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	2^333963+789	100533	Lelio R Paula	08/2011
3752	2^333919-1840087	100520	Enzo Doria	06/2015
3753	2^333911+72623	100518	Enzo Doria	04/2016
3754	24605^12168+12168^24605	100517	Hans Havermann	08/2018
3755	18^80064-67	100503	Lelio R Paula	10/2016
3756	5^143742-48	100472	Lelio R Paula	10/2016
3757	24095^14784+14784^24095	100472	Hans Havermann	08/2018
3758	2^333757-112123	100471	Enzo Doria	06/2014
3759	27358^4693+4693^27358	100444	Hans Havermann	07/2018
3760	8*10^100439-51	100440	Robert Price	08/2019
3761	2^333603-108861	100425	Enzo Doria	03/2014
3762	9*7^118818-2	100414	Lelio R Paula	11/2014
3763	2^333546-17097	100408	Enzo Doria	05/2013
3764	17^81597+72	100401	Lelio R Paula	10/2016
3765	p(20559)#/2+8	100384	Robert Price	01/2017
3766	11^96390-24	100380	Lelio R Paula	10/2016
3767	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
3768	23565^18136+18136^23565	100353	Hans Havermann	07/2018
3769	2^333354+763	100350	Lelio R Paula	08/2011
3770	(25*10^100343-67)/3	100344	Robert Price	06/2019
3771	2^333289-109483	100330	Enzo Doria	04/2014
3772	2^333240-2790209	100316	Enzo Doria	03/2016
3773	23601^17798+17798^23601	100314	Hans Havermann	05/2018
3775	(2^333227-2^166614+1)/5	100311		11/2006
3774	2^333225+719	100311	Lelio R Paula	08/2011
3776	2^333221-2785333	100310	Enzo Doria	10/2015
3777	76^53332-75	100308	Norbert Schneider	02/2015
3778	6^128892-17573	100298	Enzo Doria	03/2013
3779	(47*10^100283-119)/9	100284	Robert Price	05/2019
3780	2^333105-113215	100275	Enzo Doria	07/2014
3781	(31*2^333102+1)/2375	100272	Lelio R Paula	11/2013
3782	4*10^100257-83	100258	Robert Price	10/2018
3783	17^81476-74	100253	Lelio R Paula	10/2016
3784	23392^19207+19207^23392	100199	Hans Havermann	06/2018
3785	17^81417-16	100180	Theodore Burton	11/2005
3786	2^332739-113215	100165	Enzo Doria	07/2014
3787	2^332730-1865621	100162	Enzo Doria	03/2016
3788	91^51127-2	100160	Lelio R Paula	09/2013
3789	15^85159-32	100155	Lelio R Paula	10/2016
3790	6^128661+97	100118	Lelio R Paula	10/2016
3791	19^78285+40	100108	Lelio R Paula	07/2016
3792	6^128640+5	100102	Lelio R Paula	11/2014
3793	(14*10^100075+61)/3	100076	Robert Price	12/2018
3794	28562^3189+3189^28562	100072	Hans Havermann	05/2018
3795	6^128565-127	100044	Lelio R Paula	08/2016
3796	2^332309-133	100035	Lelio R Paula	02/2011
3797	2^332307+731	100035	Lelio R Paula	07/2011
3798	2^332301+12927	100033	Lelio R Paula	04/2013
3799	23406^18781+18781^23406	100031	Hans Havermann	04/2018
3800	2^332277-4573	100026	Yves Minet	03/2019
3801	12^92684-13	100023	Lelio R Paula	07/2016
3802	78557*2^332193+55669	100005	Jorge Menendez	04/2019
3803	78557*2^332192+72689	100005	Jorge Menendez	04/2019
3804	10^100003+45799	100004	Stefano Morozzi	04/2019
3805	10^100003+155461	100004	Stefano Morozzi	04/2019
3806	10^100003+211389	100004	Stefano Morozzi	04/2019
3807	10^100003+381027	100004	Stefano Morozzi	04/2019
3808	10^100003+540703	100004	Stefano Morozzi	04/2019
3809	10^100003+823977	100004	Stefano Morozzi	04/2019
3821	10^100002+236023	100003	Stefano Morozzi	05/2018
3822	10^100002+433741	100003	Stefano Morozzi	05/2018
3810	2^332202+104659	100003	Stefano Morozzi	04/2019
3811	2^332202+857539	100003	Stefano Morozzi	04/2019
