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	(4^167933+17)/3	101106	Robert Price	02/2017
3753	2^335858+153	101104	Lelio R Paula	10/2009
3752	(2^335872-2776871)/5/5/479	101104	Tony Prest / Never Odd Or Even	01/2019
3754	(2^335872-2758787)/23/31/20809	101101	Tony Prest / Never Odd Or Even	01/2019
3755	(2^335872-2795083)/3/3/113/283/148367	101097	Tony Prest / Never Odd Or Even	01/2019
3756	6^129918-35	101096	Lelio R Paula	10/2016
3757	3^211885-70	101095	Lelio R Paula	09/2016
3759	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
3758	(2^335872-2794771)/3/5/5/61/232312440293	101093	Tony Prest / Never Odd Or Even	01/2019
3760	2^335818-20033	101092	Enzo Doria	06/2013
3761	2^335813-110083	101090	Enzo Doria	04/2014
3762	2^335804+2155	101088	Lelio R Paula	09/2016
3763	(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021	101087	Tony Prest / Never Odd Or Even	01/2019
3764	2^335784-16145	101082	Enzo Doria	04/2013
3765	11^97051+62	101069	Lelio R Paula	10/2016
3766	3*10^101065+11	101066	Robert Price	07/2018
3767	27820^4293+4293^27820	101064	Hans Havermann	10/2018
3768	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
3769	2^335658-94395	101044	Lelio R Paula	09/2016
3770	24514^13215+13215^24514	101024	Hans Havermann	11/2018
3771	2^335586+169	101022	Lelio R Paula	10/2009
3772	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
3773	(19*10^100997+737)/9	100998	Robert Price	07/2018
3774	47599!2+1024	100991	Robert Price	02/2015
3775	2^335468-18629	100986	Enzo Doria	05/2013
3776	2^335454-20961	100982	Enzo Doria	06/2013
3777	10^100978+61	100979	Lelio R Paula	09/2016
3778	10^100978-156437	100978	Patrick De Geest	11/2016
3779	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
3780	2^335403-1859167	100967	Enzo Doria	03/2016
3781	23599^18976+18976^23599	100962	Hans Havermann	10/2018
3782	9*2^335364-5	100956	Lelio R Paula	08/2014
3783	2^335349+72287	100951	Enzo Doria	04/2016
3784	2^335329+16095	100945	Lelio R Paula	09/2016
3785	232823#+233663	100937	Makoto Morimoto	10/2017
3786	(232823#+10141)/(10141*1674461)	100927	Makoto Morimoto	06/2019
3787	2^335237-20893	100917	Enzo Doria	06/2013
3788	2^335222-19337	100912	Enzo Doria	05/2013
3789	2^335222-109985	100912	Enzo Doria	04/2014
3790	2^335182-17237	100900	Enzo Doria	05/2013
3791	2^335043-16737	100858	Enzo Doria	05/2013
3792	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
3793	2^335038-20633	100857	Enzo Doria	06/2013
3794	2^335031+1873373	100855	Enzo Doria	06/2016
3795	23489^19650+19650^23489	100847	Hans Havermann	10/2018
3796	3^211354-8816	100842	Enzo Doria	05/2014
3797	2^334984-112757	100841	Enzo Doria	06/2014
3798	29451^2648+2648^29451	100809	Hans Havermann	09/2018
3799	25583^8716+8716^25583	100806	Hans Havermann	08/2018
3801	2^334857+48527	100803	Lelio R Paula	08/2011
3800	12^93406+29	100803	Lelio R Paula	10/2016
3802	28780^3179+3179^28780	100796	Hans Havermann	09/2018
3803	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
3804	2^334809-13	100788	Lelio R Paula	04/2011
3805	(82*10^100780-1)/9	100781	Robert Price	12/2014
3806	31395^1622+1622^31395	100780	Hans Havermann	09/2018
3807	(2^334779+47)/5	100778	Lelio R Paula	12/2013
3808	2^334751+2049	100771	Lelio R Paula	09/2016
3809	13^90443-98	100749	Lelio R Paula	10/2016
3810	(7*10^100737+71)/3	100738	Robert Price	05/2018
