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	127^47012+126	98905	Norbert Schneider	01/2019
3752	(10^98890+149)/3	98890	Serge Batalov	12/2014
3753	22775^21978+21978^22775	98889	Hans Havermann	08/2017
3754	2^328497-216933	98888	Enzo Doria	05/2014
3755	2^328487+32769	98885	Lelio R Paula	08/2016
3756	3^207250-112358	98884	Enzo Doria	06/2014
3757	13^88754-90	98867	Lelio R Paula	08/2016
3758	2^328406+709	98861	Lelio R Paula	02/2013
3759	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
3760	7^116976+76	98857	Lelio R Paula	08/2016
3761	2^328335+1155	98839	Lelio R Paula	08/2016
3763	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
3762	287^40210+40210^287	98832	Norbert Schneider	11/2014
3764	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
3765	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
3766	65^54491+48	98788	Lelio R Paula	04/2016
3767	3^207042+98	98785	Lelio R Paula	08/2016
3768	3^206977-112756	98754	Enzo Doria	07/2014
3769	7^116846-50	98747	Lelio R Paula	08/2016
3770	2^327967-28635	98728	Lelio R Paula	08/2016
3771	707^34642+34642^707	98710	Norbert Schneider	12/2017
3772	6^126850-47	98709	Lelio R Paula	08/2016
3773	8*6^126830-7	98694	Lelio R Paula	11/2014
3774	11^94770-270	98693	Enzo Doria	08/2012
3775	2^327832+43	98688	Lelio R Paula	12/2012
3776	2^327795+761	98677	Lelio R Paula	02/2013
3777	10^98669+147411	98670	Patrick De Geest	11/2016
3779	10^98669-9^(98669-1)	98669	Robert Price	05/2016
3778	10^98669-105249	98669	Patrick De Geest	11/2016
3780	2^327671-109801	98639	Enzo Doria	04/2014
3781	5^141090-14	98618	Lelio R Paula	08/2016
3782	20^75799+47	98617	Lelio R Paula	08/2016
3783	2^327515-1017	98592	Lelio R Paula	08/2016
3784	6^126692+97681	98586	Mike Oakes	04/2011
3785	2^327467-741	98578	Lelio R Paula	08/2016
3786	(2^327329+9)/19	98535	Lelio R Paula	10/2013
3787	7^116577-66	98519	Lelio R Paula	08/2016
3788	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
3789	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
3790	2^327162-66945	98486	Lelio R Paula	08/2016
3791	4*10^98472-3	98473	Erik Branger	11/2013
3792	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
3793	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
3794	13^88363+94	98432	Lelio R Paula	08/2016
3795	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
3796	6^126481+41	98422	Lelio R Paula	08/2016
3797	78*10^98413-7	98415	Robert Price	05/2017
3798	7^116416+46	98383	Lelio R Paula	08/2016
3799	7^116407-24	98376	Lelio R Paula	07/2016
3800	439^37228+37228^439	98374	Norbert Schneider	08/2018
3801	2^326782-1860671	98372	Enzo Doria	03/2016
3802	17^79948+58	98372	Lelio R Paula	08/2016
3803	3^206143-98	98356	Lelio R Paula	08/2016
3804	8*5^140705+7	98350	Lelio R Paula	11/2014
3805	2^326585+11	98312	Lelio R Paula	12/2012
3806	2^326582-459161	98311	Enzo Doria	05/2015
3807	(2^326548+9)/5	98301	Lelio R Paula	10/2013
3808	2^326538+71659	98298	Enzo Doria	04/2016
3809	15^83575-58	98292	Lelio R Paula	08/2016
3810	10^98288+3	98289	Robert Price	03/2011
3811	10^98288-117017	98288	Patrick De Geest	11/2011
3812	(44*10^98284-719)/9	98285	Robert Price	12/2017
3813	2^326421-2797573	98263	Enzo Doria	04/2016
3814	2^326401+16095	98257	Lelio R Paula	07/2016
3815	7^116240-116240^7	98235	Norbert Schneider	05/2017
