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 ?
6751	2^238199-111817	71706	Enzo Doria	05/2014
6752	lucasU(46,1,43125)+lucasU(46,1,43124)	71696	Mike Oakes	04/2009
6753	2^238144+98765331	71689	Jason Earls	01/2009
6754	18^57102-4265	71679	Enzo Doria	03/2013
6755	(73*10^71670-1)/9	71671	Robert Price	01/2015
6756	2^238081+1155*238081	71670	Henri Lifchitz	02/2005
6757	2^238067-111925	71666	Enzo Doria	05/2014
6758	36^46030+35	71637	Norbert Schneider	04/2014
6759	(74*10^71621+313)/9	71622	Robert Price	11/2017
6760	2^237905-91	71617	Lelio R Paula	02/2012
6761	(31*2^237902-1)/123	71616	Lelio R Paula	01/2014
6762	(15185*2^237866-1)/43967	71605	Lelio R Paula	04/2015
6763	(24737*2^237841+1)/25	71601	Lelio R Paula	06/2014
6764	2^237846+1299	71599	Lelio R Paula	05/2012
6765	6^92004+199801	71594	Mike Oakes	02/2011
6766	159^32516+2	71581	Lelio R Paula	05/2013
6767	2^237781+855	71580	Lelio R Paula	05/2012
6768	2^237720-4079	71561	Yves Minet	06/2011
6769	2^237698-110945	71555	Enzo Doria	05/2014
6770	2^237695-113239	71554	Enzo Doria	07/2014
6771	8*5^102362-9	71549	Lelio R Paula	10/2014
6772	(4*10^71546-31)/9	71546	Erik Branger	05/2011
6773	2^237650+37	71540	Lelio R Paula	02/2012
6774	18^56977-4391	71522	Enzo Doria	03/2013
6775	(22699*2^237565+1)/4136637	71512	Lelio R Paula	06/2014
6776	((1+sqrt(7)+sqrt(6))^48479-1)((1+sqrt(7)-sqrt(6))^48479-1)((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(7	71512	Mike Oakes	05/2009
6777	(26*10^71503+7)/3	71504	Erik Branger	11/2013
6778	(4*10^71498+173)/3	71499	Robert Price	01/2017
6779	3^149848+110	71496	Lelio R Paula	11/2014
6780	2^237498+513	71495	Lelio R Paula	05/2012
6781	2^237485+107	71491	Lelio R Paula	02/2012
6782	(2^237465+9)/2419	71481	Lelio R Paula	05/2012
6783	2^237439-112237	71477	Enzo Doria	06/2014
6784	2^237407-9787	71467	Lelio R Paula	11/2009
6785	2^237383+72953	71460	Enzo Doria	04/2016
6786	82^37337-81^37337	71457	Robert Price	01/2015
6787	(1017*2^237313-1)/19	71441	Lelio R Paula	04/2015
6788	2^237311+191	71438	Lelio R Paula	02/2012
6789	2^237280-59	71429	Lelio R Paula	02/2012
6790	11^68564-98	71403	Lelio R Paula	01/2015
6791	2^237173+74801	71397	Enzo Doria	04/2016
6792	15^60697+56	71386	Lelio R Paula	01/2015
6793	2^237118+177	71380	Lelio R Paula	02/2012
6794	2^237110+69	71378	Lelio R Paula	02/2012
6795	15^60690-58	71377	Lelio R Paula	01/2015
6796	(5*2^237125-1)/599851191	71374	Lelio R Paula	01/2014
6797	(3^149567+2)/539	71359	Lelio R Paula	06/2012
6798	(5*10^71357-143)/3	71358	Robert Price	04/2016
6799	2^237039-114621	71356	Enzo Doria	05/2015
6800	12^66116-37	71352	Lelio R Paula	02/2015
6801	(3^149497+2^149497)/5	71328	Jean-Louis Charton	10/2010
6802	2^236941-66945	71327	Lelio R Paula	05/2012
6803	2^236911-1147	71318	Yves Minet	10/2009
6804	65^39337+42	71315	Lelio R Paula	01/2016
6805	6*10^71299+7	71300	Dmitry Domanov	11/2010
6806	(25*2^236843+1)/3753	71295	Lelio R Paula	06/2012
6807	10^71291+15187	71292	Patrick De Geest	03/2016
6809	10^71291-5587309119	71291	Robert Price	03/2015
6808	10^71291-273581	71291	Patrick De Geest	03/2016
6810	-numer(bernoulli(22808)/22808)	71290	T. D. Noe	09/2005
