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	10^52753+2826430609	52754	Robert Price	05/2015
8752	10^52753+183997	52754	Patrick De Geest	01/2016
8753	10^52753-50153	52753	Patrick De Geest	03/2016
8754	19846^455+455^19846	52751	Anatoly F. Selevich	02/2007
8755	2^175217+72977	52746	Enzo Doria	04/2016
8756	p(11466)#/2-256	52746	Robert Price	05/2017
8757	(4*10^52740+41)/9	52740	Robert Price	11/2014
8758	2^175189+5385	52738	Lelio R Paula	08/2009
8759	2^175160+9385	52729	Lelio R Paula	07/2008
8760	12356^12885+12885^12356	52724	Norbert Schneider	03/2016
8761	2^175137+11	52722	Lelio R Paula	01/2011
8762	65^29077-64^29077	52715	Robert Price	08/2013
8763	2*10^52713-87	52714	Robert Price	06/2016
8764	2^175106-465	52713	Lelio R Paula	08/2009
8765	2^175089-58695	52708	Lelio R Paula	08/2009
8766	2^175045+195	52694	Lelio R Paula	02/2011
8767	2^175025+149	52688	Lelio R Paula	02/2011
8768	(19^41201+1)/20	52685	Paul Bourdelais	03/2010
8769	2*12^48815-5^48815	52681	Mike Oakes	10/2010
8770	335^20862-20862^335	52678	Norbert Schneider	09/2015
8771	2^174983-7605	52676	Lelio R Paula	07/2009
8772	4*10^52667+19	52668	Robert Price	04/2016
8773	(10^52667+77)/3	52667	Robert Price	01/2017
8774	11434^12977+12977^11434	52664	Norbert Schneider	04/2016
8775	2^174941-1203	52663	Lelio R Paula	07/2009
8776	2^174910+12705	52654	Lelio R Paula	07/2012
8777	3^110338+74	52645	Lelio R Paula	10/2012
8778	5^75303+12	52635	Lelio R Paula	10/2012
8779	2^174836+255255	52631	Lelio R Paula	07/2009
8780	(66^28921+1)/67	52622	Paul Bourdelais	08/2017
8781	20^40443+9	52618	Lelio R Paula	01/2013
8782	(11*2^174788+1)/9	52617	Lelio R Paula	01/2012
8783	(11*2^174786-1)/703	52615	Lelio R Paula	01/2014
8784	11^50520-1290	52612	Enzo Doria	11/2012
8785	(9913*2^174736-1)/333	52603	Lelio R Paula	03/2015
8786	13145^10024+10024^13145	52594	Hans Havermann	05/2016
8787	5003^14217-150	52592	Enzo Doria	07/2012
8788	19^41123+10	52587	Lelio R Paula	01/2013
8789	2^174683+12909	52585	Lelio R Paula	01/2011
8790	2^174643+59	52573	Lelio R Paula	01/2011
8791	(1017*2^174640-1)/773	52572	Lelio R Paula	03/2015
8792	13529^7662+7662^13529	52552	Hans Havermann	06/2016
8793	121421#+188767	52548	Makoto Morimoto	02/2016
8794	20^40375-5923	52530	Enzo Doria	03/2013
8795	(67607*2^174503+1)/90948079	52528	Lelio R Paula	05/2014
8796	(-lucasV(1,2,349014)+2)/(7508731047043)	52521	Mike Oakes	03/2017
8797	2^174462+345	52519	Lelio R Paula	07/2009
8798	t(178863)	52509	Robert Price	10/2014
8799	2^174416+855	52505	Lelio R Paula	07/2009
8800	6^67467-103	52500	Lelio R Paula	10/2012
8801	(2^174533-1)/(193594572654550537*91917886778031629891960890057)	52494	Dario Alpern	06/2017
8802	2^174329-11265	52479	Enzo Doria	06/2014
8803	2^174314-1241	52474	Yves Minet	05/2009
8804	52^30577-51	52471	Norbert Schneider	08/2014
8805	15692^2205+2205^15692	52465	Hans Havermann	06/2016
8806	(2^174281-7)/628817029615	52453	Lelio R Paula	02/2012
8807	(2^174240+5)/3	52451	Lelio R Paula	02/2012
8808	(86*10^52450-221)/9	52451	Robert Price	06/2017
8809	(15*2^174221+1)/403	52445	Lelio R Paula	07/2012
8810	26313!2-32	52443	Robert Price	10/2015
8811	(3*2^174214-1)/3748729	52438	Lelio R Paula	01/2014
8812	2*3^109900-5	52436	Lelio R Paula	03/2014
8814	4159^14488-150	52432	Enzo Doria	07/2012
8813	(89*10^52431-71)/9	52432	Robert Price	11/2015
8815	2^174170-3941	52431	Yves Minet	04/2017
