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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	(2^377131+2018)/2	113528	Stefano Morozzi	09/2020
3752	2^377026-458903	113497	Enzo Doria	04/2015
3753	(2^377014+2202)/2	113493	Stefano Morozzi	09/2020
3754	34791^1828+1828^34791	113488	Hans Havermann	02/2021
3755	(2^376967+258)/2	113479	Stefano Morozzi	09/2020
3756	(29*10^113468-17)/3	113469	Robert Price	09/2019
3757	35^73477-34^73477	113454	Robert Price	05/2012
3758	(14*10^113451-89)/3	113452	Robert Price	05/2020
3759	2^376790+27	113426	Lelio R Paula	03/2013
3760	2^376786-112701	113424	Enzo Doria	06/2014
3761	2^376731+21	113408	Lelio R Paula	03/2013
3762	9*10^113394-73	113395	Robert Price	01/2021
3763	29660^6651+6651^29660	113387	Hans Havermann	01/2021
3765	2^376634+1871245	113379	Enzo Doria	05/2016
3764	(4^188318+17)/3	113379	Robert Price	02/2017
3766	E(29532)/492842728006750534663978950979381235	113367	Thomas Ritschel	01/2021
3767	2^376576-344369	113361	Enzo Doria	07/2015
3768	2^376549-4543	113353	Yves Minet	03/2019
3769	(17*2^376526-1)/223	113345	Lelio R Paula	03/2014
3770	(27*2^376441-1)/811	113319	Lelio R Paula	03/2014
3771	(2^376350+3538)/2	113293	Stefano Morozzi	09/2020
3772	27265^14272+14272^27265	113273	Hans Havermann	02/2021
3773	32174^3315+3315^32174	113269	Hans Havermann	02/2021
3774	(2*10^113248+73)/3	113248	Robert Price	09/2020
3775	2^376128-21237	113226	Enzo Doria	06/2013
3776	5*10^113224-81	113225	Robert Price	01/2019
3777	10^113220+51409	113221	Patrick De Geest	02/2021
3779	10^113220-1000001	113220	Robert Price	08/2020
3778	10^113220-61779	113220	Patrick De Geest	02/2021
3780	(2^376102+1578)/2	113218	Stefano Morozzi	09/2020
3781	(2^375996+3102)/2	113186	Stefano Morozzi	09/2020
3782	37258^1091+1091^37258	113184	Hans Havermann	02/2021
3783	(94*10^113176+11)/3	113178	Robert Price	04/2020
3784	(46*10^113162+521)/9	113163	Robert Price	02/2019
3785	(2^375885+3614)/2	113153	Stefano Morozzi	09/2020
3786	(2^375873+2006)/2	113149	Stefano Morozzi	09/2020
3787	(2^375726+694)/2	113105	Stefano Morozzi	09/2020
3788	26050^21959+21959^26050	113100	Hans Havermann	02/2021
3789	2^375638-1787171	113079	Enzo Doria	03/2016
3790	(2^375563+2178)/2	113056	Stefano Morozzi	09/2020
3791	2^375537+4847	113048	Yves Minet	02/2011
3792	(17^91837+16^91837)/33	113000	Robert Price	08/2013
3793	5F(270343)(F(270343)+1)+1	112997	Serge Batalov	04/2015
3794	2^375350-3221	112992	Yves Minet	07/2011
3795	(13*2^375306+1)/7	112979	Lelio R Paula	03/2014
3796	2^375305+76757	112979	Enzo Doria	05/2016
3797	2^375258+1874989	112964	Enzo Doria	07/2016
3798	(29^77237-1)/28	112950	Robert Price	04/2012
3799	26620^17483+17483^26620	112939	Hans Havermann	01/2021
3800	2^375154+74959	112933	Enzo Doria	04/2016
3801	(266*10^112930-17)/3	112932	Robert Price	07/2020
3802	(2^375134+778)/2	112927	Stefano Morozzi	09/2020
3803	(85*10^112919+293)/9	112920	Robert Price	12/2019
3804	29412^6899+6899^29412	112907	Hans Havermann	02/2021
3805	(2^375022+1210)/2	112893	Stefano Morozzi	09/2020
3806	25992^22039+22039^25992	112889	Hans Havermann	02/2021
3807	2^374993-2787163	112885	Enzo Doria	11/2015
3808	30420^5111+5111^30420	112813	Hans Havermann	02/2021
3809	13699^27268+27268^13699	112800	Norbert Schneider	12/2020
3810	123^53970+2	112793	Lelio R Paula	06/2013
3811	28942^7887+7887^28942	112785	Hans Havermann	01/2021
3812	2^374640-4685	112778	Yves Minet	05/2019
