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	3^109320+236	52159	Lelio R Paula	10/2012
8752	2^173246-28635	52153	Lelio R Paula	06/2009
8753	2*10^52147+11	52148	Robert Price	01/2015
8754	2^173208-112625	52141	Enzo Doria	06/2014
8755	(9179*2^173206-1)/2035	52141	Lelio R Paula	03/2015
8756	15^44333-76	52140	Lelio R Paula	01/2013
8757	2^173187-3189	52135	Yves Minet	10/2014
8758	2^173167+75579	52129	Enzo Doria	04/2016
8759	(2^173169+7)/92793	52125	Lelio R Paula	02/2012
8760	(25*10^52119+23)/3	52120	Robert Price	06/2017
8761	9*7^61671+4	52119	Lelio R Paula	09/2014
8763	2^173130-9221	52118	Lelio R Paula	07/2008
8762	(17*2^173129-1)/3	52118	Lelio R Paula	01/2014
8764	2^173100-112559	52109	Enzo Doria	06/2014
8765	2^173091-112339	52106	Enzo Doria	06/2014
8766	11^50030+28	52101	Lelio R Paula	01/2013
8767	(59*10^52099+13)/9	52100	Robert Price	09/2015
8768	2^173064-1829	52098	Yves Minet	09/2012
8769	2^173062-1361	52097	Yves Minet	08/2012
8770	3^109190-70	52097	Lelio R Paula	10/2012
8771	2^173059+90195	52096	Lelio R Paula	07/2012
8772	2^173048-112625	52093	Enzo Doria	06/2014
8773	92^26524+91	52088	Norbert Schneider	04/2013
8774	41^32295-40	52085	Theodore Burton	02/2007
8775	2^173002+177	52079	Lelio R Paula	02/2011
8776	p(11334)#/2+8	52075	Robert Price	01/2017
8777	2^172965-112363	52068	Enzo Doria	06/2014
8778	9*2^172935+7	52060	Lelio R Paula	03/2014
8779	11^49978-8190	52047	Enzo Doria	02/2013
8780	10^52041+633	52042	Patrick De Geest	11/2012
8781	10^52041-93	52041	Robert Price	05/2011
8782	(21*2^172815-1)/869	52021	Lelio R Paula	01/2014
8783	(182*10^52018+1)/3	52020	Robert Price	02/2017
8784	4*6^66843-5	52015	Lelio R Paula	09/2014
8785	19^40670-54	52007	Lelio R Paula	01/2013
8786	2^172756-112883	52005	Enzo Doria	06/2014
8787	11832^12763-12763^11832	51985	Norbert Schneider	02/2017
8788	7^61511-36	51983	Lelio R Paula	10/2012
8789	10591^12914-12914^10591	51979	Norbert Schneider	05/2017
8790	2^172640-75	51970	Lelio R Paula	01/2011
8791	gcd(V(932265),5F(186453)(F(186453)-1)+1)	51953	Serge Batalov	04/2015
8792	12240^12709-12709^12240	51952	Norbert Schneider	01/2017
8793	t(173589)	51951	Robert Price	12/2014
8794	7^61469+34	51948	Lelio R Paula	10/2012
8795	9*2^172553-7	51945	Lelio R Paula	03/2014
8796	11542^12787+12787^11542	51945	Norbert Schneider	01/2016
8797	35^33640-7086	51943	Enzo Doria	03/2013
8798	(7*2^172534+1)/2479	51936	Lelio R Paula	07/2012
8799	(2^86243+43467)^2+(2^86243+43467)+41	51924	Makoto Morimoto	05/2016
8800	(2^86243+84085)^2+(2^86243+84085)+41	51924	Makoto Morimoto	05/2016
8801	((2^86243+75146)^2+(2^86243+75146)+41)/61	51922	Makoto Morimoto	05/2016
8802	((2^86243+8692)^2+(2^86243+8692)+41)/3011	51920	Makoto Morimoto	05/2016
8803	((2^86243+30085)^2+(2^86243+30085)+41)/41/199	51920	Makoto Morimoto	05/2016
8804	((2^86243+36540)^2+(2^86243+36540)+41)/43/647	51920	Makoto Morimoto	05/2016
8806	2^172470+7	51919	Lelio R Paula	01/2011
8805	((2^86243+76136)^2+(2^86243+76136)+41)/60509	51919	Makoto Morimoto	05/2016
8807	((2^86243+50999)^2+(2^86243+50999)+41)/2496869	51918	Makoto Morimoto	05/2016
8808	((2^86243+80760)^2+(2^86243+80760)+41)/930481	51918	Makoto Morimoto	05/2016
8809	((2^86243+26732)^2+(2^86243+26732)+41)/223/96517	51917	Makoto Morimoto	05/2016
8810	((2^86243+51479)^2+(2^86243+51479)+41)/1607/22027	51916	Makoto Morimoto	05/2016
8813	2^172455+15	51915	Lelio R Paula	01/2011
