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 ?
3778	25206!+p(4114)	100001	Henri Lifchitz	09/2005
3779	25206!-p(5447)	100001	Henri Lifchitz	10/2005
3780	25206!-p(12402)	100001	Henri Lifchitz	04/2006
3781	25206!-p(16290)	100001	Henri Lifchitz	09/2006
3782	25206!-p(19647)	100001	Henri Lifchitz	02/2007
3783	2^332194+11473	100001	Henri Lifchitz	03/2007
3777	10^100000+342909	100001	Milton L. Brown	12/2007
3759	10^100000+346579	100001	Robert Price	04/2012
3760	10^100000+829767	100001	Robert Price	05/2012
3761	10^100000+871899	100001	Robert Price	05/2012
3762	10^100000+1475997	100001	Robert Price	07/2012
3752	10^100000+1751769	100001	Robert Price	08/2012
3753	10^100000+2155489	100001	Robert Price	10/2012
3754	10^100000+2483527	100001	Robert Price	12/2012
3755	10^100000+2503087	100001	Robert Price	12/2012
3756	10^100000+2686179	100001	Robert Price	12/2012
3757	10^100000+2688933	100001	Robert Price	12/2012
3758	10^100000+3667159	100001	Robert Price	08/2013
3766	10^100000+3938473	100001	Robert Price	05/2015
3767	10^100000+3979761	100001	Robert Price	05/2015
3768	10^100000+4293973	100001	Robert Price	09/2015
3774	10^100000+4858267	100001	Robert Price	12/2015
3775	10^100000+5113299	100001	Robert Price	02/2016
3776	10^100000+5169411	100001	Robert Price	02/2016
3784	10^100000+5354043	100001	Robert Price	05/2016
3785	10^100000+5717979	100001	Robert Price	05/2016
3786	10^100000+6080631	100001	Robert Price	07/2016
3787	10^100000+6308469	100001	Robert Price	07/2016
3788	10^100000+6512023	100001	Robert Price	08/2016
3789	10^100000+6596557	100001	Robert Price	08/2016
3790	10^100000+7115409	100001	Robert Price	10/2016
3791	10^100000+7235803	100001	Robert Price	10/2016
3792	10^100000+7867333	100001	Robert Price	12/2016
3793	10^100000+8743093	100001	Robert Price	02/2017
3794	10^100000+8955391	100001	Robert Price	03/2017
3795	10^100000+9180019	100001	Robert Price	03/2017
3796	10^100000+9225987	100001	Robert Price	04/2017
3797	10^100000+9265587	100001	Robert Price	04/2017
3798	10^100000+9287049	100001	Robert Price	04/2017
3799	10^100000+9425053	100001	Robert Price	05/2017
3800	10^100000+9450769	100001	Robert Price	05/2017
3801	10^100000+9528747	100001	Robert Smith	05/2017
3802	10^100000+9548071	100001	Robert Price	06/2017
3803	10^100000+10064287	100001	Robert Price	08/2017
3804	10^100000+10229569	100001	Robert Price	10/2017
3751	10^100000+11863467	100001	Robert Price	08/2018
3763	10^100000+11992051	100001	Robert Price	09/2018
3764	2^332196-1-2*29696	100001	Matt Stath	11/2018
3765	10^100000+12363957	100001	Robert Price	11/2018
3769	2^332196+1+2*17152	100001	Matt Stath	12/2018
3770	10^100000+12778033	100001	Robert Price	02/2019
3771	10^100000+13581679	100001	Robert Price	05/2019
3772	10^100000+13613199	100001	Robert Price	05/2019
3773	10^100000+13752327	100001	Robert Price	05/2019
3806	10^99999+309403	100000	Daniel Heuer	01/2004
3805	10^100000-260199	100000	Patrick De Geest	01/2010
3807	10^99999-59511	99999	Patrick De Geest	07/2009
3808	2^332141-113073	99985	Enzo Doria	07/2014
3809	(3^209561+2)/728101255	99978	Lelio R Paula	09/2013
3810	23827^15702+15702^23827	99978	Hans Havermann	04/2018
