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 ?
9751	(25*10^52119+23)/3	52120	Robert Price	06/2017
9752	9*7^61671+4	52119	Lelio R Paula	09/2014
9754	2^173130-9221	52118	Lelio R Paula	07/2008
9753	(17*2^173129-1)/3	52118	Lelio R Paula	01/2014
9755	6482^13673-13673^6482	52118	Norbert Schneider	08/2018
9756	215^22342-216	52112	Karsten Bonath	04/2018
9757	2^173100-112559	52109	Enzo Doria	06/2014
9758	2^173091-112339	52106	Enzo Doria	06/2014
9759	70797!6-32	52106	Robert Price	08/2018
9760	11^50030+28	52101	Lelio R Paula	01/2013
9761	(59*10^52099+13)/9	52100	Robert Price	09/2015
9762	2^173064-1829	52098	Yves Minet	09/2012
9763	2^173062-1361	52097	Yves Minet	08/2012
9764	3^109190-70	52097	Lelio R Paula	10/2012
9765	2^173059+90195	52096	Lelio R Paula	07/2012
9766	2^173048-112625	52093	Enzo Doria	06/2014
9767	92^26524+91	52088	Norbert Schneider	04/2013
9768	41^32295-40	52085	Theodore Burton	02/2007
9769	2^173002+177	52079	Lelio R Paula	02/2011
9770	p(11334)#/2+8	52075	Robert Price	01/2017
9771	2^172965-112363	52068	Enzo Doria	06/2014
9772	9*2^172935+7	52060	Lelio R Paula	03/2014
9773	11^49978-8190	52047	Enzo Doria	02/2013
9774	10^52041+633	52042	Patrick De Geest	11/2012
9775	8494^13245-13245^8494	52042	Norbert Schneider	01/2018
9776	10^52041-93	52041	Robert Price	05/2011
9777	(21*2^172815-1)/869	52021	Lelio R Paula	01/2014
9778	(182*10^52018+1)/3	52020	Robert Price	02/2017
9779	4*6^66843-5	52015	Lelio R Paula	09/2014
9780	7732^13377-13377^7732	52014	Norbert Schneider	03/2018
9781	19^40670-54	52007	Lelio R Paula	01/2013
9782	2^172756-112883	52005	Enzo Doria	06/2014
9783	11832^12763-12763^11832	51985	Norbert Schneider	02/2017
9784	7^61511-36	51983	Lelio R Paula	10/2012
9785	10591^12914-12914^10591	51979	Norbert Schneider	05/2017
9786	2^172640-75	51970	Lelio R Paula	01/2011
9787	6792^13559-13559^6792	51959	Norbert Schneider	07/2018
9788	7750^13359-13359^7750	51958	Norbert Schneider	03/2018
9789	gcd(V(932265),5F(186453)(F(186453)-1)+1)	51953	Serge Batalov	04/2015
9790	12240^12709-12709^12240	51952	Norbert Schneider	01/2017
9791	t(173589)	51951	Robert Price	12/2014
9792	7^61469+34	51948	Lelio R Paula	10/2012
9793	9*2^172553-7	51945	Lelio R Paula	03/2014
9794	11542^12787+12787^11542	51945	Norbert Schneider	01/2016
9795	35^33640-7086	51943	Enzo Doria	03/2013
9796	(7*2^172534+1)/2479	51936	Lelio R Paula	07/2012
9797	7353^13430-13430^7353	51927	Norbert Schneider	04/2018
9798	(2^86243+43467)^2+(2^86243+43467)+41	51924	Makoto Morimoto	05/2016
9799	(2^86243+84085)^2+(2^86243+84085)+41	51924	Makoto Morimoto	05/2016
9800	((2^86243+75146)^2+(2^86243+75146)+41)/61	51922	Makoto Morimoto	05/2016
9801	((2^86243+8692)^2+(2^86243+8692)+41)/3011	51920	Makoto Morimoto	05/2016
