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	2^160873+18915	48428	Lelio R Paula	10/2011
9752	13206^4645+4645^13206	48427	Hans Havermann	04/2016
9753	10^48420+6139	48421	Patrick De Geest	05/2016
9754	10^48420-2*10^1592-1	48420	Serge Batalov	01/2015
9755	10^48420-29273	48420	Patrick De Geest	03/2016
9757	2^160822-2163	48413	Yves Minet	08/2013
9756	(lucasV(1,2,321685)+2)/(571*911)	48413	Mike Oakes	02/2017
9759	10^48410+9^(48410-1)	48411	Robert Price	03/2016
9758	10^48410+90163	48411	Patrick De Geest	12/2016
9761	(3^101473+4)/264481	48410	Lelio R Paula	03/2012
9762	9*2^160811+7	48410	Lelio R Paula	02/2014
9760	10^48410-3287	48410	Patrick De Geest	12/2016
9763	(22699*2^160806+1)/1573	48409	Lelio R Paula	05/2014
9764	3*7^57278-8	48407	Lelio R Paula	09/2014
9765	2^160789-113215	48403	Enzo Doria	07/2014
9766	6900^12607-12607^6900	48397	Norbert Schneider	12/2016
9767	3^101404+2	48383	Mike Oakes	11/2009
9768	3^101395-110	48378	Lelio R Paula	06/2012
9769	2^160701+191	48376	Lelio R Paula	01/2011
9770	6*F(231436)+1	48368	Gilbert Mozzo	06/2015
9771	2^160654-15	48362	Lelio R Paula	08/2010
9772	20^37167+53	48356	Lelio R Paula	11/2012
9773	(799247^8192+1)/2	48355	Lelio R Paula	12/2014
9774	(238*10^48352-1)/3	48354	Robert Price	05/2016
9775	18661^390+390^18661	48352	Anatoly F. Selevich	01/2007
9776	21^36566+2	48349	Ray Chandler	08/2011
9777	7^57208-92	48347	Lelio R Paula	06/2012
9779	5^69165-2^69166	48345	Mike Oakes	10/2010
9778	(11867^11867+2981)/2^3/111341	48345	Makoto Morimoto	07/2016
9780	(3^101331-4)/4679	48344	Lelio R Paula	03/2012
9781	13^43396-24	48341	Lelio R Paula	10/2012
9783	Phi(85113,10)/170227/340453/2080331947/20239360723/577232068985083	48339	Serge Batalov	06/2011
9782	7*2^160574-9	48339	Lelio R Paula	02/2014
9784	lucasU(42,1,29781)+lucasU(42,1,29780)	48334	Mike Oakes	04/2009
9785	3^101296-19318	48331	Enzo Doria	02/2013
9786	(lucasV(1,2,321119)+2)/(5*53)	48331	Mike Oakes	01/2017
9788	(11863^11863+2822)/3/140681/148483	48322	Makoto Morimoto	07/2016
9787	5970^12797-12797^5970	48322	Norbert Schneider	03/2017
9789	17^39270+52	48320	Lelio R Paula	11/2012
9790	(791013^8192+1)/2	48318	Lelio R Paula	12/2014
9791	10^48314+71469	48315	Patrick De Geest	06/2016
9792	11^46393-7950	48314	Enzo Doria	02/2013
9794	10^48314-2*10^4988-1	48314	Serge Batalov	01/2015
9793	10^48314-423797	48314	Patrick De Geest	03/2016
9795	2^160491+87713	48313	Yves Minet	03/2010
9796	8*6^62084-7	48312	Lelio R Paula	09/2014
9797	2^160477+72977	48309	Enzo Doria	04/2016
9798	2^160471+99	48307	Lelio R Paula	07/2009
9799	(9913*2^160481-1)/4191875	48307	Lelio R Paula	03/2015
9801	(43^29573+1)/44	48305	Robert Price	11/2013
9800	2^160463-2907	48305	Yves Minet	09/2014
9802	(68*10^48304-257)/9	48305	Robert Price	06/2017
9803	Phi(77061,10)/4151276071/15207988351	48301	Maksym Voznyy	02/2010
9804	5^69098-14576	48298	Enzo Doria	02/2013
9805	(2*10^48297-17)/3	48297	Erik Branger	03/2013
9806	10^48292+104707	48293	Patrick De Geest	06/2016
9808	10^48292-2*10^392-1	48292	Serge Batalov	01/2015
9807	10^48292-66803	48292	Patrick De Geest	03/2016
9809	45709!4+2	48291	Robert Price	03/2017
9810	2^160402-1127	48286	Yves Minet	05/2013
9811	2^160398-1451	48285	Yves Minet	08/2012
9812	11^46365+26	48285	Lelio R Paula	10/2012