3812	2^332202+181773	100003	Stefano Morozzi	04/2019
3813	2^332202+687543	100003	Stefano Morozzi	04/2019
3814	2^332202+941595	100003	Stefano Morozzi	04/2019
3815	2^332202+445813	100003	Stefano Morozzi	04/2019
3816	2^332202+1599727	100003	Stefano Morozzi	04/2019
3817	2^332202+1389567	100003	Stefano Morozzi	04/2019
3818	2^332202+1206315	100003	Stefano Morozzi	04/2019
3819	2^332202+1958647	100003	Stefano Morozzi	04/2019
3820	10^100003-562857	100003	Patrick De Geest	07/2019
3823	(10^100002-1)/9-10^33441	100002	Akihiko Yoshida	03/2018
3824	(10^100002-1)/9-10^44692	100002	Akihiko Yoshida	03/2018
3825	10^100002-249519	100002	Patrick De Geest	07/2018
3826	10^100001+314199	100002	Patrick De Geest	07/2018
3885	25206!+p(4114)	100001	Henri Lifchitz	09/2005
3886	25206!-p(5447)	100001	Henri Lifchitz	10/2005
3887	25206!-p(12402)	100001	Henri Lifchitz	04/2006
3888	25206!-p(16290)	100001	Henri Lifchitz	09/2006
3889	25206!-p(19647)	100001	Henri Lifchitz	02/2007
3890	2^332194+11473	100001	Henri Lifchitz	03/2007
3878	10^100000+342909	100001	Milton L. Brown	12/2007
3842	10^100000+346579	100001	Robert Price	04/2012
3843	10^100000+829767	100001	Robert Price	05/2012
3844	10^100000+871899	100001	Robert Price	05/2012
3845	10^100000+1475997	100001	Robert Price	07/2012
3835	10^100000+1751769	100001	Robert Price	08/2012
3836	10^100000+2155489	100001	Robert Price	10/2012
3837	10^100000+2483527	100001	Robert Price	12/2012
3838	10^100000+2503087	100001	Robert Price	12/2012
3839	10^100000+2686179	100001	Robert Price	12/2012
3840	10^100000+2688933	100001	Robert Price	12/2012
3841	10^100000+3667159	100001	Robert Price	08/2013
3879	10^100000+3938473	100001	Robert Price	05/2015
3880	10^100000+3979761	100001	Robert Price	05/2015
3881	10^100000+4293973	100001	Robert Price	09/2015
3882	10^100000+4858267	100001	Robert Price	12/2015
3883	10^100000+5113299	100001	Robert Price	02/2016
3884	10^100000+5169411	100001	Robert Price	02/2016
3870	10^100000+5354043	100001	Robert Price	05/2016
3871	10^100000+5717979	100001	Robert Price	05/2016
3872	10^100000+6080631	100001	Robert Price	07/2016
3873	10^100000+6308469	100001	Robert Price	07/2016
3874	10^100000+6512023	100001	Robert Price	08/2016
3875	10^100000+6596557	100001	Robert Price	08/2016
3876	10^100000+7115409	100001	Robert Price	10/2016
3877	10^100000+7235803	100001	Robert Price	10/2016
3849	10^100000+7867333	100001	Robert Price	12/2016
3850	10^100000+8743093	100001	Robert Price	02/2017
3851	10^100000+8955391	100001	Robert Price	03/2017
3852	10^100000+9180019	100001	Robert Price	03/2017
3853	10^100000+9225987	100001	Robert Price	04/2017
3854	10^100000+9265587	100001	Robert Price	04/2017
3855	10^100000+9287049	100001	Robert Price	04/2017
3856	10^100000+9425053	100001	Robert Price	05/2017
3857	10^100000+9450769	100001	Robert Price	05/2017
3858	10^100000+9528747	100001	Robert Smith	05/2017
3859	10^100000+9548071	100001	Robert Price	06/2017
3860	10^100000+10064287	100001	Robert Price	08/2017
3861	10^100000+10229569	100001	Robert Price	10/2017
3827	10^100000+11187931	100001	Robert Price	03/2018
3828	10^100000+11264721	100001	Robert Price	04/2018
3829	10^100000+11477661	100001	Robert Price	05/2018