9802	((2^86243+30085)^2+(2^86243+30085)+41)/41/199	51920	Makoto Morimoto	05/2016
9803	((2^86243+36540)^2+(2^86243+36540)+41)/43/647	51920	Makoto Morimoto	05/2016
9805	2^172470+7	51919	Lelio R Paula	01/2011
9804	((2^86243+76136)^2+(2^86243+76136)+41)/60509	51919	Makoto Morimoto	05/2016
9806	((2^86243+50999)^2+(2^86243+50999)+41)/2496869	51918	Makoto Morimoto	05/2016
9807	((2^86243+80760)^2+(2^86243+80760)+41)/930481	51918	Makoto Morimoto	05/2016
9808	((2^86243+26732)^2+(2^86243+26732)+41)/223/96517	51917	Makoto Morimoto	05/2016
9809	((2^86243+51479)^2+(2^86243+51479)+41)/1607/22027	51916	Makoto Morimoto	05/2016
9812	2^172455+15	51915	Lelio R Paula	01/2011
9810	((2^86243+27637)^2+(2^86243+27637)+41)/2693/518431	51915	Makoto Morimoto	05/2016
9811	((2^86243+82275)^2+(2^86243+82275)+41)/71/9309929	51915	Makoto Morimoto	05/2016
9813	((2^86243+57757)^2+(2^86243+57757)+41)/30871/622729	51914	Makoto Morimoto	05/2016
9814	((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/65293	51913	Makoto Morimoto	05/2016
9815	((2^86243+8693)^2+(2^86243+8693)+41)/494107/2933891	51912	Makoto Morimoto	05/2016
9816	((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/1472623	51911	Makoto Morimoto	05/2016
9817	((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/2171293	51911	Makoto Morimoto	05/2016
9818	((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/12566509	51909	Makoto Morimoto	05/2016
9819	5^74263+54	51908	Lelio R Paula	10/2012
9820	13804^5755+5755^13804	51904	Hans Havermann	05/2016
9821	7*2^172403-3	51900	Henri Lifchitz	06/2003
9822	t(196078)	51892	Robert Price	02/2014
9823	2*3^108759-7	51892	Lelio R Paula	03/2014
9824	(94*10^51889+11)/3	51891	Robert Price	02/2017
9825	(73*10^51889+17)/9	51890	Robert Price	10/2015
9826	35^33603-4026	51886	Enzo Doria	03/2013
9827	2^172350-107	51883	Lelio R Paula	02/2011
9828	14419^3960+3960^14419	51876	Hans Havermann	05/2016
9829	2^172325-113185	51875	Enzo Doria	07/2014
9830	10^51872+100683	51873	Patrick De Geest	06/2016
9831	10^51872-1000000001	51872	Robert Price	05/2016
9832	10^51872-100149	51872	Patrick De Geest	06/2016
9833	2147092^8192+63	51871	Jens K. Andersen	04/2009
9834	13^46564-24	51870	Lelio R Paula	01/2013
9835	10524^12893-12893^10524	51858	Norbert Schneider	05/2017
9836	13981^5110+5110^13981	51848	Hans Havermann	05/2016
9837	2^172228+76261	51846	Enzo Doria	04/2016
9838	11^49772-1260	51833	Enzo Doria	11/2012
9839	(11*2^172157-1)/351	51823	Lelio R Paula	01/2014
9840	(43*10^51816-403)/9	51817	Robert Price	04/2017
9841	9001^13102-114	51810	Enzo Doria	07/2012
9842	(80051^10567+1)/80052	51809	Faysal YAtim	07/2007
9844	2^172101-61	51808	Lelio R Paula	01/2011
