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 ?
3751	(50^56099+43^56099)/93	95309	Serge Batalov	12/2016
3752	(23*2^316559+1)/3925	95292	Lelio R Paula	09/2013
3753	(71*10^95277-539)/9	95278	Robert Price	11/2017
3754	19^74503-56	95271	Lelio R Paula	06/2016
3755	11^91475-4380	95262	Enzo Doria	01/2013
3756	(62*10^95251-611)/9	95252	Robert Price	05/2017
3757	(2^316321-509203)/69377	95218	Lelio R Paula	06/2013
3758	(79*10^95214-43)/9	95215	Erik Branger	11/2013
3759	(9*2^316233-1)/1751	95194	Lelio R Paula	02/2014
3760	5*2^316213+9	95191	Lelio R Paula	08/2014
3761	2^316205-1848163	95188	Enzo Doria	07/2015
3762	2^316185-2787913	95182	Enzo Doria	04/2016
3763	(9787*2^316142-1)/3	95172	Lelio R Paula	04/2015
3764	2^316140-5	95168	Henri Lifchitz	02/2006
3765	(15185*2^316117-1)/3	95165	Lelio R Paula	04/2015
3766	(34*10^95153-7)/9/19/19157	95149	Makoto Morimoto	05/2016
3767	2^316069+76817	95147	Enzo Doria	05/2016
3768	(199*10^95134-7)/3	95136	Robert Price	02/2017
3769	2^316027-97305	95134	Lelio R Paula	03/2016
3770	2^316006-2798051	95128	Enzo Doria	04/2016
3771	2^315921-2797603	95102	Enzo Doria	04/2016
3772	2*10^95095+63	95096	Robert Price	10/2017
3773	2^315857+1299	95083	Lelio R Paula	03/2016
3774	14^82955-43	95078	Lelio R Paula	06/2016
3775	(2*10^95072-17)/3	95072	Robert Price	08/2014
3776	2^315727+65	95044	Lelio R Paula	11/2012
3777	2^315725+1885757	95043	Enzo Doria	03/2017
3778	1*10^94983+21	94984	Robert Price	03/2011
3779	10^94983-717	94983	Patrick De Geest	08/2013
3780	17^77187-82	94975	Lelio R Paula	07/2016
3781	3*10^94964+37	94965	Robert Price	10/2017
3782	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
3783	2^315423-110329	94952	Enzo Doria	05/2014
3784	11^91169-7230	94943	Enzo Doria	02/2013
3785	7*10^94938+61	94939	Robert Price	02/2017
3786	2^315351+1025	94931	Lelio R Paula	03/2016
3787	2^315350-112253	94930	Enzo Doria	06/2014
3790	((1001327^(15817)+1)/1001328)	94906	Faysal YAtim	10/2010
3788	2^315268+7	94906	Lelio R Paula	10/2012
3789	11^91133+62	94906	Lelio R Paula	05/2016
3791	30^64244+41	94897	Lelio R Paula	08/2012
3792	(151*10^94885-7)/9	94887	Robert Price	07/2017
3793	4^157583+22147	94875	Mike Oakes	01/2011
3794	2^315098+123	94854	Lelio R Paula	11/2012
3795	3^198791-34	94848	Robert Price	11/2013
3796	3*2^315067+7	94846	Lelio R Paula	08/2014
3797	(9*2^315057+1)/73	94841	Lelio R Paula	09/2013
3798	(16*10^94822+53)/3	94823	Robert Price	12/2016
3799	8*6^121849-7	94818	Lelio R Paula	10/2014
3800	(85*10^94802+473)/9	94803	Robert Price	03/2017
3801	2^314870-108761	94786	Enzo Doria	03/2014
3802	5*2^314841-3	94778	Lelio R Paula	08/2014
3803	6^121772+113	94758	Lelio R Paula	05/2016
3804	6^121756-16253	94745	Enzo Doria	02/2013
3805	2^314718-112793	94740	Enzo Doria	06/2014
3806	2^314697-1847293	94734	Enzo Doria	07/2015
3807	2^314548-249	94689	Yves Minet	02/2012
3808	5^135469+42	94689	Lelio R Paula	04/2016
3809	gcd(V(1137755),5F(227551)(F(227551)-1)+1)	94676	Serge Batalov	04/2015
3810	(2*10^94604+547)/9	94604	Robert Price	10/2017
3811	3*2^314152+5	94570	Lelio R Paula	08/2014
3812	2*6^121530-5	94570	Lelio R Paula	10/2014
