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	2^331256-57	99718	Lelio R Paula	12/2012
3752	28192^3443+3443^28192	99714	Hans Havermann	03/2018
3753	2^331185+737	99697	Lelio R Paula	01/2013
3754	(4*10^99693+149)/9	99693	Robert Price	03/2017
3755	2^331154+1880527	99688	Enzo Doria	10/2016
3757	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
3756	24354^12385+12385^24354	99679	Hans Havermann	03/2018
3758	2^331110+1870459	99675	Enzo Doria	05/2016
3759	5*2^331075+7	99665	Lelio R Paula	08/2014
3760	25776^7351+7351^25776	99659	Hans Havermann	02/2018
3761	(16*10^99656-31)/3	99657	Robert Price	03/2016
3762	2^330968+345	99632	Lelio R Paula	09/2016
3764	2*5^142528-7	99624	Lelio R Paula	11/2014
3763	2^330942+77329	99624	Enzo Doria	05/2016
3765	14^86914-99	99615	Lelio R Paula	08/2016
3766	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
3767	22971^21692+21692^22971	99610	Hans Havermann	03/2018
3768	2^330845+71687	99595	Enzo Doria	04/2016
3769	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
3770	24494^11613+11613^24494	99567	Hans Havermann	03/2018
3771	2^330735+8415	99562	Lelio R Paula	09/2016
3772	2^330720+74071	99557	Enzo Doria	04/2016
3773	31^66738-2	99531	Lelio R Paula	09/2013
3774	7*3^208567+4	99513	Lelio R Paula	08/2014
3775	(13*10^99508+47)/3	99509	Robert Price	01/2017
3776	2^330553+779	99507	Lelio R Paula	01/2013
3777	15^84606-94	99505	Lelio R Paula	08/2016
3778	6^127858+47	99493	Lelio R Paula	08/2016
3779	5^142337+48	99490	Lelio R Paula	08/2016
3780	7^117724-20	99489	Lelio R Paula	08/2016
3781	(29*10^99474-17)/3	99475	Erik Branger	09/2014
3782	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
3783	(68*10^99441+7)/3	99443	Robert Price	03/2016
3784	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
3785	23839^14802+14802^23839	99417	Hans Havermann	02/2018
3786	(2*10^99408+529)/9	99408	Robert Price	01/2017
3787	53^57646-2	99398	Lelio R Paula	09/2013
3788	2^330165+1870025	99390	Enzo Doria	05/2016
3789	2^330142-155	99383	Lelio R Paula	12/2012
3790	2^330088-115259	99367	Enzo Doria	06/2015
3792	24216^12671+12671^24216	99354	Hans Havermann	01/2018
3791	Phi(200548,10)/3208769	99354	Makoto Kamada	04/2019
3793	(746*10^99303+1)/9	99305	Robert Price	02/2017
3794	3^208107+40	99293	Lelio R Paula	08/2016
3795	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
3796	8*3^208093+5	99287	Lelio R Paula	08/2014
3797	5^142043+56	99284	Lelio R Paula	08/2016
3798	22*10^99275+7	99277	Robert Price	04/2016
3799	2^329778+1876189	99274	Enzo Doria	07/2016
3800	(10^99239-13)/3	99239	Robert Price	02/2017
3801	3^207987+62	99236	Lelio R Paula	08/2016
3802	2^329638+49	99231	Lelio R Paula	12/2012
3803	7^117413-18	99226	Lelio R Paula	08/2016
3804	2^329586-458903	99216	Enzo Doria	04/2015
3805	2^329553+101	99206	Lelio R Paula	12/2012
3806	2^329551-112897	99205	Enzo Doria	06/2014
3807	(3^207925+7)/50	99204	Lelio R Paula	09/2013
3808	6^127458-17993	99182	Enzo Doria	03/2013
3809	27197^4428+4428^27197	99166	Hans Havermann	10/2017
3810	(46*10^99143-1)/9	99144	Robert Price	12/2014
3811	7*10^99133+69	99134	Robert Price	10/2017
3812	18^78968-3065	99127	Enzo Doria	03/2013