8811	((2^86243+27637)^2+(2^86243+27637)+41)/2693/518431	51915	Makoto Morimoto	05/2016
8812	((2^86243+82275)^2+(2^86243+82275)+41)/71/9309929	51915	Makoto Morimoto	05/2016
8814	((2^86243+57757)^2+(2^86243+57757)+41)/30871/622729	51914	Makoto Morimoto	05/2016
8815	((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/65293	51913	Makoto Morimoto	05/2016
8816	((2^86243+8693)^2+(2^86243+8693)+41)/494107/2933891	51912	Makoto Morimoto	05/2016
8817	((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/1472623	51911	Makoto Morimoto	05/2016
8818	((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/2171293	51911	Makoto Morimoto	05/2016
8819	((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/12566509	51909	Makoto Morimoto	05/2016
8820	5^74263+54	51908	Lelio R Paula	10/2012
8821	13804^5755+5755^13804	51904	Hans Havermann	05/2016
8822	7*2^172403-3	51900	Henri Lifchitz	06/2003
8823	t(196078)	51892	Robert Price	02/2014
8824	2*3^108759-7	51892	Lelio R Paula	03/2014
8825	(94*10^51889+11)/3	51891	Robert Price	02/2017
8826	(73*10^51889+17)/9	51890	Robert Price	10/2015
8827	35^33603-4026	51886	Enzo Doria	03/2013
8828	2^172350-107	51883	Lelio R Paula	02/2011
8829	14419^3960+3960^14419	51876	Hans Havermann	05/2016
8830	2^172325-113185	51875	Enzo Doria	07/2014
8831	10^51872+100683	51873	Patrick De Geest	06/2016
8832	10^51872-1000000001	51872	Robert Price	05/2016
8833	10^51872-100149	51872	Patrick De Geest	06/2016
8834	2147092^8192+63	51871	Jens K. Andersen	04/2009
8835	13^46564-24	51870	Lelio R Paula	01/2013
8836	10524^12893-12893^10524	51858	Norbert Schneider	05/2017
8837	13981^5110+5110^13981	51848	Hans Havermann	05/2016
8838	2^172228+76261	51846	Enzo Doria	04/2016
8839	11^49772-1260	51833	Enzo Doria	11/2012
8840	(11*2^172157-1)/351	51823	Lelio R Paula	01/2014
8841	(43*10^51816-403)/9	51817	Robert Price	04/2017
8842	9001^13102-114	51810	Enzo Doria	07/2012
8843	(80051^10567+1)/80052	51809	Faysal YAtim	07/2007
8845	2^172101-61	51808	Lelio R Paula	01/2011
8844	(2^172125+3)/31125505	51808	Lelio R Paula	02/2012
8846	9*7^61301+4	51807	Lelio R Paula	09/2014
8847	(23*2^172090-1)/36509	51802	Lelio R Paula	01/2014
8848	2^172074+1459	51800	Lelio R Paula	07/2008
8849	2^172063+165	51797	Lelio R Paula	02/2011
8850	(21181*2^172061+1)/18147	51796	Lelio R Paula	05/2014
8851	28^35785-27	51787	Norbert Schneider	01/2014
8852	(65*10^51778+43)/9	51779	Ray Chandler	09/2010
8853	(15185*2^171975-1)/3	51774	Lelio R Paula	03/2015
8854	2^171978-113297	51771	Enzo Doria	07/2014
8855	11^49708+78	51766	Lelio R Paula	01/2013
8856	(26*10^51764-107)/9	51765	Robert Price	07/2016
8857	12^47956-97	51754	Lelio R Paula	12/2012
8858	2^171907-3511	51750	Yves Minet	03/2017
8859	10306^12885-12885^10306	51709	Norbert Schneider	05/2017
8860	(12611^12611+311)/2/13/13577903	51707	Makoto Morimoto	07/2016
8861	(3*2^171761+1)/29	51705	Lelio R Paula	07/2012
8862	t(195346)	51699	Robert Price	07/2014
8863	13^46409+46	51697	Lelio R Paula	01/2013
8864	2^171663+1155*171663	51676	Henri Lifchitz	01/2005
8865	15^43937+26	51674	Lelio R Paula	01/2013
8866	(3^108312-7)/124526	51673	Lelio R Paula	03/2012
8867	(12601^12601+465)/2/131	51667	Makoto Morimoto	07/2016
8868	(79*10^51663-97)/99	51663	Ray Chandler	11/2010
8869	(10^51652-31)/3	51652	Serge Batalov	12/2014
8870	2^171583+73793	51652	Enzo Doria	04/2016