3813	57290^93+93^57290	112775	Hans Havermann	01/2021
3814	(2^374556+682)/2	112753	Stefano Morozzi	09/2020
3815	p(22852)#/2+512	112745	Robert Price	05/2017
3816	(11*10^112742-131)/3	112743	Robert Price	09/2018
3817	2^374441-21049	112718	Enzo Doria	06/2013
3818	4*10^112706-93	112707	Robert Price	07/2020
3819	(2^374321+1)/3	112682	H.&R. Lifchitz	12/2000
3820	(2^374213+1766)/2	112650	Stefano Morozzi	09/2020
3821	(2^374094+2674)/2	112614	Stefano Morozzi	09/2020
3822	(13^101089-1)/12	112607	Paul Bourdelais	03/2010
3823	3^236011-8828	112606	Enzo Doria	05/2014
3824	31854^3427+3427^31854	112602	Hans Havermann	02/2021
3825	(2^373748+1090)/2	112510	Stefano Morozzi	09/2020
3826	(2^373727+1806)/2	112503	Stefano Morozzi	01/2021
3827	27618^11821+11821^27618	112479	Hans Havermann	01/2021
3828	26343^18580+18580^26343	112460	Hans Havermann	01/2021
3829	39^70666+2	112435	Lelio R Paula	11/2013
3830	(134*10^112400+7)/3	112402	Robert Price	02/2020
3831	(2^373365+326)/2	112394	Stefano Morozzi	09/2020
3832	(2^373350-7)/3	112390	Lelio R Paula	03/2014
3833	2^373306-1840931	112377	Enzo Doria	06/2015
3834	(2^373262+270)/2	112363	Stefano Morozzi	09/2020
3835	34409^1842+1842^34409	112356	Hans Havermann	02/2021
3836	(142*10^112352-7)/9	112354	Robert Price	12/2019
3837	25580^24633+24633^25580	112336	Hans Havermann	01/2021
3838	2^373117+1872107	112320	Enzo Doria	05/2016
3839	(2^373083+2226)/2	112309	Stefano Morozzi	01/2021
3840	27963^10376+10376^27963	112301	Hans Havermann	01/2021
3841	2^373040+2792761	112297	Enzo Doria	03/2016
3842	EPrime(112280)	112280	Eric W. Weisstein	10/2010
3843	2^372950+7	112270	Lelio R Paula	03/2013
3844	2^372945+1872167	112268	Enzo Doria	05/2016
3845	36274^1243+1243^36274	112249	Hans Havermann	02/2021
3846	(2^372872+3798)/2	112246	Stefano Morozzi	02/2021
3847	25513^25060+25060^25513	112232	Hans Havermann	02/2021
3848	(2^372754+3094)/2	112210	Stefano Morozzi	09/2020
3849	6*10^112208+43	112209	Robert Price	07/2020
3850	(2^372728+3058)/2	112203	Stefano Morozzi	09/2020
3851	32061^3158+3158^32061	112195	Hans Havermann	02/2021
3852	2^372695+72113	112193	Enzo Doria	04/2016
3853	2^372689-2563	112191	Yves Minet	07/2014
3854	2^372638-1859441	112176	Enzo Doria	03/2016
3855	3^235074-113056	112159	Enzo Doria	07/2014
3856	-E(29242)/489848365125303139750087	112140	Thomas Ritschel	01/2021
3857	(2^372514+1822)/2	112138	Stefano Morozzi	02/2021
3858	29468^6387+6387^29468	112135	Hans Havermann	02/2021
3859	(2^372428+3742)/2	112112	Stefano Morozzi	01/2021
3860	25375^25454-25454^25375	112110	Norbert Schneider	01/2021
3861	131^52949-130	112108	Norbert Schneider	02/2019
3862	(91*10^112098-1)/9	112100	Robert Price	04/2015
3863	2^372310-85061	112077	Paul Bourdelais	02/2012
3864	(10^112067+53)/9	112067	Serge Batalov	07/2015
3865	(2^372237+2082)/2	112055	Stefano Morozzi	09/2020
3866	75^59760+2	112054	Lelio R Paula	08/2013
3867	(2^372200+1710)/2	112044	Stefano Morozzi	09/2020
3868	(2^372181+2250)/2	112038	Stefano Morozzi	01/2021
3869	(2^372161+2574)/2	112032	Stefano Morozzi	09/2020
3870	8*10^112018-49	112019	Robert Price	08/2019
3872	2^372108+74221	112016	Enzo Doria	04/2016
3871	(2^372109+2046)/2	112016	Stefano Morozzi	09/2020
3873	(184*10^112007-1)/3	112009	Robert Price	02/2020
3874	5*10^112003+81	112004	Robert Price	03/2019
3875	215^48018+48018^215	112000	Norbert Schneider	10/2018