3813	25927^6654+6654^25927	99122	Hans Havermann	10/2017
3814	2^329259+189	99117	Lelio R Paula	12/2012
3815	8*10^99113+39	99114	Robert Price	01/2017
3816	6^127364+77	99109	Lelio R Paula	08/2016
3817	6^127285+13	99047	Lelio R Paula	08/2016
3818	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
3819	2^329007+73283	99041	Enzo Doria	04/2016
3820	5*3^207543-8	99024	Lelio R Paula	08/2014
3821	2^328885+149	99005	Lelio R Paula	12/2012
3822	23392^17075+17075^23392	99004	Hans Havermann	09/2017
3823	(2^328879-9)/119	99001	Lelio R Paula	10/2013
3824	5^141618+54	98987	Lelio R Paula	08/2016
3825	8*10^98982+51	98983	Robert Price	05/2017
3826	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
3827	2^328794-2797601	98977	Enzo Doria	04/2016
3828	6^127176+5	98963	Lelio R Paula	11/2014
3829	24262^11989+11989^24262	98960	Hans Havermann	09/2017
3830	2^328700-109709	98949	Enzo Doria	04/2014
3831	46711!2-2^46711	98916	Robert Price	09/2015
3832	9*7^117037+4	98909	Lelio R Paula	11/2014
3833	127^47012+126	98905	Norbert Schneider	01/2019
3834	(10^98890+149)/3	98890	Serge Batalov	12/2014
3835	22775^21978+21978^22775	98889	Hans Havermann	08/2017
3836	2^328497-216933	98888	Enzo Doria	05/2014
3837	2^328487+32769	98885	Lelio R Paula	08/2016
3838	3^207250-112358	98884	Enzo Doria	06/2014
3839	13^88754-90	98867	Lelio R Paula	08/2016
3840	2^328406+709	98861	Lelio R Paula	02/2013
3841	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
3842	7^116976+76	98857	Lelio R Paula	08/2016
3843	2^328335+1155	98839	Lelio R Paula	08/2016
3845	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
3844	287^40210+40210^287	98832	Norbert Schneider	11/2014
3846	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
3847	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
3848	65^54491+48	98788	Lelio R Paula	04/2016
3849	3^207042+98	98785	Lelio R Paula	08/2016
3850	3^206977-112756	98754	Enzo Doria	07/2014
3851	7^116846-50	98747	Lelio R Paula	08/2016
3852	2^327967-28635	98728	Lelio R Paula	08/2016
3853	707^34642+34642^707	98710	Norbert Schneider	12/2017
3854	6^126850-47	98709	Lelio R Paula	08/2016
3855	8*6^126830-7	98694	Lelio R Paula	11/2014
3856	11^94770-270	98693	Enzo Doria	08/2012
3857	2^327832+43	98688	Lelio R Paula	12/2012
3858	2^327795+761	98677	Lelio R Paula	02/2013
3859	10^98669+147411	98670	Patrick De Geest	11/2016
3861	10^98669-9^(98669-1)	98669	Robert Price	05/2016
3860	10^98669-105249	98669	Patrick De Geest	11/2016
3862	2^327671-109801	98639	Enzo Doria	04/2014
3863	5^141090-14	98618	Lelio R Paula	08/2016
3864	20^75799+47	98617	Lelio R Paula	08/2016
3865	2^327515-1017	98592	Lelio R Paula	08/2016
3866	6^126692+97681	98586	Mike Oakes	04/2011
3867	2^327467-741	98578	Lelio R Paula	08/2016
3868	(2^327329+9)/19	98535	Lelio R Paula	10/2013
3869	7^116577-66	98519	Lelio R Paula	08/2016
3870	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
3871	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
3872	2^327162-66945	98486	Lelio R Paula	08/2016
3873	4*10^98472-3	98473	Erik Branger	11/2013
3874	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
3875	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