3813	7*10^94563+87	94564	Robert Price	11/2016
3814	2^314114-109677	94558	Enzo Doria	04/2014
3815	(218389#+240867)/(311811)	94557	Makoto Morimoto	10/2017
3816	2^314059+76583	94542	Enzo Doria	05/2016
3817	2^314041-4035	94536	Lelio R Paula	03/2016
3818	(7*2^314003-11)/15	94524	Renaud Lifchitz	03/2011
3819	11^90760-4710	94517	Enzo Doria	01/2013
3820	(7*2^313926-1)/148821	94497	Lelio R Paula	02/2014
3821	94*10^94493-3	94495	Robert Price	11/2016
3822	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
3823	(F(375345)^2+L(375345)^2)/4	94477	Henri Lifchitz	10/2017
3824	7^111792-32	94476	Lelio R Paula	04/2016
3825	11^90680-5850	94434	Enzo Doria	01/2013
3826	2^313675-110125	94426	Enzo Doria	04/2014
3827	(2999*29^64556-2427)/4	94410	Curtis Bright	05/2015
3828	2^313609-112225	94406	Enzo Doria	06/2014
3829	2^313584+72901	94399	Enzo Doria	04/2016
3830	2^313510-112865	94376	Enzo Doria	06/2014
3831	7*10^94373+87	94374	Robert Price	11/2016
3832	(9^98897+8^98897)/17	94371	Robert Price	12/2012
3833	2^313453-114703	94359	Enzo Doria	04/2015
3834	8*10^94357-51	94358	Robert Price	10/2017
3835	(379*10^94337-1)/9	94339	Robert Price	08/2017
3836	2^313344-313344+1	94326	Robert Price	10/2014
3837	20^72481-49	94300	Lelio R Paula	05/2016
3838	44725!2+128	94289	Robert Price	03/2015
3839	4*10^94286+9	94287	Robert Price	05/2015
3840	17^76621+24	94279	Lelio R Paula	07/2016
3841	2^313156-112859	94270	Enzo Doria	06/2014
3842	6^121130-59	94258	Lelio R Paula	05/2016
3843	3^197542+28	94252	Robert Price	11/2013
3844	(3^197521+2)/51655	94237	Lelio R Paula	04/2013
3845	2^313045-5955	94236	Lelio R Paula	03/2016
3846	(67*10^94212+23)/9	94213	Ray Chandler	02/2011
3847	2^312909-1865203	94195	Enzo Doria	03/2016
3848	2^312848-149	94177	Lelio R Paula	11/2012
3849	4^156403-77597	94164	Mike Oakes	04/2011
3850	18^75004-85	94151	Lelio R Paula	06/2016
3851	19^73622-48	94145	Lelio R Paula	06/2016
3852	(11^90397-3^90397)/8	94138	Robert Price	04/2011
3853	(3^197287+5)/16	94129	Lelio R Paula	04/2013
3854	12^87212-37	94118	Lelio R Paula	06/2016
3855	11^90376+76	94117	Lelio R Paula	05/2016
3856	(6^120946-11)/5	94114	Paul Bourdelais	11/2011
3857	(10^94096+191)/3	94096	Robert Price	11/2017
3858	2^312562-112685	94091	Enzo Doria	06/2014
3859	137^44026-2	94072	Lelio R Paula	10/2017
3860	2^312404-869688105	94043	Lelio R Paula	09/2016
3861	2^312387+2793533	94038	Enzo Doria	03/2016
3863	10^94016+91	94017	Robert Price	04/2011
3862	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
3865	10^94016-188963	94016	Patrick De Geest	08/2013
3864	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
3866	6^120802+7661	94003	Mike Oakes	04/2011
3867	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
3868	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
3869	2^312201+51	93982	Lelio R Paula	11/2012
3870	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
3871	3^196892+58	93942	Lelio R Paula	05/2016
3872	2^312060+18915	93940	Lelio R Paula	03/2016
3873	2^311992-16209	93919	Enzo Doria	04/2013
3874	(85^48677+1)/86	93917	Paul Bourdelais	08/2017
3875	2^311965-39	93911	Lelio R Paula	11/2012
