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 ?
3751	2^325733-58695	98056	Lelio R Paula	07/2016
3752	2^325717-3645	98051	Lelio R Paula	07/2016
3753	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
3754	(7*10^98007-13)/3	98008	Robert Price	06/2016
3755	2^325512-459959	97989	Enzo Doria	05/2015
3756	(3^205354-8)/17	97978	Lelio R Paula	09/2013
3757	2^325433+76817	97966	Enzo Doria	05/2016
3758	5*10^97963+81	97964	Robert Price	08/2017
3759	2^325390-109061	97953	Enzo Doria	04/2014
3760	13^87921+24	97940	Lelio R Paula	08/2016
3761	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
3762	2^325215+12909	97900	Lelio R Paula	07/2016
3763	7*10^97874-69	97875	Robert Price	01/2017
3765	(17^79537+5^79537)/22	97865	Robert Price	06/2013
3764	15^83212+22	97865	Lelio R Paula	08/2016
3766	2^325087-109057	97861	Enzo Doria	04/2014
3767	2^325074+1870657	97858	Enzo Doria	05/2016
3768	2^325066-2111	97855	Yves Minet	08/2013
3769	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
3770	18^77944-89	97841	Lelio R Paula	07/2016
3771	119^47136+118	97833	Norbert Schneider	09/2018
3772	6^125720-17663	97830	Enzo Doria	02/2013
3773	2^324972-2069	97827	Yves Minet	05/2013
3774	2^324944-2788319	97818	Enzo Doria	03/2016
3776	4*10^97799-9	97800	Erik Branger	11/2013
3775	2^324882+577294575	97800	Lelio R Paula	09/2016
3777	2^324863-1867921	97794	Enzo Doria	04/2016
3778	6^125662-18473	97785	Enzo Doria	03/2013
3779	12^90604+11	97779	Lelio R Paula	07/2016
3780	5^139830+24	97737	Lelio R Paula	04/2016
3781	2^324612+1155	97718	Lelio R Paula	07/2016
3782	19^76404-44	97702	Lelio R Paula	07/2016
3783	2^324505-2983	97686	Yves Minet	04/2011
3784	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
3785	6^125488-17843	97649	Enzo Doria	02/2013
3786	7^115515-2	97622	Lelio R Paula	09/2013
3787	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
3788	6^125418-5	97595	Lelio R Paula	11/2014
3789	2^324076+1155	97557	Lelio R Paula	07/2016
3790	(2^324074+9)/13	97555	Lelio R Paula	10/2013
3791	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
3792	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
3793	2^323946+73939	97518	Enzo Doria	04/2016
3794	2^323937+1866947	97515	Enzo Doria	03/2016
3795	6^125290-18533	97495	Enzo Doria	03/2013
3796	2^323845+101	97488	Lelio R Paula	12/2012
3797	18^77662+65	97487	Lelio R Paula	07/2016
3798	2^323772+76771	97466	Enzo Doria	05/2016
3799	2^323765-112213	97463	Enzo Doria	06/2014
3800	2^323720-6555	97450	Lelio R Paula	07/2016
3801	2^323694-1860401	97442	Enzo Doria	03/2016
3802	20^74886+3	97429	Lelio R Paula	06/2016
3804	3*10^97399+73	97400	Robert Price	04/2016
3803	7^115252-50	97400	Lelio R Paula	07/2016
3805	224737#+393581	97389	Nicolas PALAU	12/2016
3806	(26*10^97353+31)/3	97354	Robert Price	07/2016
3807	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
3808	(38*10^97329+187)/9	97330	Robert Price	11/2017
3809	p(19982)#/2-1024	97293	Robert Price	09/2017
3810	6^125021-85	97286	Lelio R Paula	08/2016
3811	2^323164-47355	97283	Lelio R Paula	07/2016
3812	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
3813	2^323054-6555	97249	Lelio R Paula	07/2016