8871	12^47861-35	51651	Lelio R Paula	12/2012
8872	6^66369-26813	51646	Enzo Doria	03/2013
8873	Phi(83967,10)/2272482889	51639	Maksym Voznyy	01/2010
8874	2^171524+153	51634	Lelio R Paula	02/2011
8875	(2^171516-509203)/4869	51628	Lelio R Paula	05/2012
8876	(12589^12589+323)/2^5/3	51613	Makoto Morimoto	07/2016
8877	5*10^51608-81	51609	Robert Price	04/2017
8878	(lucasV(1,2,342870)+2)/(1325933242617)	51597	Mike Oakes	03/2017
8879	10171^12872-12872^10171	51583	Norbert Schneider	04/2017
8880	2^171351-112677	51582	Enzo Doria	06/2014
8881	(12583^12583+1695)/2/11^2/7535089	51579	Makoto Morimoto	07/2016
8882	9818^12919-12919^9818	51573	Norbert Schneider	05/2017
8883	(3^108091+7)/382	51570	Lelio R Paula	03/2012
8885	2^171287-3187	51563	Yves Minet	04/2009
8884	-lucasV(-1,2,342569)	51563	Mike Oakes	02/2017
8886	2^171280-1030709	51561	Paul Bourdelais	11/2012
8887	13300^7527+7527^13300	51560	Hans Havermann	05/2016
8888	2^171268+73711	51557	Enzo Doria	04/2016
8889	(17*2^171266+1)/6963	51554	Lelio R Paula	01/2012
8890	(1964814^8192+1)/65537	51551	Lelio R Paula	06/2013
8891	4*10^51530-63	51531	Robert Price	12/2016
8892	3*6^66216-5	51527	Lelio R Paula	09/2014
8893	12569^12569+540	51525	Makoto Morimoto	07/2016
8894	2^171152-2459	51522	Yves Minet	07/2014
8895	(13*10^51511-1)/3	51512	Robert Price	12/2014
8896	5*10^51508+3	51509	Dmitry Domanov	11/2010
8897	3^107919-46	51491	Lelio R Paula	07/2012
8898	4*10^51489+87	51490	Robert Price	05/2016
8899	(22699*2^171030+1)/3029	51487	Lelio R Paula	05/2014
8900	2^171028-3239	51485	Yves Minet	12/2014
8901	2^170992-954209	51474	Paul Bourdelais	11/2012
8902	76^27367+75	51473	Norbert Schneider	11/2012
8903	6007^13620-102	51466	Enzo Doria	07/2012
8904	gcd(V(923445),5F(184689)(F(184689)-1)+1)	51462	Serge Batalov	04/2015
8905	t(194442)	51459	Robert Price	08/2014
8906	(22*10^51457+161)/3	51458	Robert Price	02/2017
8907	9^53921+8^(53921+1)	51454	Robert Price	06/2016
8909	2^170921-16995	51453	Lelio R Paula	08/2011
8908	2^170922-2135	51453	Yves Minet	06/2013
8910	4357^14138-120	51451	Enzo Doria	06/2012
8911	153^23550+2	51450	Lelio R Paula	05/2013
8912	(3^107833+2)/25	51449	Lelio R Paula	03/2012
8913	7*10^51440-47	51441	Robert Price	02/2017
8914	(10^51431-3^51431)/7	51431	Robert Price	06/2011
8916	U(250849)	51425	Michael Porter	08/2007
8915	(86*10^51424-41)/9	51425	Robert Price	11/2015
8917	12^47649+7	51422	Lelio R Paula	12/2012
8918	(25*10^51421+11)/9	51422	Robert Price	03/2015
8919	3^107768+2660	51419	Lelio R Paula	07/2012
8920	2^170784-6555	51412	Lelio R Paula	05/2009
8921	(-lucasV(1,2,341584)-2)/79	51412	Mike Oakes	03/2017
8922	51^30106+2	51409	Lelio R Paula	05/2013
8923	5^73546-12806	51407	Enzo Doria	02/2013
8924	(12545^12545+12546^12546)/(1584571*19137767639)	51404	Walter Nissen	09/2014
8925	(3^107735-4)/431	51401	Lelio R Paula	03/2012
8926	20^39505-6483	51398	Enzo Doria	03/2013
8927	2^170736-15197	51397	Enzo Doria	04/2013
8928	2^170737-3823	51397	Yves Minet	04/2017
8929	(12541^12541+393)/2/563	51395	Makoto Morimoto	07/2016
8930	9^53857-8^53857	51393	Jean-Louis Charton	11/2004
8931	5^73524-14426	51392	Enzo Doria	02/2013
8932	2^170712+243	51390	Lelio R Paula	10/2011
8933	(15*2^170713+1)/1793	51388	Lelio R Paula	07/2012
8934	(2^170702+9)/1261	51384	Lelio R Paula	01/2012
8935	283^20956+20956^283	51380	Norbert Schneider	08/2014
8936	2^170665-31	51376	Lelio R Paula	01/2011