3830	10^100000+11644653	100001	Robert Price	07/2018
3831	10^100001-431439	100001	Patrick De Geest	07/2018
3832	10^100000+11769399	100001	Robert Price	08/2018
3833	10^100000+11848159	100001	Robert Price	08/2018
3834	10^100000+11863467	100001	Robert Price	08/2018
3846	10^100000+11992051	100001	Robert Price	09/2018
3847	2^332196-1-2*29696	100001	Matt Stath	11/2018
3848	10^100000+12363957	100001	Robert Price	11/2018
3862	2^332196+1+2*17152	100001	Matt Stath	12/2018
3863	10^100000+12778033	100001	Robert Price	02/2019
3864	10^100000+13581679	100001	Robert Price	05/2019
3865	10^100000+13613199	100001	Robert Price	05/2019
3866	10^100000+13752327	100001	Robert Price	05/2019
3867	10^100000+14139243	100001	Robert Price	06/2019
3868	10^100000+14151057	100001	Robert Price	06/2019
3869	10^100000+14218923	100001	Robert Price	06/2019
3891	10^99999+309403	100000	Daniel Heuer	01/2004
3892	10^100000-260199	100000	Patrick De Geest	01/2010
3893	10^99999-59511	99999	Patrick De Geest	07/2009
3894	2^332141-113073	99985	Enzo Doria	07/2014
3896	(3^209561+2)/728101255	99978	Lelio R Paula	09/2013
3895	23827^15702+15702^23827	99978	Hans Havermann	04/2018
3897	2^332085+1865897	99968	Enzo Doria	03/2016
3898	(9787*2^332070-1)/936402369	99959	Lelio R Paula	05/2015
3899	2^332023+191	99949	Lelio R Paula	02/2011
3900	2^331938+71149	99924	Enzo Doria	04/2016
3901	2^331932-78795	99922	Lelio R Paula	09/2016
3902	2^331921+771	99919	Lelio R Paula	01/2013
3903	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
3904	2^331860-114989	99900	Enzo Doria	05/2015
3905	2^331746-11655	99866	Lelio R Paula	09/2016
3906	11^95891-28	99861	Lelio R Paula	08/2016
3907	(2^331694-5)/11	99849	Lelio R Paula	10/2013
3908	(3^209246+7)/64	99834	Lelio R Paula	09/2013
3909	25062^9617+9617^25062	99823	Hans Havermann	04/2018
3910	15^84866-52	99811	Lelio R Paula	08/2016
3911	13^89600+30	99810	Lelio R Paula	08/2016
3912	22950^22309+22309^22950	99798	Hans Havermann	03/2018
3913	5^142772-38	99794	Lelio R Paula	08/2016
3914	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
3915	2^331416-331416+1	99767	Robert Price	10/2014
3916	2^331256-57	99718	Lelio R Paula	12/2012
3917	28192^3443+3443^28192	99714	Hans Havermann	03/2018
3918	2^331185+737	99697	Lelio R Paula	01/2013
3919	(4*10^99693+149)/9	99693	Robert Price	03/2017
3920	2^331154+1880527	99688	Enzo Doria	10/2016
3922	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
3921	24354^12385+12385^24354	99679	Hans Havermann	03/2018
3923	2^331110+1870459	99675	Enzo Doria	05/2016
3924	5*2^331075+7	99665	Lelio R Paula	08/2014
3925	25776^7351+7351^25776	99659	Hans Havermann	02/2018
3926	(16*10^99656-31)/3	99657	Robert Price	03/2016
3927	2^330968+345	99632	Lelio R Paula	09/2016
3929	2*5^142528-7	99624	Lelio R Paula	11/2014
3928	2^330942+77329	99624	Enzo Doria	05/2016
3930	14^86914-99	99615	Lelio R Paula	08/2016
3931	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
3932	22971^21692+21692^22971	99610	Hans Havermann	03/2018
3933	2^330845+71687	99595	Enzo Doria	04/2016
3934	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
3935	24494^11613+11613^24494	99567	Hans Havermann	03/2018
3936	2^330735+8415	99562	Lelio R Paula	09/2016
3937	2^330720+74071	99557	Enzo Doria	04/2016