3876	2^311920-111689	93898	Enzo Doria	05/2014
3877	7*10^93887-47	93888	Robert Price	02/2017
3878	12^86965-13	93851	Lelio R Paula	06/2016
3879	2^311705+16095	93833	Lelio R Paula	03/2016
3880	2^311665-81	93821	Lelio R Paula	11/2012
3881	730^32761+32761^730	93806	Norbert Schneider	09/2017
3882	11^90073+92	93802	Lelio R Paula	05/2016
3883	6*10^93792+41	93793	Robert Price	01/2017
3884	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
3885	12^86900-77	93781	Lelio R Paula	06/2016
3886	2^311508-109769	93774	Enzo Doria	04/2014
3887	2^311486-1859621	93767	Enzo Doria	03/2016
3888	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
3889	2^311471+311469	93763	Renaud Lifchitz	01/2003
3890	(88*10^93760-1)/3	93762	Robert Price	10/2017
3891	2^311426+79459	93749	Enzo Doria	06/2016
3892	2^311294+5775	93709	Lelio R Paula	03/2016
3893	2^311252-1017	93697	Lelio R Paula	03/2016
3894	2^311247-112041	93695	Enzo Doria	06/2014
3895	7*10^93692-83	93693	Robert Price	09/2017
3896	2^311205-109645	93683	Enzo Doria	04/2014
3897	5^134027-84	93681	Lelio R Paula	04/2016
3898	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
3899	(2^311027-2^155514+1)/5	93628		11/2006
3900	3^196192-28	93608	Robert Price	12/2013
3901	216091#+261433	93606	Makoto Morimoto	12/2015
3902	5^133917+68	93604	Lelio R Paula	04/2016
3903	2^310924-1709	93598	Yves Minet	03/2013
3904	(266*10^93577-11)/3	93579	Robert Price	09/2016
3905	(16*10^93577+161)/3	93578	Robert Price	05/2016
3906	3^196113-56	93570	Lelio R Paula	04/2016
3907	2^310806-110345	93562	Enzo Doria	05/2014
3908	3^196093+86	93561	Lelio R Paula	04/2016
3909	2^310780-2327	93555	Yves Minet	10/2013
3910	30^63332+41	93550	Lelio R Paula	08/2012
3911	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
3912	8*5^133807+7	93528	Lelio R Paula	10/2014
3913	2^310686+8193	93526	Lelio R Paula	03/2016
3914	2^310646+63	93514	Lelio R Paula	11/2012
3915	(77*10^93508+31)/9	93509	Robert Price	10/2015
3916	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
3917	(2*10^93497+7)/9	93497	Erik Branger	03/2011
3918	3^195958-112852	93496	Enzo Doria	07/2014
3919	2^310583+16385	93495	Lelio R Paula	03/2016
3920	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
3921	9*7^110614+2	93481	Lelio R Paula	11/2014
3922	2^310469-8295	93461	Lelio R Paula	03/2016
3923	2^310459-1159	93458	Yves Minet	11/2012
3924	6^120075-95	93437	Lelio R Paula	05/2016
3925	2^310289+98327	93407	Yves Minet	11/2010
3926	2^310217-113143	93385	Enzo Doria	07/2014
3927	7^110494-68	93379	Lelio R Paula	04/2016
3928	2^310184-113093	93375	Enzo Doria	07/2014
3929	2^310180-110417	93374	Enzo Doria	05/2014
3930	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
3931	3^195669+68	93358	Lelio R Paula	04/2016
3932	10^93356+91	93357	Robert Price	04/2011
3933	10^93356-28313	93356	Patrick De Geest	08/2013
3934	(85*10^93346+23)/9	93347	Robert Price	11/2015
3935	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
3936	3^195556+8680	93304	Lelio R Paula	04/2016
3937	2^309942-109991	93302	Enzo Doria	04/2014
3938	2^309926-1867301	93298	Enzo Doria	03/2016