9813	t(160462)	48285	Robert Price	05/2015
9814	(3^50599-75)^2-77	48284	Jorge Menendez	02/2017
9815	2^160387-3721	48282	Yves Minet	04/2017
9816	3^101192+2^101193	48281	Mike Oakes	10/2009
9817	5^69063-18	48273	Lelio R Paula	05/2012
9818	5^69060-15416	48271	Enzo Doria	02/2013
9819	2^160343-667	48269	Yves Minet	01/2012
9820	2^160302-2145	48256	Lelio R Paula	04/2009
9821	12^44705-85	48245	Lelio R Paula	10/2012
9822	(58695*2^160249-1)/149	48243	Lelio R Paula	03/2015
9823	2^160218+12705	48231	Lelio R Paula	10/2011
9824	(F(14425)^17-F(14424)^17)/F(14423)	48230	Wayne Halsdorf	02/2010
9825	(771035^8192+1)/2	48227	Lelio R Paula	12/2014
9827	18348^425+425^18348	48226	Anatoly F. Selevich	12/2006
9826	(29*2^160204-1)/67	48226	Lelio R Paula	01/2014
9828	2^160166+5775	48215	Lelio R Paula	04/2009
9829	11875^11478+11478^11875	48211	Anatoly F. Selevich	10/2009
9830	17^39177-40	48206	Lelio R Paula	11/2012
9831	(5*2^160135-1)/4290399	48200	Lelio R Paula	01/2014
9832	(763957^8192+1)/2	48194	Lelio R Paula	12/2014
9833	(11833^11833+1278)/7/89/107	48193	Makoto Morimoto	06/2016
9834	gcd(V(576505),5F(115301)(F(115301)+1)+1)	48192	Serge Batalov	04/2015
9835	8788^12217+12217^8788	48183	Norbert Schneider	01/2014
9836	(11831^11831+1584)/5/23/97/1409	48181	Makoto Morimoto	07/2016
9837	(760473^8192+1)/2	48178	Lelio R Paula	12/2014
9838	-lucasV(-1,2,320104)/31	48178	Mike Oakes	01/2017
9839	gcd(V(864525),5F(172905)(F(172905)-1)+1)	48176	Serge Batalov	04/2015
9840	(760135^8192+1)/294914	48171	Lelio R Paula	12/2014
9842	4357^13236-110	48169	Enzo Doria	06/2012
9841	(11827^11827+4120)/17	48169	Makoto Morimoto	07/2016
9843	(3*2^160013-1)/2425	48166	Lelio R Paula	01/2014
9844	13^43238+82	48165	Lelio R Paula	11/2012
9845	2^159992+657	48163	Lelio R Paula	02/2013
9846	2^159984-383009	48160	Gary Barnes	08/2009
9847	2^159958-58695	48153	Lelio R Paula	03/2009
9848	6408*10^48143+11821^11821-24	48147	Gilbert Mozzo	12/2012
9849	(755045^8192+1)/229378	48147	Lelio R Paula	12/2014
9850	11821^11821-24	48143	Henri Lifchitz	10/2011
9851	(33*2^159934+1)/1936969	48141	Michael Porter	10/2015
9852	(11821^11821+1240)/19/13789	48138	Makoto Morimoto	06/2016
9853	20^36997-51	48135	Lelio R Paula	11/2012
9854	(3^100895+7)/24321775034	48129	Lelio R Paula	03/2012
9855	(15185*2^159869-1)/1827	48127	Lelio R Paula	03/2015
9856	3*7^56945+8	48125	Lelio R Paula	09/2014
9857	(749655^8192+1)/131074	48122	Lelio R Paula	12/2014
9858	4*5^68835+9	48115	Lelio R Paula	09/2014
9859	(148^22171+1)/149	48115	Richard Fischer	12/2016
9860	(2^159841+78557)/923	48114	Lelio R Paula	05/2012
9861	(3^50420+59)^2+61	48113	Jorge Menendez	02/2017
9862	10^48109+9	48110	Jason Earls	12/2007
9863	10^48108+39531	48109	Patrick De Geest	01/2009
9864	10^48109-104591	48109	Patrick De Geest	07/2009
9868	10^48107-48107	48108	Henri Lifchitz	07/2002
9865	10^48107+126229	48108	Patrick De Geest	04/2007
9866	10^48108-61343	48108	Patrick De Geest	07/2009
9867	23^35328+22	48108	Norbert Schneider	12/2013
9870	6213^12682+12682^6213	48107	Norbert Schneider	01/2016
9869	(64*10^48106+287)/9	48107	Robert Price	04/2016
9871	18^38321-97	48104	Lelio R Paula	11/2012
9872	(11813^11813+748)/3/679807	48101	Makoto Morimoto	06/2016
9873	(743679^8192+1)/2	48099	Lelio R Paula	12/2014
9874	2^159777-1333	48098	Yves Minet	05/2013