3811	2^332085+1865897	99968	Enzo Doria	03/2016
3812	(9787*2^332070-1)/936402369	99959	Lelio R Paula	05/2015
3813	2^332023+191	99949	Lelio R Paula	02/2011
3814	2^331938+71149	99924	Enzo Doria	04/2016
3815	2^331932-78795	99922	Lelio R Paula	09/2016
3816	2^331921+771	99919	Lelio R Paula	01/2013
3817	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
3818	2^331860-114989	99900	Enzo Doria	05/2015
3819	2^331746-11655	99866	Lelio R Paula	09/2016
3820	11^95891-28	99861	Lelio R Paula	08/2016
3821	(2^331694-5)/11	99849	Lelio R Paula	10/2013
3822	(3^209246+7)/64	99834	Lelio R Paula	09/2013
3823	25062^9617+9617^25062	99823	Hans Havermann	04/2018
3824	15^84866-52	99811	Lelio R Paula	08/2016
3825	13^89600+30	99810	Lelio R Paula	08/2016
3826	22950^22309+22309^22950	99798	Hans Havermann	03/2018
3827	5^142772-38	99794	Lelio R Paula	08/2016
3828	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
3829	2^331416-331416+1	99767	Robert Price	10/2014
3830	2^331256-57	99718	Lelio R Paula	12/2012
3831	28192^3443+3443^28192	99714	Hans Havermann	03/2018
3832	2^331185+737	99697	Lelio R Paula	01/2013
3833	(4*10^99693+149)/9	99693	Robert Price	03/2017
3834	2^331154+1880527	99688	Enzo Doria	10/2016
3836	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
3835	24354^12385+12385^24354	99679	Hans Havermann	03/2018
3837	2^331110+1870459	99675	Enzo Doria	05/2016
3838	5*2^331075+7	99665	Lelio R Paula	08/2014
3839	25776^7351+7351^25776	99659	Hans Havermann	02/2018
3840	(16*10^99656-31)/3	99657	Robert Price	03/2016
3841	2^330968+345	99632	Lelio R Paula	09/2016
3843	2*5^142528-7	99624	Lelio R Paula	11/2014
3842	2^330942+77329	99624	Enzo Doria	05/2016
3844	14^86914-99	99615	Lelio R Paula	08/2016
3845	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
3846	22971^21692+21692^22971	99610	Hans Havermann	03/2018
3847	2^330845+71687	99595	Enzo Doria	04/2016
3848	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
3849	24494^11613+11613^24494	99567	Hans Havermann	03/2018
3850	2^330735+8415	99562	Lelio R Paula	09/2016
3851	2^330720+74071	99557	Enzo Doria	04/2016
3852	31^66738-2	99531	Lelio R Paula	09/2013
3853	7*3^208567+4	99513	Lelio R Paula	08/2014
3854	(13*10^99508+47)/3	99509	Robert Price	01/2017
3855	2^330553+779	99507	Lelio R Paula	01/2013
3856	15^84606-94	99505	Lelio R Paula	08/2016
3857	6^127858+47	99493	Lelio R Paula	08/2016
3858	5^142337+48	99490	Lelio R Paula	08/2016
3859	7^117724-20	99489	Lelio R Paula	08/2016
3860	(29*10^99474-17)/3	99475	Erik Branger	09/2014
3861	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
3862	(68*10^99441+7)/3	99443	Robert Price	03/2016
3863	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
3864	23839^14802+14802^23839	99417	Hans Havermann	02/2018
3865	(2*10^99408+529)/9	99408	Robert Price	01/2017
3866	53^57646-2	99398	Lelio R Paula	09/2013
3867	2^330165+1870025	99390	Enzo Doria	05/2016
3868	2^330142-155	99383	Lelio R Paula	12/2012
3869	2^330088-115259	99367	Enzo Doria	06/2015
3870	24216^12671+12671^24216	99354	Hans Havermann	01/2018
3871	Phi(200548,10)/3208769	99354	Makoto Kamada	04/2019
3872	(746*10^99303+1)/9	99305	Robert Price	02/2017
3873	3^208107+40	99293	Lelio R Paula	08/2016