3939	2^309924+85951	93297	Yves Minet	03/2011
3940	(86*10^93263-77)/9	93264	Robert Price	05/2016
3941	6^119836-125	93251	Lelio R Paula	05/2016
3942	(77*10^93249-257)/9	93250	Robert Price	10/2017
3943	3^195430-2	93244	Theodore Burton	02/2007
3944	(13*10^93236+47)/3	93237	Robert Price	01/2017
3945	(67*10^93226-7)/3	93228	Robert Price	10/2017
3946	(86*10^93217-221)/9	93218	Robert Price	06/2017
3947	2^309637-16329	93211	Enzo Doria	04/2013
3948	(41*10^93207+49)/9	93208	Robert Price	04/2016
3949	14^81312-57	93194	Lelio R Paula	06/2016
3950	41^57783-40	93192	Theodore Burton	02/2007
3951	3*10^93179-97	93180	Robert Price	08/2017
3952	5*7^110252-4	93175	Lelio R Paula	11/2014
3953	2^309380-27	93133	Lelio R Paula	11/2012
3954	23*10^93116-7	93118	Robert Price	03/2016
3955	(29*10^93082+1)/3	93083	Robert Price	11/2015
3956	(58*10^93062-13)/9	93063	Robert Price	09/2015
3957	2^309131+1869383	93058	Enzo Doria	05/2016
3958	2^309066-93	93039	Lelio R Paula	11/2012
3959	2^309063-113269	93038	Enzo Doria	07/2014
3960	3^194965+16	93022	Robert Price	10/2013
3961	2^308979+1869143	93012	Enzo Doria	05/2016
3962	5^133064+54	93008	Lelio R Paula	04/2016
3963	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
3964	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
3965	(2*10^92976-17)/3	92976	Robert Price	08/2014
3966	2^308809+37967	92961	Phil Moore	03/2008
3967	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
3968	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
3969	2^308650+513	92913	Lelio R Paula	02/2016
3970	5*7^109936+6	92908	Lelio R Paula	10/2014
3971	2*10^92897+89	92898	Robert Price	07/2016
3972	12^86073-29	92889	Lelio R Paula	06/2016
3973	2^308566-117	92888	Lelio R Paula	11/2012
3974	(17*10^92869-11)/3	92870	Robert Price	07/2015
3975	2^308459+75431	92856	Enzo Doria	04/2016
3976	2^308426-1866377	92846	Enzo Doria	03/2016
3977	(96^46831-1)/95	92830	Paul Bourdelais	09/2017
3978	2^308349-112111	92823	Enzo Doria	06/2014
3979	9*10^92821+19	92822	Robert Price	05/2016
3980	2^308337-75	92819	Lelio R Paula	11/2012
3981	4*3^194508+7	92805	Lelio R Paula	08/2014
3982	22*25^66379-113	92796	Curtis Bright	05/2015
3983	11^89101-1080	92790	Enzo Doria	12/2012
3984	2^308236-1867859	92789	Enzo Doria	04/2016
3985	12^85963+25	92770	Lelio R Paula	06/2016
3986	7^109750-66	92750	Lelio R Paula	04/2016
3987	9*10^92742+11	92743	Robert Kinser	01/2017
3988	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
3989	2^307997-110655	92717	Enzo Doria	05/2014
3990	L(443609)	92709	Renaud Lifchitz	11/2003
3991	10^92691+9	92692	Robert Price	03/2011
3992	10^92691-252291	92691	Patrick De Geest	08/2013
3993	2^307879-2521	92681	Yves Minet	07/2014
3994	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
3995	14^80831+47	92643	Lelio R Paula	06/2016
3996	15^78744+92	92611	Lelio R Paula	07/2016
3997	65^51083-64	92610	Norbert Schneider	11/2014
3998	6^118996-16943	92597	Enzo Doria	02/2013
3999	(16*10^92591+41)/3	92592	Robert Price	10/2017
4000	(3^194014-7)/2	92568	Lelio R Paula	04/2013

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Probable Primes Top 10000

(211563 PRPs in the top)