3876	25549^24148+24148^25549	111979	Hans Havermann	02/2021
3877	2^371970-459491	111975	Enzo Doria	05/2015
3878	41^69427-40^69427	111971	Robert Price	07/2012
3879	(2^371782+358)/2	111918	Stefano Morozzi	01/2021
3880	(34*10^111902-547)/9	111903	Robert Price	03/2021
3881	(10^111902+71)/9	111902	Serge Batalov	07/2015
3882	(2^371625+1610)/2	111870	Stefano Morozzi	09/2020
3883	29080^7027+7027^29080	111865	Hans Havermann	01/2021
3884	31307^3730+3730^31307	111820	Hans Havermann	02/2021
3885	2^371440-112865	111815	Enzo Doria	06/2014
3886	2^371426-459161	111811	Enzo Doria	05/2015
3887	25768^21771+21771^25768	111779	Hans Havermann	02/2021
3888	28022^9747+9747^28022	111777	Hans Havermann	02/2021
3889	(94*10^111770+11)/3	111772	Robert Price	04/2020
3890	2^371276-461267	111766	Enzo Doria	07/2015
3891	6*10^111760+43	111761	Robert Price	07/2020
3892	98079!4-1024	111747	Robert Price	11/2019
3893	(2^371186+3162)/2	111738	Stefano Morozzi	09/2020
3894	2^371098-113261	111712	Enzo Doria	07/2014
3895	(7*10^111706-61)/9	111706	Erik Branger	01/2011
3896	2^371044+1869391	111696	Enzo Doria	05/2016
3897	26310^17581+17581^26310	111688	Hans Havermann	01/2021
3898	88^57416+87	111645	Norbert Schneider	11/2015
3899	2^370829-109693	111631	Enzo Doria	04/2014
3900	15^94906-2	111619	Lelio R Paula	11/2013
3901	25835^20904+20904^25835	111614	Hans Havermann	02/2021
3902	(2^370726+1198)/2	111600	Stefano Morozzi	09/2020
3903	27758^10479+10479^27758	111597	Hans Havermann	02/2021
3904	2^370695-4627	111591	Yves Minet	05/2019
3905	7*10^111579-87	111580	Robert Price	06/2020
3907	2^370643-37	111575	Yves Minet	01/2012
3906	(2^370655-5)/2439	111575	Lelio R Paula	03/2014
3908	2^370610-3911	111565	Yves Minet	04/2017
3909	26200^18097+18097^26200	111550	Hans Havermann	01/2021
3910	286^45405+45405^286	111532	Norbert Schneider	04/2015
3911	4*5^159563-9	111531	Lelio R Paula	11/2014
3912	(4^185225+23)/3	111517	Robert Price	10/2018
3913	2^370393-2797093	111500	Enzo Doria	03/2016
3914	(21*2^370382-1)/629	111495	Lelio R Paula	03/2014
3915	(2^370371+554)/2	111493	Stefano Morozzi	09/2020
3916	6^143273-5	111489	Paul Bourdelais	01/2021
3917	2^370292-2791979	111469	Enzo Doria	03/2016
3918	2^370177-461551	111435	Enzo Doria	07/2015
3919	(2^370169+1706)/2	111432	Stefano Morozzi	09/2020
3920	109^54683-108	111413	Norbert Schneider	02/2017
3921	(2^370043+1010)/2	111394	Stefano Morozzi	09/2020
3922	32961^2396+2396^32961	111392	Hans Havermann	10/2020
3923	numbpart(10^10+76282)	111391	Serge Batalov	04/2015
3924	2^369974+733	111374	Lelio R Paula	05/2013
3925	121^53470+120	111367	Norbert Schneider	10/2018
3926	2^369915-286267	111356	Enzo Doria	07/2015
3927	2^369855-1615	111338	Lelio R Paula	05/2017
3928	7*10^111325+3	111326	Robert Price	08/2015
3929	51^65176+2	111293	Lelio R Paula	08/2013
3930	2^369643-1865767	111274	Enzo Doria	03/2016
3931	2^369603+885	111262	Lelio R Paula	05/2017
3932	25555^22564+22564^25555	111252	Hans Havermann	10/2020
3933	L(532277)	111240	Renaud Lifchitz	03/2004
3935	105^55033-2	111233	Lelio R Paula	10/2017
3934	(35*10^111232-737)/9	111233	Robert Price	07/2018
3936	26970^13307+13307^26970	111227	Hans Havermann	10/2020
3937	25419^23716+23716^25419	111210	Hans Havermann	10/2020
3938	9*10^111201-29	111202	Robert Price	09/2019
3939	2^369392+29835	111199	Lelio R Paula	05/2017
3940	3^233059+16	111198	Robert Price	03/2020
3941	2^369354-3413	111187	Yves Minet	12/2016