9843	(2^172125+3)/31125505	51808	Lelio R Paula	02/2012
9845	9*7^61301+4	51807	Lelio R Paula	09/2014
9846	(23*2^172090-1)/36509	51802	Lelio R Paula	01/2014
9847	2^172074+1459	51800	Lelio R Paula	07/2008
9848	2^172063+165	51797	Lelio R Paula	02/2011
9849	(21181*2^172061+1)/18147	51796	Lelio R Paula	05/2014
9850	(56*10^51793+367)/9	51794	Robert Price	10/2017
9851	28^35785-27	51787	Norbert Schneider	01/2014
9852	(65*10^51778+43)/9	51779	Ray Chandler	09/2010
9853	(15185*2^171975-1)/3	51774	Lelio R Paula	03/2015
9854	2^171978-113297	51771	Enzo Doria	07/2014
9855	11^49708+78	51766	Lelio R Paula	01/2013
9856	(26*10^51764-107)/9	51765	Robert Price	07/2016
9857	12^47956-97	51754	Lelio R Paula	12/2012
9858	2^171907-3511	51750	Yves Minet	03/2017
9859	8203^13220-13220^8203	51743	Norbert Schneider	12/2017
9860	7706^13307-13307^7706	51723	Norbert Schneider	02/2018
9861	8*10^51721+87	51722	Robert Price	10/2017
9862	10306^12885-12885^10306	51709	Norbert Schneider	05/2017
9863	(12611^12611+311)/2/13/13577903	51707	Makoto Morimoto	07/2016
9864	(3*2^171761+1)/29	51705	Lelio R Paula	07/2012
9865	t(195346)	51699	Robert Price	07/2014
9866	13^46409+46	51697	Lelio R Paula	01/2013
9867	2^171663+1155*171663	51676	Henri Lifchitz	01/2005
9868	15^43937+26	51674	Lelio R Paula	01/2013
9869	(3^108312-7)/124526	51673	Lelio R Paula	03/2012
9870	(12601^12601+465)/2/131	51667	Makoto Morimoto	07/2016
9871	(79*10^51663-97)/99	51663	Ray Chandler	11/2010
9872	48589!4+1024	51656	Robert Price	08/2017
9875	(10^51652-31)/3	51652	Serge Batalov	12/2014
9874	2^171583+73793	51652	Enzo Doria	04/2016
9873	(28*10^51651-31)/3	51652	Robert Price	10/2017
9876	12^47861-35	51651	Lelio R Paula	12/2012
9877	6^66369-26813	51646	Enzo Doria	03/2013
9878	Phi(83967,10)/2272482889	51639	Maksym Voznyy	01/2010
9879	2^171524+153	51634	Lelio R Paula	02/2011
9880	(2^171516-509203)/4869	51628	Lelio R Paula	05/2012
9881	(12589^12589+323)/2^5/3	51613	Makoto Morimoto	07/2016
9882	5*10^51608-81	51609	Robert Price	04/2017
9883	(lucasV(1,2,342870)+2)/(1325933242617)	51597	Mike Oakes	03/2017
9884	(2*10^51597-23)/3	51597	Robert Price	09/2017
9885	10171^12872-12872^10171	51583	Norbert Schneider	04/2017
9886	2^171351-112677	51582	Enzo Doria	06/2014
9887	(12583^12583+1695)/2/11^2/7535089	51579	Makoto Morimoto	07/2016
9888	9818^12919-12919^9818	51573	Norbert Schneider	05/2017
9889	(3^108091+7)/382	51570	Lelio R Paula	03/2012
9891	2^171287-3187	51563	Yves Minet	04/2009
9890	-lucasV(-1,2,342569)	51563	Mike Oakes	02/2017
9892	2^171280-1030709	51561	Paul Bourdelais	11/2012
9893	13300^7527+7527^13300	51560	Hans Havermann	05/2016
9894	2^171268+73711	51557	Enzo Doria	04/2016
9895	(17*2^171266+1)/6963	51554	Lelio R Paula	01/2012