9875	2^159765+717	48095	Lelio R Paula	02/2013
9876	35^31143-3958	48087	Enzo Doria	03/2013
9877	8*10^48081-9	48082	Dmitry Domanov	11/2010
9878	12^44553-59	48081	Lelio R Paula	10/2012
9879	35086!3+2187	48080	Robert Price	12/2015
9880	(11807^11807+9647)/2/5	48079	Makoto Morimoto	07/2016
9881	1338^15377+15377^1338	48076	Serge Batalov	05/2014
9882	2^159692-1259	48073	Yves Minet	08/2012
9883	(lucasV(1,2,319367)+2)/(5*11)	48068	Mike Oakes	01/2017
9884	2^159669+941	48066	Lelio R Paula	02/2013
9885	2^159660-2879	48063	Yves Minet	09/2014
9886	2^159647+573	48059	Lelio R Paula	02/2013
9887	19^37581+94	48057	Lelio R Paula	11/2012
9888	2^159633-577063	48055	Paul Bourdelais	11/2012
9889	5436^12865-12865^5436	48055	Norbert Schneider	04/2017
9890	(11801^11801+8503)/2^4/3/17/137	48048	Makoto Morimoto	07/2016
9891	(23*2^159599+1)/25	48045	Lelio R Paula	07/2012
9892	2^159597+1307	48044	Lelio R Paula	07/2008
9893	3^100693-34	48043	Lelio R Paula	06/2012
9894	(349*10^48036-7)/9	48038	Robert Price	03/2017
9895	(68*10^48032+7)/3	48034	Robert Price	03/2016
9897	24^34797-1207	48028	Enzo Doria	03/2013
9896	(106*10^48026-1)/3	48028	Serge Batalov	12/2014
9898	2^159522+679	48021	Lelio R Paula	02/2013
9899	(726998^8192+1)/147457	48013	Lelio R Paula	11/2014
9900	(725753^8192+1)/131074	48007	Lelio R Paula	12/2014
9901	10^48003+21	48004	Robert Price	01/2011
9902	10^48003-36521	48003	Patrick De Geest	01/2012
9903	20^36896-4043	48003	Enzo Doria	03/2013
9904	10^48000+73909	48001	Patrick De Geest	05/2012
9905	10^48000-82407	48000	Patrick De Geest	05/2012
9906	10^47999+78093	48000	Patrick De Geest	05/2012
9907	10^47999-1227	47999	Patrick De Geest	05/2012
9908	2^159440-12609	47997	Enzo Doria	10/2012
9909	(11789^11789+297)/2/17/23	47996	Makoto Morimoto	06/2016
9910	(40^29959+1)/41	47995	Robert Price	09/2013
9913	(49*10^47989+41)/9	47990	Erik Branger	05/2013
9911	10^47989+2*47989-1	47990	Robert Price	03/2015
9912	10^47989+30283	47990	Patrick De Geest	01/2016
9914	10^47989-10463	47989	Patrick De Geest	01/2016
9915	(11*2^159409-1)/21	47987	Lelio R Paula	01/2014
9916	(298*10^47983-7)/3	47985	Robert Price	06/2017
9917	5^68644+94	47981	Lelio R Paula	05/2012
9918	2^159386-2145	47980	Lelio R Paula	03/2009
9919	Linear(0,1,1,-1,318751)	47977	Henri Lifchitz	04/2007
9920	(720710^8192+1)/9663889409	47977	Lelio R Paula	11/2014
9921	(2^159392+5)/117798669	47974	Lelio R Paula	01/2012
9922	6576^12565-12565^6576	47973	Norbert Schneider	11/2016
9923	10^47969+585043	47970	Robert Price	03/2015
9924	10^47969+153291	47970	Patrick De Geest	01/2016
9925	10^47969-151407	47969	Patrick De Geest	01/2016
9926	(9*2^159332+1)/5	47964	Lelio R Paula	07/2012
9927	(11783^11783+65)/2^3/89/2686037	47963	Makoto Morimoto	06/2016
9928	20^36864+31	47962	Lelio R Paula	11/2012
9929	(2^159324+78557)/2409	47958	Lelio R Paula	05/2012
9931	2^159293-1051	47952	Yves Minet	05/2009
9930	(355*29^32789-61)/14	47952	Curtis Bright	05/2015
9932	lucasU(1856,1,14670)-lucasU(1856,1,14669)	47947	Mike Oakes	05/2009
9933	(11779^11779+1425)/2^2/11/5456791	47946	Makoto Morimoto	07/2016
9934	3^100482-310	47943	Lelio R Paula	06/2012
9935	(11777^11777+5123)/2^2/5/13/2251	47939	Makoto Morimoto	07/2016
9936	17^38959+8	47938	Lelio R Paula	11/2012
9937	7*10^47936-69	47937	Robert Price	01/2017
