
8843	10^58437+110721	58438	Patrick De Geest	12/2012
8844	10^58437-11	58437	Robert Price	05/2011
8845	2^194095+69	58429	Lelio R Paula	04/2011
8846	(29*10^58417-77)/3	58418	Robert Price	01/2017
8847	2^194034+177	58411	Lelio R Paula	04/2011
8848	789^20158+20158^789	58400	Norbert Schneider	06/2016
8849	14^50949+75	58395	Lelio R Paula	03/2013
8850	2^193974-114761	58392	Enzo Doria	05/2015
8851	2^193965+5	58390	Henri Lifchitz	12/2002
8852	(5*10^58384-29)/3	58385	Robert Price	02/2017
8853	3^122360+80	58381	Lelio R Paula	10/2012
8854	10103^14577-114	58373	Enzo Doria	07/2012
8855	(22699*2^193883+1)/21	58368	Lelio R Paula	06/2014
8856	(31*2^193886+1)/140765	58362	Lelio R Paula	07/2012
8857	11^56041-1560	58361	Enzo Doria	11/2012
8858	(2^193881+9)/17699	58360	Lelio R Paula	02/2012
8859	3^122313+58	58359	Lelio R Paula	10/2012
8860	6^74996-119	58359	Lelio R Paula	10/2012
8861	(11*2^193859+1)/13	58358	Lelio R Paula	07/2012
8862	2^193861-112255	58358	Enzo Doria	06/2014
8863	(22699*2^193854+1)/4927	58357	Lelio R Paula	06/2014
8864	18^46487+37	58354	Lelio R Paula	03/2013
8865	17^47419+54	58347	Lelio R Paula	03/2013
8866	(31*2^193791+1)/3	58338	Lelio R Paula	02/2012
8867	(27*2^193805-1)/982249	58337	Lelio R Paula	01/2014
8868	144^27025-143	58330	Norbert Schneider	11/2018
8869	3^122219-2^122219	58314	Mike Oakes	09/2003
8870	(199*10^58306+11)/3	58308	Robert Price	05/2017
8871	2^193674-18825	58302	Lelio R Paula	05/2011
8872	5*10^58275+3	58276	Dmitry Domanov	11/2010
8873	2^193578-112913	58273	Enzo Doria	06/2014
8874	2^193541+1299	58262	Lelio R Paula	05/2011
8875	10^58250+93	58251	Robert Price	01/2011
8876	10^58250-175607	58250	Patrick De Geest	12/2012
8877	(107^28703+1)/108	58248	Richard Fischer	05/2018
8878	2^193492+8415	58247	Lelio R Paula	10/2012
8879	2^193444+157	58233	Lelio R Paula	04/2011
8880	Phi(28754,28754)	58231	Henri Lifchitz	08/2013
8881	2^193430-111881	58229	Enzo Doria	05/2014
8882	10^58225+124579	58226	Patrick De Geest	12/2012
8883	10^58225-93	58225	Robert Price	05/2011
8884	2^193375-295	58212	Yves Minet	05/2013
8885	14018^14037-14037^14018	58208	Norbert Schneider	10/2018
8886	2^193345+77267	58203	Enzo Doria	05/2016
8887	21^44017-20^44017	58201	Robert Price	05/2012
8888	(17*2^193329-1)/9	58199	Lelio R Paula	01/2014
8889	17^47291+20	58190	Lelio R Paula	03/2013
8890	p(12528)#/2-128	58170	Robert Price	05/2017
8891	2^193214-135	58164	Lelio R Paula	04/2011
8892	19^45483-80	58162	Lelio R Paula	03/2013
8893	(4*10^58155+83)/3	58156	Robert Price	01/2017
8894	14^50739-13	58154	Lelio R Paula	03/2013
8895	(1017*2^193184-1)/4823	58154	Lelio R Paula	04/2015
8896	(2*10^58151+457)/9	58151	Robert Price	01/2017