8816	(7*2^174171-1)/685	52429	Lelio R Paula	01/2014
8818	(260137^9679+1)/260138	52409	Faysal YAtim	03/2008
8817	2^174098+79	52409	Lelio R Paula	01/2011
8819	35^33940-2214	52406	Enzo Doria	03/2013
8820	15^44557+2	52404	Ray Chandler	07/2011
8821	2^174049-439	52394	Yves Minet	01/2012
8822	6^67329+115	52393	Lelio R Paula	10/2012
8824	2^174041+262145	52392	Lelio R Paula	07/2009
8823	141^24377+2	52392	Lelio R Paula	05/2013
8825	lucasU(285,1,21339)-lucasU(285,1,21338)	52382	Mike Oakes	05/2009
8826	2^174001-5955	52380	Lelio R Paula	07/2009
8827	lucasV(-1,2,347969)	52375	Mike Oakes	02/2017
8828	3^109764-140	52371	Lelio R Paula	10/2012
8829	2*3^109761+7	52370	Lelio R Paula	03/2014
8830	2^173944-112253	52363	Enzo Doria	06/2014
8832	2^173940+1111	52362	Lelio R Paula	01/2011
8831	(3126^14983-1)/3125	52362	Richard Fischer	03/2015
8833	15214^2763+2763^15214	52358	Hans Havermann	05/2016
8834	13200^9247+9247^13200	52352	Hans Havermann	05/2016
8835	(1017*2^173867-1)/7175	52339	Lelio R Paula	03/2015
8836	13732^6465+6465^13732	52327	Hans Havermann	05/2016
8837	(2^173867-1)/52536637502689	52326	Donovan Johnson	06/2005
8838	2^173811-684877	52323	Paul Bourdelais	11/2012
8839	2^173807-5955	52322	Lelio R Paula	06/2009
8840	2^173796-1044689	52318	Paul Bourdelais	11/2012
8841	10^52317+64497	52318	Patrick De Geest	12/2012
8842	10^52317+64743	52318	Patrick De Geest	12/2012
8843	10^52317-71	52317	Robert Price	05/2011
8844	10821^12968+12968^10821	52317	Norbert Schneider	04/2016
8845	(298*10^52308-7)/3	52310	Robert Price	06/2017
8846	(2^173778-3)/57959	52308	Lelio R Paula	02/2012
8847	10232^13043-13043^10232	52302	Norbert Schneider	08/2017
8849	2^173727+9	52298	Lelio R Paula	01/2011
8848	(14^45631+13^45631)/27	52298	Robert Price	04/2013
8850	37856!3+6561	52293	Robert Price	11/2015
8851	4*3^109596+5	52292	Lelio R Paula	03/2014
8852	15436^2441+2441^15436	52291	Hans Havermann	05/2016
8853	43^32005+24	52280	Robert Price	11/2013
8854	2^173650-165	52274	Lelio R Paula	02/2011
8855	4*10^52272+93	52273	Robert Price	01/2017
8856	19^40873+84	52267	Lelio R Paula	01/2013
8857	2^173621+4242429	52266	Jason Earls	09/2008
8858	numbpart(46909^2-1)	52247	Serge Batalov	04/2017
8859	14^45579-31	52240	Lelio R Paula	01/2013
8860	(10223*2^173518+1)/903	52236	Lelio R Paula	05/2014
8861	20^40147-6123	52233	Enzo Doria	03/2013
8862	4^86754-3^(86754+1)	52232	Robert Price	04/2016
8863	2^173477-3433	52222	Yves Minet	04/2009
8864	(25*2^173446+1)/61	52213	Lelio R Paula	07/2012
8865	3^109431-38	52212	Lelio R Paula	10/2012
8866	2^173424-3959	52206	Yves Minet	04/2017
8867	13^46861-72	52201	Lelio R Paula	01/2013
8868	2^173373-1363	52191	Yves Minet	03/2009
8869	11^50114-1740	52189	Enzo Doria	11/2012
8870	13735^6304+6304^13735	52188	Hans Havermann	05/2016
8871	11^50111-1110	52186	Enzo Doria	11/2012
8872	lucasU(46,1,31387)+lucasU(46,1,31386)	52181	Mike Oakes	04/2009
8873	20^40105-8583	52178	Enzo Doria	03/2013
8874	(10322^13001+2679^13001)/13001^2	52175	Lelio R Paula	08/2008
8875	2^173314-3941	52173	Yves Minet	04/2017
8876	2^173294+1155	52167	Lelio R Paula	07/2012
8878	(19*2^173301-1)/23489	52166	Lelio R Paula	01/2014
8877	15146^2781+2781^15146	52166	Hans Havermann	06/2016
8879	11^50088-32	52162	Lelio R Paula	01/2013
8880	3^109320+236	52159	Lelio R Paula	10/2012
8881	2^173246-28635	52153	Lelio R Paula	06/2009