3814	9*10^97247-29	97248	Robert Price	05/2017
3815	(31*10^97242+41)/9	97243	Robert Price	04/2015
3816	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
3817	12^90098-41	97233	Lelio R Paula	07/2016
3818	2^322928-216929	97212	Enzo Doria	05/2014
3819	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
3820	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
3821	2^322725+75761	97150	Enzo Doria	04/2016
3822	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
3823	(41*10^97085+373)/9	97086	Robert Price	04/2017
3824	2^322413+77	97056	Lelio R Paula	12/2012
3825	2^322406+177	97054	Lelio R Paula	12/2012
3826	(14*10^97044+31)/9	97045	Robert Price	02/2015
3827	2^322302+255255	97023	Lelio R Paula	07/2016
3828	2^322196-113093	96991	Enzo Doria	07/2014
3829	2^322000-1861469	96932	Enzo Doria	03/2016
3830	2^321971-112747	96923	Enzo Doria	06/2014
3831	11^93062-92	96915	Lelio R Paula	06/2016
3832	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
3833	3^203051+34	96880	Lelio R Paula	05/2016
3834	2*10^96867-51	96868	Robert Price	11/2017
3835	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
3836	2^321716-2786939	96847	Enzo Doria	03/2016
3837	2^321701-113053	96842	Enzo Doria	07/2014
3838	2^321700-28635	96842	Lelio R Paula	06/2016
3839	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
3840	6^124433-124433	96828	Robert Price	01/2014
3841	2^321631+69	96821	Lelio R Paula	12/2012
3842	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
3843	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
3844	(59*10^96798+31)/9	96799	Robert Price	09/2015
3845	223319#+231223	96790	Makoto Morimoto	02/2016
3846	2^321519-28635	96787	Lelio R Paula	06/2016
3847	2^321487-1867237	96778	Enzo Doria	03/2016
3848	2^321461-63	96770	Lelio R Paula	12/2012
3849	2^321439+123	96763	Lelio R Paula	12/2012
3850	2^321434+709	96762	Lelio R Paula	02/2013
3851	14^84413+89	96749	Lelio R Paula	07/2016
3852	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
3853	13^86847+96	96743	Lelio R Paula	06/2016
3854	9*2^321336-7	96733	Lelio R Paula	08/2014
3855	(209*10^96722-17)/3	96724	Robert Price	05/2017
3856	2^321187-1159	96687	Yves Minet	11/2012
3857	2^321182-1850081	96686	Enzo Doria	08/2015
3858	2^321116-112829	96666	Enzo Doria	06/2014
3859	2^321108-109499	96664	Enzo Doria	04/2014
3860	2^321098+2793859	96661	Enzo Doria	03/2016
3861	2^321057+4097	96648	Lelio R Paula	06/2016
3862	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
3863	p(19849)#/2-64	96581	Robert Price	04/2017
3864	2^320817+189	96576	Lelio R Paula	12/2012
3865	(361*10^96567-163)/9	96569	Robert Price	10/2017
3866	2^320788-110327	96567	Enzo Doria	05/2014
3867	2^320764+793	96560	Lelio R Paula	02/2013
3868	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
3869	2^320616-78795	96516	Lelio R Paula	03/2016
3870	2^320612-461939	96514	Enzo Doria	07/2015
3871	5*2^320431+7	96461	Lelio R Paula	08/2014
3872	19^75431-90	96458	Lelio R Paula	06/2016
3873	(2^320370+3)/67	96440	Lelio R Paula	10/2013
3874	2^320309+1871477	96423	Enzo Doria	05/2016
3875	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
3876	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