9896	(1964814^8192+1)/65537	51551	Lelio R Paula	06/2013
9897	(26*10^51537-503)/9	51538	Robert Price	12/2017
9898	4*10^51530-63	51531	Robert Price	12/2016
9899	3*6^66216-5	51527	Lelio R Paula	09/2014
9900	12569^12569+540	51525	Makoto Morimoto	07/2016
9901	2^171152-2459	51522	Yves Minet	07/2014
9902	(13*10^51511-1)/3	51512	Robert Price	12/2014
9903	5*10^51508+3	51509	Dmitry Domanov	11/2010
9904	3^107919-46	51491	Lelio R Paula	07/2012
9905	4*10^51489+87	51490	Robert Price	05/2016
9906	(22699*2^171030+1)/3029	51487	Lelio R Paula	05/2014
9907	2^171028-3239	51485	Yves Minet	12/2014
9908	2^170992-954209	51474	Paul Bourdelais	11/2012
9909	76^27367+75	51473	Norbert Schneider	11/2012
9910	6007^13620-102	51466	Enzo Doria	07/2012
9911	gcd(V(923445),5F(184689)(F(184689)-1)+1)	51462	Serge Batalov	04/2015
9912	t(194442)	51459	Robert Price	08/2014
9913	6470^13503-13503^6470	51459	Norbert Schneider	05/2018
9914	(22*10^51457+161)/3	51458	Robert Price	02/2017
9915	9^53921+8^(53921+1)	51454	Robert Price	06/2016
9917	2^170921-16995	51453	Lelio R Paula	08/2011
9916	2^170922-2135	51453	Yves Minet	06/2013
9918	4357^14138-120	51451	Enzo Doria	06/2012
9919	153^23550+2	51450	Lelio R Paula	05/2013
9920	(3^107833+2)/25	51449	Lelio R Paula	03/2012
9921	(159^23369+1)/160	51443	Eric Chen	12/2017
9922	7*10^51440-47	51441	Robert Price	02/2017
9923	(10^51431-3^51431)/7	51431	Robert Price	06/2011
9925	U(250849)	51425	Michael Porter	08/2007
9924	(86*10^51424-41)/9	51425	Robert Price	11/2015
9927	12^47649+7	51422	Lelio R Paula	12/2012
9926	(25*10^51421+11)/9	51422	Robert Price	03/2015
9928	3^107768+2660	51419	Lelio R Paula	07/2012
9930	2^170784-6555	51412	Lelio R Paula	05/2009
9929	(-lucasV(1,2,341584)-2)/79	51412	Mike Oakes	03/2017
9932	51^30106+2	51409	Lelio R Paula	05/2013
9931	2^170777-4159	51409	Yves Minet	02/2018
9933	5^73546-12806	51407	Enzo Doria	02/2013
9934	(12545^12545+12546^12546)/(1584571*19137767639)	51404	Walter Nissen	09/2014
9935	(3^107735-4)/431	51401	Lelio R Paula	03/2012
9936	20^39505-6483	51398	Enzo Doria	03/2013
9937	2^170736-15197	51397	Enzo Doria	04/2013
9938	2^170737-3823	51397	Yves Minet	04/2017
9939	(12541^12541+393)/2/563	51395	Makoto Morimoto	07/2016
9940	9^53857-8^53857	51393	Jean-Louis Charton	11/2004
9941	5^73524-14426	51392	Enzo Doria	02/2013
9942	2^170712+243	51390	Lelio R Paula	10/2011
9943	(15*2^170713+1)/1793	51388	Lelio R Paula	07/2012
9944	(2^170702+9)/1261	51384	Lelio R Paula	01/2012
9945	283^20956+20956^283	51380	Norbert Schneider	08/2014
9946	2^170665-31	51376	Lelio R Paula	01/2011
9947	11^49330-12	51372	Lelio R Paula	01/2013
9948	(25*10^51366-73)/3	51367	Robert Price	09/2016
9949	5^73486-2^73487	51365	Mike Oakes	10/2010
9950	(10^51364+119)/3	51364	Serge Batalov	12/2014