8897	(9179*2^193183-1)/3999267879	58149	Lelio R Paula	04/2015
8898	(19*2^193114-1)/1186755	58129	Lelio R Paula	01/2014
8900	2^193091-1237	58127	Yves Minet	08/2012
8899	9*7^68780-2	58127	Lelio R Paula	09/2014
8901	2473^17130+17130^2473	58126	Norbert Schneider	10/2018
8902	2^193083-869688105	58124	Lelio R Paula	10/2012
8903	2^193058-45	58117	Lelio R Paula	04/2011
8904	(14016^14016+14017^14017)/(23710319913)	58115	David Broadhurst	09/2009
8905	11^55795-42	58105	Lelio R Paula	03/2013
8906	3^121779-16	58104	Lelio R Paula	10/2012
8907	(13*10^58103+191)/3	58104	Robert Price	08/2017
8908	2^192986+195	58095	Lelio R Paula	04/2011
8909	7^68740+2*3^68740	58093	Mike Oakes	07/2010
8910	(85*10^58091-1)/3	58093	Robert Price	07/2017
8911	(404*10^58087-53)/9	58089	Robert Price	11/2017
8912	12^53821+11	58083	Lelio R Paula	02/2013
8913	119^27979-118	58072	Norbert Schneider	10/2013
8914	(10223*2^192828+1)/243	58049	Lelio R Paula	05/2014
8915	2^192808-1127	58041	Yves Minet	05/2013
8916	(27*2^192803+1)/9827	58037	Lelio R Paula	07/2012
8918	(2^192781+lucasV(1,2,192781)+1)/4	58033	Mike Oakes	11/2016
8917	3*10^58032-23	58033	Robert Price	11/2017
8919	2^192678+72943	58002	Enzo Doria	04/2016
8920	(13*10^57997-37)/3	57998	Robert Price	08/2017
8921	2^192657-3189	57996	Yves Minet	10/2014
8922	6^74525-149	57992	Lelio R Paula	10/2012
8923	42^35723-41	57988	Norbert Schneider	06/2014
8924	(29*2^192625-1)/183	57986	Lelio R Paula	01/2014
8925	(3^121520-8)/3847	57977	Lelio R Paula	03/2012
8926	(2^192596-5)/139	57976	Lelio R Paula	02/2012
8927	10^57975+67833	57976	Patrick De Geest	09/2013
8928	10^57975-47693	57975	Patrick De Geest	09/2013
8929	(F(7707)^37-F(7706)^37)/F(7705)	57972	Wayne Halsdorf	03/2012
8930	(29*10^57967+673)/9	57968	Robert Price	10/2017
8931	(3^121492-5)/4	57966	Lelio R Paula	03/2012
8932	2^192549+35	57964	Lelio R Paula	04/2011
8933	28799!2+2	57962	Robert Price	10/2012
8934	(7*2^192534-1)/1347	57957	Lelio R Paula	01/2014
8935	7001^15069-100	57943	Enzo Doria	07/2012
8936	L(277273)/11090921	57940	Donovan Johnson	11/2005
8937	(2^192469-1017)/35	57938	Lelio R Paula	02/2012
8938	2^192457-1155*192457	57936	Henri Lifchitz	02/2005
8939	12752^14111-14111^12752	57934	Norbert Schneider	01/2019
8940	2^192443+1385	57932	Lelio R Paula	05/2011
8941	132^27317-131	57928	Norbert Schneider	03/2015
8942	41522!3-59049	57912	Robert Price	12/2015
8943	(3*2^192380-1)/169	57911	Lelio R Paula	01/2014
8944	2^192339-2515	57900	Yves Minet	07/2014
8945	2^192303+7695	57889	Lelio R Paula	10/2012
8946	2^192273-5955	57880	Lelio R Paula	05/2011
8947	2^192257+16095	57876	Lelio R Paula	05/2011
8948	109^28401-2	57865	Lelio R Paula	10/2017