3877	2^320232-173	96400	Lelio R Paula	12/2012
3878	175^42975-2	96395	Lelio R Paula	10/2017
3879	10^96377+199911	96378	Patrick De Geest	12/2016
3880	10^96377-20001	96377	Robert Price	11/2016
3881	2^320124-2790449	96367	Enzo Doria	03/2016
3882	2^320043-108775	96343	Enzo Doria	04/2014
3883	10^96338+424939	96339	Patrick De Geest	03/2016
3884	10^96338-9281	96338	Robert Price	09/2015
3885	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
3886	2^319838+4257	96281	Lelio R Paula	03/2016
3887	2^319830-16995	96279	Lelio R Paula	03/2016
3888	6^123713+143	96268	Lelio R Paula	05/2016
3889	(28*10^96265-97)/3	96266	Robert Price	07/2016
3890	103^47825-102	96264	Norbert Schneider	10/2016
3891	2^319713-81	96244	Lelio R Paula	11/2012
3892	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
3893	12^89153-43	96213	Lelio R Paula	06/2016
3894	(2*10^96195-59)/3	96195	Robert Price	05/2017
3895	2^319545+147	96193	Lelio R Paula	11/2012
3896	(50^56597+1)/51	96155	Robert Price	03/2014
3897	(41*10^96137-59)/9	96138	Robert Price	10/2017
3898	2^319353-110343	96135	Enzo Doria	05/2014
3899	11^92309-42	96130	Lelio R Paula	05/2016
3900	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
3901	(7*10^96112+143)/3	96113	Robert Price	04/2016
3902	2^319237+65835	96100	Lelio R Paula	03/2016
3903	2^319194-1841	96087	Yves Minet	03/2013
3904	20^73847-31	96078	Lelio R Paula	05/2016
3905	50^56543-49	96065	Norbert Schneider	09/2018
3906	2^319107-109555	96061	Enzo Doria	04/2014
3907	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
3908	2^319098-112157	96059	Enzo Doria	06/2014
3909	15^81673+94	96055	Lelio R Paula	07/2016
3910	2^319074+1871749	96051	Enzo Doria	05/2016
3911	2^319007-112111	96031	Enzo Doria	06/2014
3912	2^318946-1421	96013	Yves Minet	01/2013
3913	2^318834-110411	95979	Enzo Doria	05/2014
3914	2^318831-1965	95978	Lelio R Paula	03/2016
3915	(5*10^95976+7)/3	95977	Erik Branger	03/2014
3916	5*3^201089-8	95945	Lelio R Paula	08/2014
3917	2^318711-139	95942	Lelio R Paula	11/2012
3918	2^318635-1167	95919	Lelio R Paula	03/2016
3919	15^81555+16	95917	Lelio R Paula	07/2016
3920	(37*10^95895+377)/9	95896	Robert Price	10/2017
3921	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
3922	2^318496-97305	95877	Lelio R Paula	03/2016
3923	2^318466+15015	95868	Lelio R Paula	03/2016
3924	6^123187-173129	95859	Mike Oakes	04/2011
3925	2^318423-487	95855	Yves Minet	03/2012
3926	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
3927	45369!2+1024	95787	Robert Price	02/2015
3928	3^200758-86	95786	Lelio R Paula	05/2016
3929	(2^318271+1)/(346031404238891654090604244843)	95781	Gord Palameta	12/2018
3930	3*10^95776-59	95777	Robert Price	10/2017
3931	193^41901-2	95768	Lelio R Paula	10/2017
3932	4*10^95752-71	95753	Robert Price	11/2017
3933	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
3934	4*10^95672+91	95673	Robert Price	11/2017
3935	(11*10^95641-113)/3	95642	Robert Price	01/2017
3936	(13*10^95588+11)/3	95589	Robert Price	05/2015
3937	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
3938	3^200325+70	95580	Lelio R Paula	05/2016
3939	(25*10^95574-7)/9	95575	Robert Price	12/2014