9951	15^43672+68	51363	Lelio R Paula	01/2013
9952	2^170609-113143	51359	Enzo Doria	07/2014
9953	760^17827-759^17827	51357	Jean-Louis Charton	12/2010
9954	(22699*2^170592+1)/4435	51355	Lelio R Paula	05/2014
9955	8*7^60767+3	51355	Lelio R Paula	09/2014
9956	7009^13352-13352^7009	51348	Norbert Schneider	03/2018
9957	5^73452-20646	51341	Enzo Doria	03/2013
9958	2^170531-230407	51335	Gary Barnes	08/2009
9959	35^33243-2112	51330	Enzo Doria	03/2013
9960	(1845768^8192+1)/65537	51328	Lelio R Paula	06/2013
9961	13^46072+42	51322	Lelio R Paula	01/2013
9962	14^44778-95	51322	Lelio R Paula	01/2013
9963	11008^12697+12697^11008	51318	Norbert Schneider	01/2016
9964	(11^49279+7^49279)/18	51318	Eric Chen	05/2018
9965	t(180039)	51312	Robert Price	09/2014
9966	2^170444-443	51309	Yves Minet	05/2013
9967	(-lucasV(1,2,340915)+2)/(34091342201898187163)	51294	Mike Oakes	03/2017
9968	(2*10^51285-71)/3	51285	Robert Price	01/2017
9969	(23*10^51283-47)/3	51284	Robert Price	10/2017
9970	(1819288^8192+1)/65537	51277	Lelio R Paula	06/2013
9971	4714^13959-13959^4714	51277	Norbert Schneider	09/2018
9972	8907^12982-12982^8907	51276	Norbert Schneider	06/2017
9973	5^73350+28	51270	Lelio R Paula	10/2012
9974	3^107450+2	51267	Mike Oakes	11/2009
9975	2^170296+2533	51265	Henri Lifchitz	07/2004
9976	2^170293+76481	51264	Enzo Doria	05/2016
9977	11835^12584+12584^11835	51257	Norbert Schneider	11/2015
9978	(12511^12511+193)/2^5/39371	51256	Makoto Morimoto	07/2016
9980	12^47489+47489^12	51250	Serge Batalov	02/2012
9979	14637^3172+3172^14637	51250	Hans Havermann	04/2016
9981	(2^170245+7)/9	51248	Lelio R Paula	02/2012
9982	5^73308-19926	51241	Enzo Doria	03/2013
9983	8966^12963-12963^8966	51238	Norbert Schneider	06/2017
9984	3*2^170203+5	51237	Lelio R Paula	02/2014
9985	5^73300+46	51235	Lelio R Paula	10/2012
9986	2^170167+71	51226	Lelio R Paula	01/2011
9987	((2^42543+1)^4+1)/2	51226	Harsh Aggarwal	10/2018
9988	2^170140-15077	51218	Enzo Doria	04/2013
9989	15^43542-46	51210	Lelio R Paula	01/2013
9991	2^170111-1017	51209	Lelio R Paula	06/2008
9990	4*10^51208-87	51209	Robert Price	03/2017
9993	14^44679+83	51208	Lelio R Paula	01/2013
9992	10^51207+100147	51208	Patrick De Geest	06/2016
9994	10^51207-801	51207	Robert Price	04/2016
9996	t(170300)	51191	Robert Price	03/2015
9995	11966^12553-12553^11966	51191	Norbert Schneider	11/2016
9997	14670^3083+3083^14670	51184	Hans Havermann	04/2016
9998	99^25644-98	51177	Norbert Schneider	07/2013
9999	13211^7468+7468^13211	51169	Hans Havermann	04/2016
10000	(2^169969-1017)/35	51165	Lelio R Paula	01/2012

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Probable Primes Top 10000

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