6811	15105^17054+17054^15105	71271	Norbert Schneider	08/2018
6812	(2^236738+9)/13	71265	Lelio R Paula	05/2012
6813	5^101949+42	71260	Lelio R Paula	07/2014
6814	5*10^71237+9	71238	Dmitry Domanov	11/2010
6815	2^236634-16025	71234	Enzo Doria	04/2013
6816	71^38478+70	71233	Norbert Schneider	12/2014
6817	9*7^84280+8	71226	Lelio R Paula	10/2014
6818	(10^71223+59)/3	71223	Serge Batalov	12/2014
6819	(15185*2^236569-1)/453	71216	Lelio R Paula	04/2015
6820	51829#+(216091#)/(51829#)	71208	Makoto Morimoto	03/2016
6821	2^236528-173	71203	Lelio R Paula	02/2012
6822	3*2^236511-5	71198	Lelio R Paula	04/2014
6823	2^236477-99	71187	Lelio R Paula	02/2012
6824	11^68356-2130	71186	Enzo Doria	12/2012
6825	15128^17031+17031^15128	71186	Norbert Schneider	08/2018
6826	11^68355-3120	71185	Enzo Doria	12/2012
6827	36^45737-35^45737	71181	Robert Price	10/2012
6828	(3^149183-lucasV(1,3,149183)+1)/3	71178	Paul Vanderveen	12/2017
6829	2^236432+25	71174	Lelio R Paula	02/2012
6830	5^101818-12806	71168	Enzo Doria	02/2013
6831	(7*10^71166-457)/9	71166	Robert Price	09/2017
6832	65^39253+62	71163	Lelio R Paula	01/2016
6833	39^44718+38	71150	Norbert Schneider	05/2014
6834	2^236296-407	71133	Yves Minet	02/2012
6835	2^236286-117	71130	Lelio R Paula	02/2012
6836	2^236257-111193	71121	Enzo Doria	05/2014
6837	7^84149-36	71115	Lelio R Paula	08/2014
6838	164176#-p(164176)	71108	Henri Lifchitz	12/2018
6839	2^236209-112123	71106	Enzo Doria	06/2014
6840	18^56644-4985	71104	Enzo Doria	03/2013
6841	(46*10^71077+521)/9	71078	Robert Price	08/2017
6842	21^53753+2	71074	Ray Chandler	08/2011
6843	(86*10^71068-311)/9	71069	Robert Price	10/2017
6844	2^236081-110923	71068	Enzo Doria	05/2014
6845	(293*27^49642-1736)/13	71058	Curtis Bright	05/2015
6846	65^39192+22	71052	Lelio R Paula	01/2016
6847	(439#+1)^397-439#^397	71038	Mike Oakes	11/2010
6848	7^84050-2	71031	Lelio R Paula	09/2013
6849	20^54558-23	70982	Lelio R Paula	01/2015
6850	2^235793-112555	70981	Enzo Doria	06/2014
6851	49936!3-3^49936	70981	Robert Price	08/2015
6852	2^235787-78795	70979	Lelio R Paula	05/2012
6853	Perrin(581132)	70970	Eric W. Weisstein	02/2011
6854	14^61913-97	70961	Lelio R Paula	01/2015
6856	2^235720+16321	70959	Yves Minet	03/2010
6855	2^235718+16095	70959	Lelio R Paula	05/2012
6857	163841#+349933	70957	Nicolas PALAU	11/2016
6858	2^235710+7	70956	Lelio R Paula	02/2012
6859	(175^31627+1)/176	70939	Eric Chen	10/2017
6860	2^235635-112087	70934	Enzo Doria	06/2014
6861	153^32467+152	70931	Norbert Schneider	11/2018
6863	2^235575-1965	70916	Lelio R Paula	05/2012
6862	6^91133+101	70916	Lelio R Paula	01/2015
6864	(21181*2^235505+1)/3	70898	Lelio R Paula	06/2014
6865	(14*10^70896+211)/9	70897	Robert Price	11/2017
6866	5^101425+84	70894	Lelio R Paula	07/2014
6867	177^31536+2	70893	Lelio R Paula	05/2013
6868	43*71^38292+4	70891	Serge Batalov	03/2016
6869	(29*2^235506-1)/112029785	70888	Lelio R Paula	01/2014
6870	11^68045-1530	70862	Enzo Doria	12/2012
6871	5*10^70858+21	70859	Robert Price	01/2017
6873	2^235326+3	70841	Donovan Johnson	02/2006
6872	34523!2+4	70841	Robert Price	02/2015
6874	(31*2^235307+1)/3	70836	Lelio R Paula	06/2012
6875	2^235308+135	70835	Lelio R Paula	02/2012