8937	11^49330-12	51372	Lelio R Paula	01/2013
8938	(25*10^51366-73)/3	51367	Robert Price	09/2016
8939	5^73486-2^73487	51365	Mike Oakes	10/2010
8940	(10^51364+119)/3	51364	Serge Batalov	12/2014
8941	15^43672+68	51363	Lelio R Paula	01/2013
8942	2^170609-113143	51359	Enzo Doria	07/2014
8943	760^17827-759^17827	51357	Jean-Louis Charton	12/2010
8944	(22699*2^170592+1)/4435	51355	Lelio R Paula	05/2014
8945	8*7^60767+3	51355	Lelio R Paula	09/2014
8946	5^73452-20646	51341	Enzo Doria	03/2013
8947	2^170531-230407	51335	Gary Barnes	08/2009
8948	35^33243-2112	51330	Enzo Doria	03/2013
8949	(1845768^8192+1)/65537	51328	Lelio R Paula	06/2013
8950	13^46072+42	51322	Lelio R Paula	01/2013
8951	14^44778-95	51322	Lelio R Paula	01/2013
8952	11008^12697+12697^11008	51318	Norbert Schneider	01/2016
8953	t(180039)	51312	Robert Price	09/2014
8954	2^170444-443	51309	Yves Minet	05/2013
8955	(-lucasV(1,2,340915)+2)/(34091342201898187163)	51294	Mike Oakes	03/2017
8956	(2*10^51285-71)/3	51285	Robert Price	01/2017
8957	(1819288^8192+1)/65537	51277	Lelio R Paula	06/2013
8958	8907^12982-12982^8907	51276	Norbert Schneider	06/2017
8959	5^73350+28	51270	Lelio R Paula	10/2012
8960	3^107450+2	51267	Mike Oakes	11/2009
8961	2^170296+2533	51265	Henri Lifchitz	07/2004
8962	2^170293+76481	51264	Enzo Doria	05/2016
8963	11835^12584+12584^11835	51257	Norbert Schneider	11/2015
8964	(12511^12511+193)/2^5/39371	51256	Makoto Morimoto	07/2016
8966	12^47489+47489^12	51250	Serge Batalov	02/2012
8965	14637^3172+3172^14637	51250	Hans Havermann	04/2016
8967	(2^170245+7)/9	51248	Lelio R Paula	02/2012
8968	5^73308-19926	51241	Enzo Doria	03/2013
8969	8966^12963-12963^8966	51238	Norbert Schneider	06/2017
8970	3*2^170203+5	51237	Lelio R Paula	02/2014
8971	5^73300+46	51235	Lelio R Paula	10/2012
8972	2^170167+71	51226	Lelio R Paula	01/2011
8973	2^170140-15077	51218	Enzo Doria	04/2013
8974	15^43542-46	51210	Lelio R Paula	01/2013
8976	2^170111-1017	51209	Lelio R Paula	06/2008
8975	4*10^51208-87	51209	Robert Price	03/2017
8977	14^44679+83	51208	Lelio R Paula	01/2013
8978	10^51207+100147	51208	Patrick De Geest	06/2016
8979	10^51207-801	51207	Robert Price	04/2016
8980	t(170300)	51191	Robert Price	03/2015
8981	11966^12553-12553^11966	51191	Norbert Schneider	11/2016
8982	14670^3083+3083^14670	51184	Hans Havermann	04/2016
8983	99^25644-98	51177	Norbert Schneider	07/2013
8984	13211^7468+7468^13211	51169	Hans Havermann	04/2016
8985	(2^169969-1017)/35	51165	Lelio R Paula	01/2012
8986	5*10^51163-7	51164	Dmitry Domanov	11/2010
8987	(73*10^51162-1)/9	51163	Robert Price	01/2015
8988	2^169899+63	51145	Lelio R Paula	05/2009
8989	2^169898+513	51145	Lelio R Paula	05/2009
8990	3^107186-12388	51141	Enzo Doria	02/2013
8991	(12487^12487+173)/2^2/3/2917/3463/44483	51140	Makoto Morimoto	07/2016
8992	3*6^65715-7	51137	Lelio R Paula	09/2014
8993	116^24768+115	51133	Norbert Schneider	10/2013
8994	35^33113-4026	51129	Enzo Doria	03/2013
8995	(13*2^169830-1)/84477	51121	Lelio R Paula	01/2014
8996	(46*10^51111-1)/9	51112	Serge Batalov	10/2014
8997	15^43452-34	51104	Lelio R Paula	01/2013
8998	2^169750-137	51100	Lelio R Paula	01/2011
8999	2^169739+94065	51097	Lelio R Paula	10/2011
9000	15^43442-26	51092	Lelio R Paula	01/2013

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Probable Primes Top 10000

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