8882	2*10^52147+11	52148	Robert Price	01/2015
8883	2^173208-112625	52141	Enzo Doria	06/2014
8884	(9179*2^173206-1)/2035	52141	Lelio R Paula	03/2015
8885	15^44333-76	52140	Lelio R Paula	01/2013
8886	2^173187-3189	52135	Yves Minet	10/2014
8887	2^173167+75579	52129	Enzo Doria	04/2016
8888	(2^173169+7)/92793	52125	Lelio R Paula	02/2012
8889	(25*10^52119+23)/3	52120	Robert Price	06/2017
8890	9*7^61671+4	52119	Lelio R Paula	09/2014
8892	2^173130-9221	52118	Lelio R Paula	07/2008
8891	(17*2^173129-1)/3	52118	Lelio R Paula	01/2014
8893	2^173100-112559	52109	Enzo Doria	06/2014
8894	2^173091-112339	52106	Enzo Doria	06/2014
8895	11^50030+28	52101	Lelio R Paula	01/2013
8896	(59*10^52099+13)/9	52100	Robert Price	09/2015
8897	2^173064-1829	52098	Yves Minet	09/2012
8898	2^173062-1361	52097	Yves Minet	08/2012
8899	3^109190-70	52097	Lelio R Paula	10/2012
8900	2^173059+90195	52096	Lelio R Paula	07/2012
8901	2^173048-112625	52093	Enzo Doria	06/2014
8902	92^26524+91	52088	Norbert Schneider	04/2013
8903	41^32295-40	52085	Theodore Burton	02/2007
8904	2^173002+177	52079	Lelio R Paula	02/2011
8905	p(11334)#/2+8	52075	Robert Price	01/2017
8906	2^172965-112363	52068	Enzo Doria	06/2014
8907	9*2^172935+7	52060	Lelio R Paula	03/2014
8908	11^49978-8190	52047	Enzo Doria	02/2013
8909	10^52041+633	52042	Patrick De Geest	11/2012
8910	10^52041-93	52041	Robert Price	05/2011
8911	(21*2^172815-1)/869	52021	Lelio R Paula	01/2014
8912	(182*10^52018+1)/3	52020	Robert Price	02/2017
8913	4*6^66843-5	52015	Lelio R Paula	09/2014
8914	19^40670-54	52007	Lelio R Paula	01/2013
8915	2^172756-112883	52005	Enzo Doria	06/2014
8916	11832^12763-12763^11832	51985	Norbert Schneider	02/2017
8917	7^61511-36	51983	Lelio R Paula	10/2012
8918	10591^12914-12914^10591	51979	Norbert Schneider	05/2017
8919	2^172640-75	51970	Lelio R Paula	01/2011
8920	gcd(V(932265),5F(186453)(F(186453)-1)+1)	51953	Serge Batalov	04/2015
8921	12240^12709-12709^12240	51952	Norbert Schneider	01/2017
8922	t(173589)	51951	Robert Price	12/2014
8923	7^61469+34	51948	Lelio R Paula	10/2012
8925	9*2^172553-7	51945	Lelio R Paula	03/2014
8924	11542^12787+12787^11542	51945	Norbert Schneider	01/2016
8926	35^33640-7086	51943	Enzo Doria	03/2013
8927	(7*2^172534+1)/2479	51936	Lelio R Paula	07/2012
8928	(2^86243+43467)^2+(2^86243+43467)+41	51924	Makoto Morimoto	05/2016
8929	(2^86243+84085)^2+(2^86243+84085)+41	51924	Makoto Morimoto	05/2016
8930	((2^86243+75146)^2+(2^86243+75146)+41)/61	51922	Makoto Morimoto	05/2016
8931	((2^86243+8692)^2+(2^86243+8692)+41)/3011	51920	Makoto Morimoto	05/2016
8932	((2^86243+30085)^2+(2^86243+30085)+41)/41/199	51920	Makoto Morimoto	05/2016
8933	((2^86243+36540)^2+(2^86243+36540)+41)/43/647	51920	Makoto Morimoto	05/2016
8935	2^172470+7	51919	Lelio R Paula	01/2011
8934	((2^86243+76136)^2+(2^86243+76136)+41)/60509	51919	Makoto Morimoto	05/2016
8936	((2^86243+50999)^2+(2^86243+50999)+41)/2496869	51918	Makoto Morimoto	05/2016
8937	((2^86243+80760)^2+(2^86243+80760)+41)/930481	51918	Makoto Morimoto	05/2016
8938	((2^86243+26732)^2+(2^86243+26732)+41)/223/96517	51917	Makoto Morimoto	05/2016
8939	((2^86243+51479)^2+(2^86243+51479)+41)/1607/22027	51916	Makoto Morimoto	05/2016
8942	2^172455+15	51915	Lelio R Paula	01/2011
8940	((2^86243+27637)^2+(2^86243+27637)+41)/2693/518431	51915	Makoto Morimoto	05/2016