6876	r(35414,90)*1000+911	70831	Patrick De Geest	07/2004
6877	2^235274+159	70825	Lelio R Paula	02/2012
6878	3^148409+70	70810	Lelio R Paula	11/2014
6879	(19*10^70794+17)/9	70795	Robert Price	03/2015
6880	2^235108-232709	70775	Paul Bourdelais	03/2013
6881	(2^235099-2^117550+1)/5	70772		11/2006
6882	19^55325-6	70748	Lelio R Paula	08/2014
6883	257^29356+29356^257	70746	Norbert Schneider	10/2014
6884	22*10^70729+3	70731	Robert Price	10/2017
6885	2^234956+11715	70729	Lelio R Paula	05/2012
6886	(7*10^70727-43)/9	70727	Robert Price	10/2014
6887	2^234890-30341	70709	Enzo Doria	11/2012
6888	17^57461+14	70703	Lelio R Paula	01/2015
6889	(9179*2^234834-1)/5	70696	Lelio R Paula	04/2015
6890	2*10^70688+51	70689	Robert Price	10/2017
6891	123^33822-122	70685	Norbert Schneider	01/2015
6892	7*10^70680-99	70681	Robert Price	11/2017
6893	(21*2^234772-1)/2095	70672	Lelio R Paula	01/2014
6894	(29*2^234686-1)/21145	70645	Lelio R Paula	01/2014
6895	(15*2^234688-1)/5278141	70643	Lelio R Paula	01/2014
6897	2^234655-67	70639	Lelio R Paula	02/2012
6896	(79*10^70638-61)/9	70639	Robert Price	10/2015
6898	2^234652-173	70638	Lelio R Paula	02/2012
6899	2^234618-3645	70628	Lelio R Paula	05/2012
6900	(2^234610-5)/19	70624	Lelio R Paula	05/2012
6901	4*5^101038+9	70624	Lelio R Paula	10/2014
6902	2^234603+71963	70623	Enzo Doria	04/2016
6903	2^234600-113129	70622	Enzo Doria	07/2014
6905	2^234586+9	70618	Lelio R Paula	02/2012
6904	3^148008+26	70618	Robert Price	11/2013
6906	(7*10^70616-151)/9	70616	Robert Price	09/2017
6907	65^38947+32	70608	Lelio R Paula	01/2016
6908	(2^234488-3)/11	70587	Lelio R Paula	05/2012
6909	(3*2^234451+1)/35	70576	Lelio R Paula	08/2012
6910	Phi(159495,10)	70560	Maksym Voznyy	09/2015
6911	2^234383-4035	70557	Lelio R Paula	05/2012
6912	2^234315-111241	70536	Enzo Doria	05/2014
6913	14^61526+97	70517	Lelio R Paula	01/2015
6914	(3*2^234170+1)/13	70492	Lelio R Paula	08/2012
6915	51^41281-50^41281	70491	Robert Price	02/2013
6916	2^234141-112123	70484	Enzo Doria	06/2014
6917	2^234139+12285	70483	Lelio R Paula	04/2012
6918	2^234133-3163	70482	Yves Minet	04/2009
6919	2^234115+83	70476	Lelio R Paula	02/2012
6920	2^234114-1595	70476	Lelio R Paula	05/2012
6921	24^51061-23^51061	70475	Robert Price	07/2012
6922	19471^16428-2	70467	Faysal YAtim	09/2005
6923	7^83381+12	70466	Robert Price	01/2014
6924	2^234067-111427	70462	Enzo Doria	05/2014
6925	(266*10^70457+1)/3	70459	Robert Price	02/2016
6926	(31*2^234041-1)/97	70453	Lelio R Paula	01/2014
6927	2^234026+12909	70449	Lelio R Paula	04/2012
6928	2^233965-19	70431	Lelio R Paula	02/2012
6929	(5*2^233932-1)/179	70419	Lelio R Paula	01/2014
6930	2^233908-17109	70414	Enzo Doria	05/2013
6931	695^24772+24772^695	70402	Norbert Schneider	09/2016
6932	3*5^100719-2	70401	Lelio R Paula	10/2014
6933	2^233829-111355	70390	Enzo Doria	05/2014
6934	(19775^16384+1)/2	70388	Henri Lifchitz	03/2007
6935	7*3^147519+8	70386	Lelio R Paula	04/2014
6936	141^32749-2	70385	Lelio R Paula	10/2017
6937	5*7^83265+2	70368	Lelio R Paula	10/2014
6938	(23*10^70363+97)/3	70364	Robert Price	02/2017
6939	(23*2^233749-1)/35325	70363	Lelio R Paula	01/2014