3811	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
3812	15^85639-28	100720	Lelio R Paula	10/2016
3813	27068^5259+5259^27068	100718	Hans Havermann	08/2018
3814	2^334562+577294575	100711	Lelio R Paula	09/2016
3815	4*3^211077-5	100710	Lelio R Paula	08/2014
3816	2^334524+145	100702	Lelio R Paula	07/2009
3817	27648^4375+4375^27648	100666	Hans Havermann	09/2018
3818	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
3819	2^334294-113111	100633	Enzo Doria	07/2014
3820	25581^8582+8582^25581	100626	Hans Havermann	08/2018
3821	6^129308-17723	100622	Enzo Doria	03/2013
3822	6^129305+95	100619	Lelio R Paula	10/2016
3823	2^334244-1167	100618	Lelio R Paula	09/2016
3824	(76*10^100611+77)/9	100612	Robert Price	10/2019
3825	(26*10^100566+49)/3	100567	Robert Price	08/2019
3826	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
3827	24885^10984+10984^24885	100555	Hans Havermann	07/2018
3828	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
3829	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
3830	23578^18367+18367^23578	100538	Hans Havermann	07/2018
3831	13^90251+24	100535	Lelio R Paula	10/2016
3832	2^333963+789	100533	Lelio R Paula	08/2011
3833	2^333919-1840087	100520	Enzo Doria	06/2015
3834	2^333911+72623	100518	Enzo Doria	04/2016
3835	24605^12168+12168^24605	100517	Hans Havermann	08/2018
3836	18^80064-67	100503	Lelio R Paula	10/2016
3837	5^143742-48	100472	Lelio R Paula	10/2016
3838	24095^14784+14784^24095	100472	Hans Havermann	08/2018
3839	2^333757-112123	100471	Enzo Doria	06/2014
3840	27358^4693+4693^27358	100444	Hans Havermann	07/2018
3841	8*10^100439-51	100440	Robert Price	08/2019
3842	2^333603-108861	100425	Enzo Doria	03/2014
3843	9*7^118818-2	100414	Lelio R Paula	11/2014
3844	2^333546-17097	100408	Enzo Doria	05/2013
3845	17^81597+72	100401	Lelio R Paula	10/2016
3846	p(20559)#/2+8	100384	Robert Price	01/2017
3847	11^96390-24	100380	Lelio R Paula	10/2016
3849	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
3848	23565^18136+18136^23565	100353	Hans Havermann	07/2018
3850	2^333354+763	100350	Lelio R Paula	08/2011
3851	(25*10^100343-67)/3	100344	Robert Price	06/2019
3852	2^333289-109483	100330	Enzo Doria	04/2014
3853	2^333240-2790209	100316	Enzo Doria	03/2016
3854	23601^17798+17798^23601	100314	Hans Havermann	05/2018
3856	(2^333227-2^166614+1)/5	100311		11/2006
3855	2^333225+719	100311	Lelio R Paula	08/2011
3857	2^333221-2785333	100310	Enzo Doria	10/2015
3858	76^53332-75	100308	Norbert Schneider	02/2015
3859	6^128892-17573	100298	Enzo Doria	03/2013
3860	(47*10^100283-119)/9	100284	Robert Price	05/2019
3861	2^333105-113215	100275	Enzo Doria	07/2014
3862	(31*2^333102+1)/2375	100272	Lelio R Paula	11/2013
3863	4*10^100257-83	100258	Robert Price	10/2018
3864	17^81476-74	100253	Lelio R Paula	10/2016
3865	23392^19207+19207^23392	100199	Hans Havermann	06/2018
3866	17^81417-16	100180	Theodore Burton	11/2005
3867	2^332739-113215	100165	Enzo Doria	07/2014
3868	2^332730-1865621	100162	Enzo Doria	03/2016
3869	91^51127-2	100160	Lelio R Paula	09/2013
3870	15^85159-32	100155	Lelio R Paula	10/2016
3871	6^128661+97	100118	Lelio R Paula	10/2016
3872	19^78285+40	100108	Lelio R Paula	07/2016
3873	6^128640+5	100102	Lelio R Paula	11/2014
3874	(14*10^100075+61)/3	100076	Robert Price	12/2018
3875	28562^3189+3189^28562	100072	Hans Havermann	05/2018