9938	(708709^8192+1)/2	47927	Lelio R Paula	12/2014
9939	(709609^8192+1)/294914	47927	Lelio R Paula	12/2014
9941	Phi(104749,3)	47923	Lelio R Paula	02/2012
9940	24^34721-1691	47923	Enzo Doria	03/2013
9942	7*5^68554+6	47919	Lelio R Paula	09/2014
9943	(16*10^47918-19)/3	47919	Robert Price	03/2016
9945	11836^11179+11179^11836	47917	Anatoly F. Selevich	07/2009
9944	Phi(65680,67)	47917	Enzo Doria	04/2012
9946	3^100418-52	47912	Lelio R Paula	06/2012
9947	2^159145-112813	47908	Enzo Doria	06/2014
9948	6*F(229213)+1	47904	Gilbert Mozzo	06/2015
9949	6750^12509-12509^6750	47901	Norbert Schneider	10/2016
9950	(5*2^159123-1)/39	47900	Lelio R Paula	01/2014
9951	2^159105-112513	47896	Enzo Doria	06/2014
9952	(11*2^159097-1)/21	47893	Lelio R Paula	01/2014
9953	2^159092+211	47892	Lelio R Paula	02/2013
9954	10^47890+224901	47891	Patrick De Geest	06/2016
9955	10^47890-2*10^4844-1	47890	Serge Batalov	01/2015
9956	10^47890-57911	47890	Patrick De Geest	03/2016
9957	2^159078+1155	47888	Lelio R Paula	10/2011
9958	(5*2^159081+1)/143	47887	Lelio R Paula	07/2012
9959	Phi(69053,5)	47885	Lelio R Paula	01/2012
9960	3^100362-98	47885	Lelio R Paula	06/2012
9961	(9913*2^159034-1)/9	47878	Lelio R Paula	03/2015
9962	5^68484-68484^5	47869	Donovan Johnson	08/2005
9964	2^159001-278713	47865	Gary Barnes	08/2009
9963	2^159003-14095	47865	Enzo Doria	04/2013
9965	5^68476-21036	47863	Enzo Doria	03/2013
9966	(695277^8192+1)/2	47859	Lelio R Paula	12/2014
9967	2^158977+74717	47857	Yves Minet	12/2009
9968	3*5^68464-8	47855	Lelio R Paula	09/2014
9969	13855^2844+2844^13855	47855	Hans Havermann	08/2015
9970	12030^9503+9503^12030	47854	Jens K. Andersen	01/2009
9971	110597#+131317	47853	Nicolas PALAU	09/2016
9972	(3*2^158960+1)/499	47850	Lelio R Paula	07/2012
9973	2^158948+19683	47849	Lelio R Paula	10/2011
9974	lucasU(1873,1,14622)-lucasU(1873,1,14621)	47848	Mike Oakes	05/2009
9976	(266*10^47844-17)/3	47846	Robert Price	06/2016
9975	6411^12568-12568^6411	47846	Norbert Schneider	11/2016
9977	lucasU(1656,1,14862)-lucasU(1656,1,14861)	47839	Mike Oakes	05/2009
9978	(2^158894-3)/37	47831	Lelio R Paula	01/2012
9979	34918!3-27	47826	Robert Price	09/2014
9980	2*10^47823+89	47824	Robert Price	07/2016
9981	6950^12447-12447^6950	47822	Norbert Schneider	03/2013
9982	2^158838-13853	47816	Enzo Doria	04/2013
9983	18^38087+37	47810	Lelio R Paula	11/2012
9984	(685559^8192+1)/2	47809	Lelio R Paula	12/2014
9985	(684701^8192+1)/2	47805	Lelio R Paula	12/2014
9987	(11*2^158796+1)/3	47803	Lelio R Paula	01/2012
9986	(684463^8192+1)/2	47803	Lelio R Paula	12/2014
9988	110503#+208391	47798	Makoto Morimoto	12/2015
9989	(11^45893-4^45893)/7	47792	Robert Price	03/2013
9990	(58*10^47791+23)/9	47792	Erik Branger	05/2013
9991	(11743^11743+5271)/2	47792	Makoto Morimoto	07/2016
9994	2^158757+29	47791	Henri Lifchitz	05/2005
9992	2^158758+205	47791	Lelio R Paula	02/2013
9993	35^30951-36	47791	Enzo Doria	03/2013
9995	10^47784+141	47785	Patrick De Geest	06/2016
9997	10^47784-2*10^10720-1	47784	Serge Batalov	01/2015
9996	10^47784-131927	47784	Patrick De Geest	03/2016
9998	2^158710-112607	47777	Enzo Doria	06/2014
9999	(677621^8192+1)/2	47768	Lelio R Paula	12/2014
10000	2^158656+661	47761	Lelio R Paula	02/2013

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