6940	5^100652-13916	70353	Enzo Doria	02/2013
6941	45^42555-2	70353	Lelio R Paula	08/2013
6942	2^233661-61	70339	Lelio R Paula	02/2012
6943	2^233523-112249	70298	Enzo Doria	06/2014
6944	5*3^147324-8	70293	Lelio R Paula	04/2014
6945	2^233488-13065	70287	Enzo Doria	11/2012
6946	(3^147322+8)/42851	70286	Lelio R Paula	06/2012
6947	(22*10^70259+161)/3	70260	Robert Price	02/2017
6948	2^233388+465	70257	Lelio R Paula	11/2012
6949	14^61299+59	70257	Lelio R Paula	01/2015
6950	2^233383+94065	70256	Lelio R Paula	04/2012
6951	49471!3-6561	70253	Robert Price	11/2015
6952	7^83121+6^(83121-1)	70246	Robert Price	03/2016
6953	(197*10^70241-11)/3	70243	Robert Price	10/2017
6954	23*10^70240-7	70242	Robert Price	03/2016
6955	(71*10^70227-53)/9	70228	Robert Price	10/2015
6956	(2^233247-9)/17	70214	Lelio R Paula	05/2012
6957	(11^67421-2^67421)/9	70211	Robert Price	01/2013
6958	(23*10^70209-41)/9	70210	Robert Price	03/2015
6959	(29*10^70194-11)/9	70195	Robert Price	04/2015
6960	3^147109+196	70189	Lelio R Paula	05/2014
6961	(34*10^70191-7)/9/3/40583/573047	70181	Makoto Morimoto	05/2016
6962	9^73538+8^(73538+1)	70174	Robert Price	06/2016
6963	2*5^100391+7	70171	Lelio R Paula	10/2014
6964	99^35156-2	70159	Lelio R Paula	08/2013
6965	(68*10^70148+7)/3	70150	Robert Price	03/2016
6966	11^67360-6030	70149	Enzo Doria	01/2013
6967	(35*10^70130-377)/9	70131	Robert Price	12/2017
6968	49391!3+3^49391	70128	Robert Price	09/2015
6969	(229*10^70122-1)/3	70124	Robert Price	12/2016
6970	7^82975-92	70123	Lelio R Paula	07/2014
6971	65^38670+58	70106	Lelio R Paula	01/2016
6972	105^34684+34684^105	70103	Serge Batalov	05/2014
6973	134^32955-133	70099	Norbert Schneider	03/2015
6974	2^232836-227903	70091	Enzo Doria	12/2012
6975	2^232837-1859173	70091	Enzo Doria	03/2016
6976	3*2^232820+5	70087	Lelio R Paula	04/2014
6978	2^232799+90195	70080	Lelio R Paula	02/2013
6977	2^232799-112237	70080	Enzo Doria	06/2014
6979	2^232759+262145	70068	Lelio R Paula	04/2012
6980	3*2^232750+7	70066	Lelio R Paula	04/2014
6981	12^64918-11	70059	Lelio R Paula	01/2015
6982	7^82899-12	70058	Lelio R Paula	09/2013
6983	(22*10^70051-13)/9	70052	Robert Price	03/2015
6984	(2^232685-7)/2514625	70039	Lelio R Paula	04/2012
6985	18^55786-5363	70027	Enzo Doria	03/2013
6986	(2^(77537*3+1)+243)/7	70023	Kevin Acres	11/2013
6987	2^232602+169	70021	Lelio R Paula	02/2012
6988	(137^32768+29^32768)/2	70016	Jeppe Stig Nielsen	04/2018
6989	2^232580+72133	70014	Enzo Doria	04/2016
6990	4*6^89958-7	70002	Lelio R Paula	09/2014
6991	10^70000+80487	70001	Milton L. Brown	05/2006
6992	10^69999+134857	70000	Patrick De Geest	02/2007
6996	10^70000-9273	70000	Patrick De Geest	08/2009
6997	(79*10^69999-7)/9	70000	Robert Price	01/2015
6993	((2^43112609)/10^38420)%10^70000	70000	Michael Vang	10/2016
6994	(2^756839/10^36014)%10^70000	70000	Michael Vang	12/2016
6995	(2^74207281/10^32641)%10^70000	70000	Michael Vang	12/2016
6998	10^69999-88251	69999	Patrick De Geest	08/2009
6999	2^232507+1089	69992	Lelio R Paula	04/2012
7000	(17*2^232445+1)/5	69974	Lelio R Paula	08/2012

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Probable Primes Top 10000

(252538 PRPs in the top)