3874	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
3875	8*3^208093+5	99287	Lelio R Paula	08/2014
3876	5^142043+56	99284	Lelio R Paula	08/2016
3877	22*10^99275+7	99277	Robert Price	04/2016
3878	2^329778+1876189	99274	Enzo Doria	07/2016
3879	(10^99239-13)/3	99239	Robert Price	02/2017
3880	3^207987+62	99236	Lelio R Paula	08/2016
3881	2^329638+49	99231	Lelio R Paula	12/2012
3882	7^117413-18	99226	Lelio R Paula	08/2016
3883	2^329586-458903	99216	Enzo Doria	04/2015
3884	2^329553+101	99206	Lelio R Paula	12/2012
3885	2^329551-112897	99205	Enzo Doria	06/2014
3886	(3^207925+7)/50	99204	Lelio R Paula	09/2013
3887	6^127458-17993	99182	Enzo Doria	03/2013
3888	27197^4428+4428^27197	99166	Hans Havermann	10/2017
3889	(46*10^99143-1)/9	99144	Robert Price	12/2014
3890	7*10^99133+69	99134	Robert Price	10/2017
3891	18^78968-3065	99127	Enzo Doria	03/2013
3892	25927^6654+6654^25927	99122	Hans Havermann	10/2017
3893	2^329259+189	99117	Lelio R Paula	12/2012
3894	8*10^99113+39	99114	Robert Price	01/2017
3895	6^127364+77	99109	Lelio R Paula	08/2016
3896	6^127285+13	99047	Lelio R Paula	08/2016
3897	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
3898	2^329007+73283	99041	Enzo Doria	04/2016
3899	5*3^207543-8	99024	Lelio R Paula	08/2014
3900	2^328885+149	99005	Lelio R Paula	12/2012
3901	23392^17075+17075^23392	99004	Hans Havermann	09/2017
3902	(2^328879-9)/119	99001	Lelio R Paula	10/2013
3903	5^141618+54	98987	Lelio R Paula	08/2016
3904	8*10^98982+51	98983	Robert Price	05/2017
3905	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
3906	2^328794-2797601	98977	Enzo Doria	04/2016
3907	6^127176+5	98963	Lelio R Paula	11/2014
3908	24262^11989+11989^24262	98960	Hans Havermann	09/2017
3909	2^328700-109709	98949	Enzo Doria	04/2014
3910	46711!2-2^46711	98916	Robert Price	09/2015
3911	9*7^117037+4	98909	Lelio R Paula	11/2014
3912	127^47012+126	98905	Norbert Schneider	01/2019
3913	(10^98890+149)/3	98890	Serge Batalov	12/2014
3914	22775^21978+21978^22775	98889	Hans Havermann	08/2017
3915	2^328497-216933	98888	Enzo Doria	05/2014
3916	2^328487+32769	98885	Lelio R Paula	08/2016
3917	3^207250-112358	98884	Enzo Doria	06/2014
3918	13^88754-90	98867	Lelio R Paula	08/2016
3919	2^328406+709	98861	Lelio R Paula	02/2013
3920	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
3921	7^116976+76	98857	Lelio R Paula	08/2016
3922	2^328335+1155	98839	Lelio R Paula	08/2016
3923	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
3924	287^40210+40210^287	98832	Norbert Schneider	11/2014
3925	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
3926	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
3927	65^54491+48	98788	Lelio R Paula	04/2016
3928	3^207042+98	98785	Lelio R Paula	08/2016
3929	3^206977-112756	98754	Enzo Doria	07/2014
3930	7^116846-50	98747	Lelio R Paula	08/2016
3931	2^327967-28635	98728	Lelio R Paula	08/2016
3932	707^34642+34642^707	98710	Norbert Schneider	12/2017
3933	6^126850-47	98709	Lelio R Paula	08/2016
3934	8*6^126830-7	98694	Lelio R Paula	11/2014
3935	11^94770-270	98693	Enzo Doria	08/2012
3936	2^327832+43	98688	Lelio R Paula	12/2012
3937	2^327795+761	98677	Lelio R Paula	02/2013
3938	10^98669+147411	98670	Patrick De Geest	11/2016