3876	6^128565-127	100044	Lelio R Paula	08/2016
3877	2^332309-133	100035	Lelio R Paula	02/2011
3878	2^332307+731	100035	Lelio R Paula	07/2011
3879	2^332301+12927	100033	Lelio R Paula	04/2013
3880	23406^18781+18781^23406	100031	Hans Havermann	04/2018
3881	2^332277-4573	100026	Yves Minet	03/2019
3882	12^92684-13	100023	Lelio R Paula	07/2016
3883	78557*2^332193+55669	100005	Jorge Menendez	04/2019
3884	78557*2^332192+72689	100005	Jorge Menendez	04/2019
3885	10^100003+45799	100004	Stefano Morozzi	04/2019
3886	10^100003+155461	100004	Stefano Morozzi	04/2019
3887	10^100003+211389	100004	Stefano Morozzi	04/2019
3888	10^100003+381027	100004	Stefano Morozzi	04/2019
3889	10^100003+540703	100004	Stefano Morozzi	04/2019
3890	10^100003+823977	100004	Stefano Morozzi	04/2019
3902	10^100002+236023	100003	Stefano Morozzi	05/2018
3903	10^100002+433741	100003	Stefano Morozzi	05/2018
3891	2^332202+104659	100003	Stefano Morozzi	04/2019
3892	2^332202+857539	100003	Stefano Morozzi	04/2019
3893	2^332202+181773	100003	Stefano Morozzi	04/2019
3894	2^332202+687543	100003	Stefano Morozzi	04/2019
3895	2^332202+941595	100003	Stefano Morozzi	04/2019
3896	2^332202+445813	100003	Stefano Morozzi	04/2019
3897	2^332202+1599727	100003	Stefano Morozzi	04/2019
3898	2^332202+1389567	100003	Stefano Morozzi	04/2019
3899	2^332202+1206315	100003	Stefano Morozzi	04/2019
3900	2^332202+1958647	100003	Stefano Morozzi	04/2019
3901	10^100003-562857	100003	Patrick De Geest	07/2019
3904	(10^100002-1)/9-10^33441	100002	Akihiko Yoshida	03/2018
3905	(10^100002-1)/9-10^44692	100002	Akihiko Yoshida	03/2018
3906	10^100002-249519	100002	Patrick De Geest	07/2018
3907	10^100001+314199	100002	Patrick De Geest	07/2018
3971	25206!+p(4114)	100001	Henri Lifchitz	09/2005
3972	25206!-p(5447)	100001	Henri Lifchitz	10/2005
3973	25206!-p(12402)	100001	Henri Lifchitz	04/2006
3974	25206!-p(16290)	100001	Henri Lifchitz	09/2006
3975	25206!-p(19647)	100001	Henri Lifchitz	02/2007
3976	2^332194+11473	100001	Henri Lifchitz	03/2007
3966	10^100000+342909	100001	Milton L. Brown	12/2007
3967	10^100000+346579	100001	Robert Price	04/2012
3968	10^100000+829767	100001	Robert Price	05/2012
3969	10^100000+871899	100001	Robert Price	05/2012
3970	10^100000+1475997	100001	Robert Price	07/2012
3959	10^100000+1751769	100001	Robert Price	08/2012
3960	10^100000+2155489	100001	Robert Price	10/2012
3961	10^100000+2483527	100001	Robert Price	12/2012
3962	10^100000+2503087	100001	Robert Price	12/2012
3963	10^100000+2686179	100001	Robert Price	12/2012
3964	10^100000+2688933	100001	Robert Price	12/2012
3965	10^100000+3667159	100001	Robert Price	08/2013
3956	10^100000+3938473	100001	Robert Price	05/2015
3957	10^100000+3979761	100001	Robert Price	05/2015
3958	10^100000+4293973	100001	Robert Price	09/2015
3924	10^100000+4858267	100001	Robert Price	12/2015
3925	10^100000+5113299	100001	Robert Price	02/2016
3926	10^100000+5169411	100001	Robert Price	02/2016
3935	10^100000+5354043	100001	Robert Price	05/2016
3936	10^100000+5717979	100001	Robert Price	05/2016
3937	10^100000+6080631	100001	Robert Price	07/2016
3938	10^100000+6308469	100001	Robert Price	07/2016
3939	10^100000+6512023	100001	Robert Price	08/2016
3940	10^100000+6596557	100001	Robert Price	08/2016
3941	10^100000+7115409	100001	Robert Price	10/2016