8941	((2^86243+82275)^2+(2^86243+82275)+41)/71/9309929	51915	Makoto Morimoto	05/2016
8943	((2^86243+57757)^2+(2^86243+57757)+41)/30871/622729	51914	Makoto Morimoto	05/2016
8944	((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/65293	51913	Makoto Morimoto	05/2016
8945	((2^86243+8693)^2+(2^86243+8693)+41)/494107/2933891	51912	Makoto Morimoto	05/2016
8946	((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/1472623	51911	Makoto Morimoto	05/2016
8947	((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/2171293	51911	Makoto Morimoto	05/2016
8948	((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/12566509	51909	Makoto Morimoto	05/2016
8949	5^74263+54	51908	Lelio R Paula	10/2012
8950	13804^5755+5755^13804	51904	Hans Havermann	05/2016
8951	7*2^172403-3	51900	Henri Lifchitz	06/2003
8952	t(196078)	51892	Robert Price	02/2014
8953	2*3^108759-7	51892	Lelio R Paula	03/2014
8954	(94*10^51889+11)/3	51891	Robert Price	02/2017
8955	(73*10^51889+17)/9	51890	Robert Price	10/2015
8956	35^33603-4026	51886	Enzo Doria	03/2013
8957	2^172350-107	51883	Lelio R Paula	02/2011
8958	14419^3960+3960^14419	51876	Hans Havermann	05/2016
8959	2^172325-113185	51875	Enzo Doria	07/2014
8960	10^51872+100683	51873	Patrick De Geest	06/2016
8961	10^51872-1000000001	51872	Robert Price	05/2016
8962	10^51872-100149	51872	Patrick De Geest	06/2016
8963	2147092^8192+63	51871	Jens K. Andersen	04/2009
8964	13^46564-24	51870	Lelio R Paula	01/2013
8965	10524^12893-12893^10524	51858	Norbert Schneider	05/2017
8966	13981^5110+5110^13981	51848	Hans Havermann	05/2016
8967	2^172228+76261	51846	Enzo Doria	04/2016
8968	11^49772-1260	51833	Enzo Doria	11/2012
8969	(11*2^172157-1)/351	51823	Lelio R Paula	01/2014
8970	(43*10^51816-403)/9	51817	Robert Price	04/2017
8971	9001^13102-114	51810	Enzo Doria	07/2012
8972	(80051^10567+1)/80052	51809	Faysal YAtim	07/2007
8974	2^172101-61	51808	Lelio R Paula	01/2011
8973	(2^172125+3)/31125505	51808	Lelio R Paula	02/2012
8975	9*7^61301+4	51807	Lelio R Paula	09/2014
8976	(23*2^172090-1)/36509	51802	Lelio R Paula	01/2014
8977	2^172074+1459	51800	Lelio R Paula	07/2008
8978	2^172063+165	51797	Lelio R Paula	02/2011
8979	(21181*2^172061+1)/18147	51796	Lelio R Paula	05/2014
8980	28^35785-27	51787	Norbert Schneider	01/2014
8981	(65*10^51778+43)/9	51779	Ray Chandler	09/2010
8982	(15185*2^171975-1)/3	51774	Lelio R Paula	03/2015
8983	2^171978-113297	51771	Enzo Doria	07/2014
8984	11^49708+78	51766	Lelio R Paula	01/2013
8985	(26*10^51764-107)/9	51765	Robert Price	07/2016
8986	12^47956-97	51754	Lelio R Paula	12/2012
8987	2^171907-3511	51750	Yves Minet	03/2017
8988	10306^12885-12885^10306	51709	Norbert Schneider	05/2017
8989	(12611^12611+311)/2/13/13577903	51707	Makoto Morimoto	07/2016
8990	(3*2^171761+1)/29	51705	Lelio R Paula	07/2012
8991	t(195346)	51699	Robert Price	07/2014
8992	13^46409+46	51697	Lelio R Paula	01/2013
8993	2^171663+1155*171663	51676	Henri Lifchitz	01/2005
8994	15^43937+26	51674	Lelio R Paula	01/2013
8995	(3^108312-7)/124526	51673	Lelio R Paula	03/2012
8996	(12601^12601+465)/2/131	51667	Makoto Morimoto	07/2016
8997	(79*10^51663-97)/99	51663	Ray Chandler	11/2010
8998	48589!4+1024	51656	Robert Price	08/2017
8999	(10^51652-31)/3	51652	Serge Batalov	12/2014
9000	2^171583+73793	51652	Enzo Doria	04/2016

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