3940	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
3941	2^317464+31	95567	Lelio R Paula	11/2012
3942	7^113073+82	95558	Lelio R Paula	04/2016
3943	2^317251+465	95503	Lelio R Paula	03/2016
3944	19^74684+58	95503	Lelio R Paula	06/2016
3945	(2^317250-7)/339	95500	Lelio R Paula	07/2013
3946	6^122718-79	95494	Lelio R Paula	05/2016
3947	2^317141-110491	95469	Enzo Doria	05/2014
3948	2^317094+76309	95455	Enzo Doria	05/2016
3949	2^317085+95	95453	Lelio R Paula	11/2012
3950	(17*10^95451-377)/9	95452	Robert Price	11/2017
3951	2^317057-109551	95444	Enzo Doria	04/2014
3952	3^200026+28	95437	Lelio R Paula	05/2016
3953	2^317024+93	95434	Donovan Johnson	06/2008
3954	2^316999+1605	95427	Lelio R Paula	03/2016
3955	2^316995-110427	95426	Enzo Doria	05/2014
3957	2^316937+177	95408	Lelio R Paula	11/2012
3956	4*10^95407+91	95408	Robert Price	11/2017
3958	2^316908+1915	95399	Lelio R Paula	03/2016
3959	2^316894+99	95395	Lelio R Paula	11/2012
3960	6^122547+11	95361	Lelio R Paula	05/2016
3961	2^316771+82875	95358	Lelio R Paula	03/2016
3963	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
3962	1*10^95326+57	95327	Robert Price	03/2011
3964	10^95326-393687	95326	Patrick De Geest	09/2013
3965	(3^199803+4)/479539	95325	Lelio R Paula	04/2013
3966	2^316654-109481	95323	Enzo Doria	04/2014
3967	8*10^95316+51	95317	Robert Price	05/2017
3968	(50^56099+43^56099)/93	95309	Serge Batalov	12/2016
3969	(23*2^316559+1)/3925	95292	Lelio R Paula	09/2013
3970	(71*10^95277-539)/9	95278	Robert Price	11/2017
3971	19^74503-56	95271	Lelio R Paula	06/2016
3972	11^91475-4380	95262	Enzo Doria	01/2013
3973	(62*10^95251-611)/9	95252	Robert Price	05/2017
3974	(2^316321-509203)/69377	95218	Lelio R Paula	06/2013
3975	(79*10^95214-43)/9	95215	Erik Branger	11/2013
3976	(9*2^316233-1)/1751	95194	Lelio R Paula	02/2014
3977	5*2^316213+9	95191	Lelio R Paula	08/2014
3978	2^316205-1848163	95188	Enzo Doria	07/2015
3979	2^316185-2787913	95182	Enzo Doria	04/2016
3980	(9787*2^316142-1)/3	95172	Lelio R Paula	04/2015
3981	2^316140-5	95168	Henri Lifchitz	02/2006
3982	(15185*2^316117-1)/3	95165	Lelio R Paula	04/2015
3983	(34*10^95153-7)/9/19/19157	95149	Makoto Morimoto	05/2016
3984	2^316069+76817	95147	Enzo Doria	05/2016
3985	(199*10^95134-7)/3	95136	Robert Price	02/2017
3986	2^316027-97305	95134	Lelio R Paula	03/2016
3987	2^316006-2798051	95128	Enzo Doria	04/2016
3988	2^315921-2797603	95102	Enzo Doria	04/2016
3989	2*10^95095+63	95096	Robert Price	10/2017
3990	2^315857+1299	95083	Lelio R Paula	03/2016
3991	14^82955-43	95078	Lelio R Paula	06/2016
3992	(2*10^95072-17)/3	95072	Robert Price	08/2014
3993	2^315727+65	95044	Lelio R Paula	11/2012
3994	2^315725+1885757	95043	Enzo Doria	03/2017
3995	1*10^94983+21	94984	Robert Price	03/2011
3996	10^94983-717	94983	Patrick De Geest	08/2013
3997	17^77187-82	94975	Lelio R Paula	07/2016
3998	3*10^94964+37	94965	Robert Price	10/2017
3999	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
4000	2^315423-110329	94952	Enzo Doria	05/2014

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PRP Records

Probable Primes Top 10000

(252402 PRPs in the top)