3938	31^66738-2	99531	Lelio R Paula	09/2013
3939	7*3^208567+4	99513	Lelio R Paula	08/2014
3940	(13*10^99508+47)/3	99509	Robert Price	01/2017
3941	2^330553+779	99507	Lelio R Paula	01/2013
3942	15^84606-94	99505	Lelio R Paula	08/2016
3943	6^127858+47	99493	Lelio R Paula	08/2016
3944	5^142337+48	99490	Lelio R Paula	08/2016
3945	7^117724-20	99489	Lelio R Paula	08/2016
3946	(29*10^99474-17)/3	99475	Erik Branger	09/2014
3947	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
3948	(68*10^99441+7)/3	99443	Robert Price	03/2016
3949	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
3950	23839^14802+14802^23839	99417	Hans Havermann	02/2018
3951	(2*10^99408+529)/9	99408	Robert Price	01/2017
3952	53^57646-2	99398	Lelio R Paula	09/2013
3953	2^330165+1870025	99390	Enzo Doria	05/2016
3954	2^330142-155	99383	Lelio R Paula	12/2012
3955	2^330088-115259	99367	Enzo Doria	06/2015
3957	24216^12671+12671^24216	99354	Hans Havermann	01/2018
3956	Phi(200548,10)/3208769	99354	Makoto Kamada	04/2019
3958	(746*10^99303+1)/9	99305	Robert Price	02/2017
3959	3^208107+40	99293	Lelio R Paula	08/2016
3960	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
3961	8*3^208093+5	99287	Lelio R Paula	08/2014
3962	5^142043+56	99284	Lelio R Paula	08/2016
3963	22*10^99275+7	99277	Robert Price	04/2016
3964	2^329778+1876189	99274	Enzo Doria	07/2016
3965	(10^99239-13)/3	99239	Robert Price	02/2017
3966	3^207987+62	99236	Lelio R Paula	08/2016
3967	2^329638+49	99231	Lelio R Paula	12/2012
3968	7^117413-18	99226	Lelio R Paula	08/2016
3969	2^329586-458903	99216	Enzo Doria	04/2015
3970	2^329553+101	99206	Lelio R Paula	12/2012
3971	2^329551-112897	99205	Enzo Doria	06/2014
3972	(3^207925+7)/50	99204	Lelio R Paula	09/2013
3973	6^127458-17993	99182	Enzo Doria	03/2013
3974	27197^4428+4428^27197	99166	Hans Havermann	10/2017
3975	(46*10^99143-1)/9	99144	Robert Price	12/2014
3976	7*10^99133+69	99134	Robert Price	10/2017
3977	18^78968-3065	99127	Enzo Doria	03/2013
3978	25927^6654+6654^25927	99122	Hans Havermann	10/2017
3979	2^329259+189	99117	Lelio R Paula	12/2012
3980	8*10^99113+39	99114	Robert Price	01/2017
3981	6^127364+77	99109	Lelio R Paula	08/2016
3982	6^127285+13	99047	Lelio R Paula	08/2016
3983	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
3984	2^329007+73283	99041	Enzo Doria	04/2016
3985	5*3^207543-8	99024	Lelio R Paula	08/2014
3986	2^328885+149	99005	Lelio R Paula	12/2012
3987	23392^17075+17075^23392	99004	Hans Havermann	09/2017
3988	(2^328879-9)/119	99001	Lelio R Paula	10/2013
3989	5^141618+54	98987	Lelio R Paula	08/2016
3990	8*10^98982+51	98983	Robert Price	05/2017
3991	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
3992	2^328794-2797601	98977	Enzo Doria	04/2016
3993	6^127176+5	98963	Lelio R Paula	11/2014
3994	24262^11989+11989^24262	98960	Hans Havermann	09/2017
3995	2^328700-109709	98949	Enzo Doria	04/2014
3996	46711!2-2^46711	98916	Robert Price	09/2015
3997	9*7^117037+4	98909	Lelio R Paula	11/2014
3998	127^47012+126	98905	Norbert Schneider	01/2019
3999	(10^98890+149)/3	98890	Serge Batalov	12/2014
4000	22775^21978+21978^22775	98889	Hans Havermann	08/2017

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PRP Records

Probable Primes Top 10000

(253476 PRPs in the top)