3940	10^98669-9^(98669-1)	98669	Robert Price	05/2016
3939	10^98669-105249	98669	Patrick De Geest	11/2016
3941	2^327671-109801	98639	Enzo Doria	04/2014
3942	5^141090-14	98618	Lelio R Paula	08/2016
3943	20^75799+47	98617	Lelio R Paula	08/2016
3944	2^327515-1017	98592	Lelio R Paula	08/2016
3945	6^126692+97681	98586	Mike Oakes	04/2011
3946	2^327467-741	98578	Lelio R Paula	08/2016
3947	(2^327329+9)/19	98535	Lelio R Paula	10/2013
3948	7^116577-66	98519	Lelio R Paula	08/2016
3949	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
3950	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
3951	2^327162-66945	98486	Lelio R Paula	08/2016
3952	4*10^98472-3	98473	Erik Branger	11/2013
3953	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
3954	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
3955	13^88363+94	98432	Lelio R Paula	08/2016
3956	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
3957	6^126481+41	98422	Lelio R Paula	08/2016
3958	78*10^98413-7	98415	Robert Price	05/2017
3959	7^116416+46	98383	Lelio R Paula	08/2016
3960	7^116407-24	98376	Lelio R Paula	07/2016
3961	439^37228+37228^439	98374	Norbert Schneider	08/2018
3963	2^326782-1860671	98372	Enzo Doria	03/2016
3962	17^79948+58	98372	Lelio R Paula	08/2016
3964	3^206143-98	98356	Lelio R Paula	08/2016
3965	8*5^140705+7	98350	Lelio R Paula	11/2014
3966	2^326585+11	98312	Lelio R Paula	12/2012
3967	2^326582-459161	98311	Enzo Doria	05/2015
3968	(2^326548+9)/5	98301	Lelio R Paula	10/2013
3969	2^326538+71659	98298	Enzo Doria	04/2016
3970	15^83575-58	98292	Lelio R Paula	08/2016
3971	10^98288+3	98289	Robert Price	03/2011
3972	10^98288-117017	98288	Patrick De Geest	11/2011
3973	(44*10^98284-719)/9	98285	Robert Price	12/2017
3974	2^326421-2797573	98263	Enzo Doria	04/2016
3975	2^326401+16095	98257	Lelio R Paula	07/2016
3976	7^116240-116240^7	98235	Norbert Schneider	05/2017
3977	17^79826-78	98222	Lelio R Paula	08/2016
3978	2^326268-809	98217	Yves Minet	04/2011
3979	(418*10^98199+23)/9	98201	Robert Price	08/2017
3980	12*10^98198-7	98200	Robert Price	11/2017
3981	15^83496-76	98199	Lelio R Paula	08/2016
3982	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
3983	9*5^140471-4	98186	Lelio R Paula	11/2014
3984	2^326069-2383	98157	Yves Minet	10/2013
3985	2^325973+1185	98128	Lelio R Paula	07/2016
3986	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
3987	2^325945-1847269	98120	Enzo Doria	07/2015
3988	8*10^98111-67	98112	Robert Price	10/2017
3989	2^325866+15	98096	Lelio R Paula	12/2012
3990	2^325765+1974305	98066	Enzo Doria	06/2016
3991	2^325733-58695	98056	Lelio R Paula	07/2016
3992	2^325717-3645	98051	Lelio R Paula	07/2016
3993	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
3994	(7*10^98007-13)/3	98008	Robert Price	06/2016
3995	2^325512-459959	97989	Enzo Doria	05/2015
3996	(3^205354-8)/17	97978	Lelio R Paula	09/2013
3997	2^325433+76817	97966	Enzo Doria	05/2016
3998	5*10^97963+81	97964	Robert Price	08/2017
3999	2^325390-109061	97953	Enzo Doria	04/2014
4000	13^87921+24	97940	Lelio R Paula	08/2016

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PRP Records

Probable Primes Top 10000

(252932 PRPs in the top)