8949	2^192218-111861	57864	Enzo Doria	05/2014
8950	2^192214-3941	57863	Yves Minet	04/2017
8951	(2^192212+3)/259	57860	Lelio R Paula	02/2012
8952	(3^121270+8)/155939753	57853	Lelio R Paula	03/2012
8953	80^30393-79	57841	Norbert Schneider	03/2015
8954	20^44455-3123	57838	Enzo Doria	03/2013
8955	2^192122-195	57835	Lelio R Paula	04/2011
8956	(29*10^57834+91)/3	57835	Robert Price	03/2016
8957	8*6^74306+5	57823	Lelio R Paula	09/2014
8958	(39^36341-1)/38	57820	Robert Price	04/2012
8959	2^192037-111805	57809	Enzo Doria	05/2014
8960	2^192023-192023^2	57805	Henri Lifchitz	05/2005
8961	21^43717+2	57804	Ray Chandler	08/2011
8962	8*5^82687+7	57797	Lelio R Paula	09/2014
8963	5^82680-24	57791	Lelio R Paula	10/2012
8964	(2^191915+47)/95	57771	Lelio R Paula	02/2012
8965	(74*10^57763+133)/9	57764	Robert Price	10/2017
8966	6^74227-95	57760	Lelio R Paula	10/2012
8967	2^191861+29835	57756	Lelio R Paula	10/2012
8968	1908^17605+17605^1908	57755	Serge Batalov	05/2014
8969	5*10^57754+59	57755	Robert Price	09/2016
8970	(5*2^191821-1)/8924067	57738	Lelio R Paula	01/2014
8971	38^63917+5^63917-34^63917+3*2^63917	57724	Mike Oakes	11/2010
8972	41399!3-6561	57723	Robert Price	11/2015
8973	(44*10^57721-233)/9	57722	Robert Price	10/2017
8974	2^191745+17	57721	Lelio R Paula	04/2011
8975	2^191730-761	57717	Yves Minet	01/2012
8976	(2^191733-3)/2251	57715	Lelio R Paula	02/2012
8977	2^191698-111	57707	Lelio R Paula	04/2011
8978	(13*10^57691+23)/9	57692	Robert Price	02/2015
8979	20^44340-5423	57688	Enzo Doria	03/2013
8980	(27*2^191629+1)/125	57686	Lelio R Paula	07/2012
8981	410^57684+37^57684	57685	Mike Oakes	11/2010
8982	2*3^120898+5	57684	Lelio R Paula	04/2014
8983	(6883*2^191610-1)/7347	57681	Lelio R Paula	04/2015
8984	6^74117-49	57675	Lelio R Paula	10/2012
8985	2^191586-113201	57674	Enzo Doria	07/2014
8986	2^191580+193	57672	Lelio R Paula	04/2011
8987	(103*29^39433+10401)/4	57669	Curtis Bright	05/2015
8988	2^191560+255255	57666	Lelio R Paula	05/2011
8989	2^191515-85	57652	Lelio R Paula	04/2011
8990	2^191502-1127	57648	Yves Minet	05/2013
8991	2*5^82473-3^82473	57647	Mike Oakes	08/2010
8992	(13*10^57634-61)/3	57635	Robert Price	08/2017
8993	85^29868-29868^85	57628	Norbert Schneider	11/2017
8994	2^191430+103	57627	Lelio R Paula	04/2011
8995	3*2^191408+5	57621	Lelio R Paula	03/2014
8996	2^191382-1858931	57612	Enzo Doria	04/2016
8997	6*7^68163+5	57606	Lelio R Paula	09/2014
8998	91^29403-2	57602	Lelio R Paula	08/2013
8999	11^55308-7950	57598	Enzo Doria	02/2013
9000	2^191329+65	57596	Lelio R Paula	04/2011

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PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)