3942	2^369296-27	111170	Lelio R Paula	02/2013
3943	2^369239-109837	111153	Enzo Doria	05/2014
3944	2^369224-291839	111148	Enzo Doria	07/2015
3945	2^369216+2798881	111146	Enzo Doria	04/2016
3946	26842^13817+13817^26842	111137	Hans Havermann	11/2020
3947	10^111111+163849	111112	Patrick De Geest	03/2017
3948	10^111111-312911	111111	Patrick De Geest	03/2017
3949	2^369092-216923	111108	Enzo Doria	05/2014
3950	2^369081-55	111105	Lelio R Paula	02/2013
3951	(2^369047+3618)/2	111094	Stefano Morozzi	09/2020
3952	88^57124-87	111077	Norbert Schneider	11/2015
3953	2^368980+753	111075	Lelio R Paula	05/2013
3954	2^368946-3623	111064	Yves Minet	03/2017
3955	2^368929+29835	111059	Lelio R Paula	05/2017
3956	4^184463-3^184463	111058	Jean-Louis Charton	12/2004
3957	111^54298+110	111057	Norbert Schneider	04/2017
3958	(4*10^111032-7)/3	111033	Ray Chandler	04/2011
3959	35799^1262+1262^35799	111015	Hans Havermann	10/2020
3960	(298*10^111004+11)/3	111006	Robert Price	11/2020
3961	27648^10349+10349^27648	111004	Hans Havermann	11/2020
3962	28899^6932+6932^28899	110997	Hans Havermann	11/2020
3963	2^368641-460303	110972	Enzo Doria	06/2015
3964	2^368619-109087	110966	Enzo Doria	04/2014
3965	(74*10^110961+313)/9	110962	Robert Price	06/2019
3966	25258^24711+24711^25258	110956	Hans Havermann	11/2020
3967	(2^368539+1290)/2	110941	Stefano Morozzi	01/2021
3968	3*2^368489+7	110927	Lelio R Paula	09/2014
3969	(14*10^110922+61)/3	110923	Robert Price	12/2018
3970	97411!4-2	110913	Robert Price	07/2017
3971	(9179*2^368330-1)/35	110881	Lelio R Paula	05/2015
3972	25830^19619+19619^25830	110880	Hans Havermann	10/2020
3973	(34*10^110882-7)/9/13/29/1019374319	110871	Makoto Morimoto	05/2016
3974	26022^18191+18191^26022	110850	Hans Havermann	10/2020
3975	(2^368211+2250)/2	110843	Stefano Morozzi	01/2021
3976	2^368050-64875	110795	Lelio R Paula	05/2017
3977	2^368048+25	110794	Lelio R Paula	02/2013
3978	(2^368017+2262)/2	110784	Stefano Morozzi	02/2021
3979	69^60239-2	110771	Lelio R Paula	10/2013
3980	(23*2^367952+1)/15717	110762	Lelio R Paula	03/2014
3981	2^367924-69	110757	Lelio R Paula	02/2013
3982	(2^367779+3750)/2	110713	Stefano Morozzi	01/2021
3983	2^367709-109723	110692	Enzo Doria	04/2014
3984	(3*2^367644-1)/107	110671	Lelio R Paula	03/2014
3985	(2^367626+3514)/2	110667	Stefano Morozzi	09/2020
3986	(23*2^367398+1)/57963	110595	Lelio R Paula	03/2014
3987	140^51515-139	110558	Norbert Schneider	04/2019
3988	2^367215+1879223	110543	Enzo Doria	09/2016
3989	25782^19375+19375^25782	110534	Hans Havermann	10/2020
3990	26117^17058+17058^26117	110526	Hans Havermann	10/2020
3991	2^367141+41	110521	Lelio R Paula	02/2013
3992	2^367126+29835	110516	Lelio R Paula	05/2017
3993	(10^110503-1)/9+2(10^59183-1)/910^25660	110503	Makoto Morimoto	09/2020
3994	(10^110503-1)/9+2(10^65511-1)/910^22496	110503	Makoto Morimoto	09/2020
3995	(10^110503-1)/9+210^108327+210^2175	110503	Makoto Morimoto	09/2020
3996	(10^110503-1)/9+210^66251+210^44251	110503	Makoto Morimoto	09/2020
3997	(10^110503-1)/9+3(10^28813-1)/910^40845	110503	Makoto Morimoto	09/2020
3998	(10^110503-1)/9+3(10^82573-1)/910^13965	110503	Makoto Morimoto	09/2020
3999	(10^110503-1)/9+4(10^43305-1)/910^33599	110503	Makoto Morimoto	09/2020
4000	(10^110503-1)/9+510^70327+510^40175	110503	Makoto Morimoto	09/2020

Find by discoverer :

PRP Records

Probable Primes Top 10000

(280932 PRPs in the top)