3876	13^88363+94	98432	Lelio R Paula	08/2016
3877	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
3878	6^126481+41	98422	Lelio R Paula	08/2016
3879	78*10^98413-7	98415	Robert Price	05/2017
3880	7^116416+46	98383	Lelio R Paula	08/2016
3881	7^116407-24	98376	Lelio R Paula	07/2016
3882	439^37228+37228^439	98374	Norbert Schneider	08/2018
3883	2^326782-1860671	98372	Enzo Doria	03/2016
3884	17^79948+58	98372	Lelio R Paula	08/2016
3885	3^206143-98	98356	Lelio R Paula	08/2016
3886	8*5^140705+7	98350	Lelio R Paula	11/2014
3887	2^326585+11	98312	Lelio R Paula	12/2012
3888	2^326582-459161	98311	Enzo Doria	05/2015
3889	(2^326548+9)/5	98301	Lelio R Paula	10/2013
3890	2^326538+71659	98298	Enzo Doria	04/2016
3891	15^83575-58	98292	Lelio R Paula	08/2016
3892	10^98288+3	98289	Robert Price	03/2011
3893	10^98288-117017	98288	Patrick De Geest	11/2011
3894	(44*10^98284-719)/9	98285	Robert Price	12/2017
3895	2^326421-2797573	98263	Enzo Doria	04/2016
3896	2^326401+16095	98257	Lelio R Paula	07/2016
3897	7^116240-116240^7	98235	Norbert Schneider	05/2017
3898	17^79826-78	98222	Lelio R Paula	08/2016
3899	2^326268-809	98217	Yves Minet	04/2011
3900	(418*10^98199+23)/9	98201	Robert Price	08/2017
3901	12*10^98198-7	98200	Robert Price	11/2017
3902	15^83496-76	98199	Lelio R Paula	08/2016
3903	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
3904	9*5^140471-4	98186	Lelio R Paula	11/2014
3905	2^326069-2383	98157	Yves Minet	10/2013
3906	2^325973+1185	98128	Lelio R Paula	07/2016
3907	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
3908	2^325945-1847269	98120	Enzo Doria	07/2015
3909	8*10^98111-67	98112	Robert Price	10/2017
3910	2^325866+15	98096	Lelio R Paula	12/2012
3911	2^325765+1974305	98066	Enzo Doria	06/2016
3912	2^325733-58695	98056	Lelio R Paula	07/2016
3913	2^325717-3645	98051	Lelio R Paula	07/2016
3914	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
3915	(7*10^98007-13)/3	98008	Robert Price	06/2016
3916	2^325512-459959	97989	Enzo Doria	05/2015
3917	(3^205354-8)/17	97978	Lelio R Paula	09/2013
3918	2^325433+76817	97966	Enzo Doria	05/2016
3919	5*10^97963+81	97964	Robert Price	08/2017
3920	2^325390-109061	97953	Enzo Doria	04/2014
3921	13^87921+24	97940	Lelio R Paula	08/2016
3922	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
3923	2^325215+12909	97900	Lelio R Paula	07/2016
3924	7*10^97874-69	97875	Robert Price	01/2017
3926	(17^79537+5^79537)/22	97865	Robert Price	06/2013
3925	15^83212+22	97865	Lelio R Paula	08/2016
3927	2^325087-109057	97861	Enzo Doria	04/2014
3928	2^325074+1870657	97858	Enzo Doria	05/2016
3929	2^325066-2111	97855	Yves Minet	08/2013
3930	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
3931	18^77944-89	97841	Lelio R Paula	07/2016
3932	119^47136+118	97833	Norbert Schneider	09/2018
3933	6^125720-17663	97830	Enzo Doria	02/2013
3934	2^324972-2069	97827	Yves Minet	05/2013
3935	2^324944-2788319	97818	Enzo Doria	03/2016
3937	4*10^97799-9	97800	Erik Branger	11/2013
3936	2^324882+577294575	97800	Lelio R Paula	09/2016
3938	2^324863-1867921	97794	Enzo Doria	04/2016
3939	6^125662-18473	97785	Enzo Doria	03/2013