3942	10^100000+7235803	100001	Robert Price	10/2016
3943	10^100000+7867333	100001	Robert Price	12/2016
3944	10^100000+8743093	100001	Robert Price	02/2017
3945	10^100000+8955391	100001	Robert Price	03/2017
3946	10^100000+9180019	100001	Robert Price	03/2017
3947	10^100000+9225987	100001	Robert Price	04/2017
3948	10^100000+9265587	100001	Robert Price	04/2017
3949	10^100000+9287049	100001	Robert Price	04/2017
3950	10^100000+9425053	100001	Robert Price	05/2017
3951	10^100000+9450769	100001	Robert Price	05/2017
3952	10^100000+9528747	100001	Robert Smith	05/2017
3953	10^100000+9548071	100001	Robert Price	06/2017
3954	10^100000+10064287	100001	Robert Price	08/2017
3955	10^100000+10229569	100001	Robert Price	10/2017
3908	10^100000+11187931	100001	Robert Price	03/2018
3909	10^100000+11264721	100001	Robert Price	04/2018
3910	10^100000+11477661	100001	Robert Price	05/2018
3911	10^100000+11644653	100001	Robert Price	07/2018
3912	10^100001-431439	100001	Patrick De Geest	07/2018
3913	10^100000+11769399	100001	Robert Price	08/2018
3914	10^100000+11848159	100001	Robert Price	08/2018
3915	10^100000+11863467	100001	Robert Price	08/2018
3927	10^100000+11992051	100001	Robert Price	09/2018
3928	2^332196-1-2*29696	100001	Matt Stath	11/2018
3929	10^100000+12363957	100001	Robert Price	11/2018
3916	2^332196+1+2*17152	100001	Matt Stath	12/2018
3917	10^100000+12778033	100001	Robert Price	02/2019
3918	10^100000+13581679	100001	Robert Price	05/2019
3919	10^100000+13613199	100001	Robert Price	05/2019
3920	10^100000+13752327	100001	Robert Price	05/2019
3921	10^100000+14139243	100001	Robert Price	06/2019
3922	10^100000+14151057	100001	Robert Price	06/2019
3923	10^100000+14218923	100001	Robert Price	06/2019
3930	10^100000+15136771	100001	Robert Price	09/2019
3931	10^100000+15219873	100001	Robert Price	10/2019
3932	10^100000+15274039	100001	Robert Price	10/2019
3933	10^100000+15394069	100001	Robert Price	10/2019
3934	10^100000+15547119	100001	Robert Price	10/2019
3977	10^99999+309403	100000	Daniel Heuer	01/2004
3978	10^100000-260199	100000	Patrick De Geest	01/2010
3979	10^99999-59511	99999	Patrick De Geest	07/2009
3980	2^332141-113073	99985	Enzo Doria	07/2014
3982	(3^209561+2)/728101255	99978	Lelio R Paula	09/2013
3981	23827^15702+15702^23827	99978	Hans Havermann	04/2018
3983	2^332085+1865897	99968	Enzo Doria	03/2016
3984	(9787*2^332070-1)/936402369	99959	Lelio R Paula	05/2015
3985	2^332023+191	99949	Lelio R Paula	02/2011
3986	2^331938+71149	99924	Enzo Doria	04/2016
3987	2^331932-78795	99922	Lelio R Paula	09/2016
3988	2^331921+771	99919	Lelio R Paula	01/2013
3989	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
3990	2^331860-114989	99900	Enzo Doria	05/2015
3991	2^331746-11655	99866	Lelio R Paula	09/2016
3992	11^95891-28	99861	Lelio R Paula	08/2016
3993	(2^331694-5)/11	99849	Lelio R Paula	10/2013
3994	(3^209246+7)/64	99834	Lelio R Paula	09/2013
3995	25062^9617+9617^25062	99823	Hans Havermann	04/2018
3996	15^84866-52	99811	Lelio R Paula	08/2016
3997	13^89600+30	99810	Lelio R Paula	08/2016
3998	22950^22309+22309^22950	99798	Hans Havermann	03/2018
3999	5^142772-38	99794	Lelio R Paula	08/2016
4000	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013

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PRP Records

Probable Primes Top 10000

(255244 PRPs in the top)