3940	12^90604+11	97779	Lelio R Paula	07/2016
3941	5^139830+24	97737	Lelio R Paula	04/2016
3942	2^324612+1155	97718	Lelio R Paula	07/2016
3943	19^76404-44	97702	Lelio R Paula	07/2016
3944	2^324505-2983	97686	Yves Minet	04/2011
3945	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
3946	6^125488-17843	97649	Enzo Doria	02/2013
3947	7^115515-2	97622	Lelio R Paula	09/2013
3948	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
3949	6^125418-5	97595	Lelio R Paula	11/2014
3950	2^324076+1155	97557	Lelio R Paula	07/2016
3951	(2^324074+9)/13	97555	Lelio R Paula	10/2013
3952	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
3953	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
3954	2^323946+73939	97518	Enzo Doria	04/2016
3955	2^323937+1866947	97515	Enzo Doria	03/2016
3956	6^125290-18533	97495	Enzo Doria	03/2013
3957	2^323845+101	97488	Lelio R Paula	12/2012
3958	18^77662+65	97487	Lelio R Paula	07/2016
3959	2^323772+76771	97466	Enzo Doria	05/2016
3960	2^323765-112213	97463	Enzo Doria	06/2014
3961	2^323720-6555	97450	Lelio R Paula	07/2016
3962	2^323694-1860401	97442	Enzo Doria	03/2016
3963	20^74886+3	97429	Lelio R Paula	06/2016
3965	3*10^97399+73	97400	Robert Price	04/2016
3964	7^115252-50	97400	Lelio R Paula	07/2016
3966	224737#+393581	97389	Nicolas PALAU	12/2016
3967	(26*10^97353+31)/3	97354	Robert Price	07/2016
3968	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
3969	(38*10^97329+187)/9	97330	Robert Price	11/2017
3970	p(19982)#/2-1024	97293	Robert Price	09/2017
3971	6^125021-85	97286	Lelio R Paula	08/2016
3972	2^323164-47355	97283	Lelio R Paula	07/2016
3973	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
3974	2^323054-6555	97249	Lelio R Paula	07/2016
3975	9*10^97247-29	97248	Robert Price	05/2017
3976	(31*10^97242+41)/9	97243	Robert Price	04/2015
3977	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
3978	12^90098-41	97233	Lelio R Paula	07/2016
3979	2^322928-216929	97212	Enzo Doria	05/2014
3980	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
3981	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
3982	2^322725+75761	97150	Enzo Doria	04/2016
3983	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
3984	(41*10^97085+373)/9	97086	Robert Price	04/2017
3985	2^322413+77	97056	Lelio R Paula	12/2012
3986	2^322406+177	97054	Lelio R Paula	12/2012
3987	(14*10^97044+31)/9	97045	Robert Price	02/2015
3988	2^322302+255255	97023	Lelio R Paula	07/2016
3989	2^322196-113093	96991	Enzo Doria	07/2014
3990	2^322000-1861469	96932	Enzo Doria	03/2016
3991	2^321971-112747	96923	Enzo Doria	06/2014
3992	11^93062-92	96915	Lelio R Paula	06/2016
3993	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
3994	3^203051+34	96880	Lelio R Paula	05/2016
3995	2*10^96867-51	96868	Robert Price	11/2017
3996	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
3997	2^321716-2786939	96847	Enzo Doria	03/2016
3999	2^321701-113053	96842	Enzo Doria	07/2014
3998	2^321700-28635	96842	Lelio R Paula	06/2016
4000	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014

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PRP Records

Probable Primes Top 10000

(252675 PRPs in the top)