3816	17^79826-78	98222	Lelio R Paula	08/2016
3817	2^326268-809	98217	Yves Minet	04/2011
3818	(418*10^98199+23)/9	98201	Robert Price	08/2017
3819	12*10^98198-7	98200	Robert Price	11/2017
3820	15^83496-76	98199	Lelio R Paula	08/2016
3821	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
3822	9*5^140471-4	98186	Lelio R Paula	11/2014
3823	2^326069-2383	98157	Yves Minet	10/2013
3824	2^325973+1185	98128	Lelio R Paula	07/2016
3825	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
3826	2^325945-1847269	98120	Enzo Doria	07/2015
3827	8*10^98111-67	98112	Robert Price	10/2017
3828	2^325866+15	98096	Lelio R Paula	12/2012
3829	2^325765+1974305	98066	Enzo Doria	06/2016
3830	2^325733-58695	98056	Lelio R Paula	07/2016
3831	2^325717-3645	98051	Lelio R Paula	07/2016
3832	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
3833	(7*10^98007-13)/3	98008	Robert Price	06/2016
3834	2^325512-459959	97989	Enzo Doria	05/2015
3835	(3^205354-8)/17	97978	Lelio R Paula	09/2013
3836	2^325433+76817	97966	Enzo Doria	05/2016
3837	5*10^97963+81	97964	Robert Price	08/2017
3838	2^325390-109061	97953	Enzo Doria	04/2014
3839	13^87921+24	97940	Lelio R Paula	08/2016
3840	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
3841	2^325215+12909	97900	Lelio R Paula	07/2016
3842	7*10^97874-69	97875	Robert Price	01/2017
3844	(17^79537+5^79537)/22	97865	Robert Price	06/2013
3843	15^83212+22	97865	Lelio R Paula	08/2016
3845	2^325087-109057	97861	Enzo Doria	04/2014
3846	2^325074+1870657	97858	Enzo Doria	05/2016
3847	2^325066-2111	97855	Yves Minet	08/2013
3848	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
3849	18^77944-89	97841	Lelio R Paula	07/2016
3850	119^47136+118	97833	Norbert Schneider	09/2018
3851	6^125720-17663	97830	Enzo Doria	02/2013
3852	2^324972-2069	97827	Yves Minet	05/2013
3853	2^324944-2788319	97818	Enzo Doria	03/2016
3855	4*10^97799-9	97800	Erik Branger	11/2013
3854	2^324882+577294575	97800	Lelio R Paula	09/2016
3856	2^324863-1867921	97794	Enzo Doria	04/2016
3857	6^125662-18473	97785	Enzo Doria	03/2013
3858	12^90604+11	97779	Lelio R Paula	07/2016
3859	5^139830+24	97737	Lelio R Paula	04/2016
3860	2^324612+1155	97718	Lelio R Paula	07/2016
3861	19^76404-44	97702	Lelio R Paula	07/2016
3862	2^324505-2983	97686	Yves Minet	04/2011
3863	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
3864	6^125488-17843	97649	Enzo Doria	02/2013
3865	7^115515-2	97622	Lelio R Paula	09/2013
3866	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
3867	6^125418-5	97595	Lelio R Paula	11/2014
3868	2^324076+1155	97557	Lelio R Paula	07/2016
3869	(2^324074+9)/13	97555	Lelio R Paula	10/2013
3870	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
3871	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
3872	2^323946+73939	97518	Enzo Doria	04/2016
3873	2^323937+1866947	97515	Enzo Doria	03/2016
3874	6^125290-18533	97495	Enzo Doria	03/2013
3875	2^323845+101	97488	Lelio R Paula	12/2012
3876	18^77662+65	97487	Lelio R Paula	07/2016
3877	2^323772+76771	97466	Enzo Doria	05/2016
3878	2^323765-112213	97463	Enzo Doria	06/2014
3879	2^323720-6555	97450	Lelio R Paula	07/2016
3880	2^323694-1860401	97442	Enzo Doria	03/2016
3881	20^74886+3	97429	Lelio R Paula	06/2016
3883	3*10^97399+73	97400	Robert Price	04/2016
3882	7^115252-50	97400	Lelio R Paula	07/2016
3884	224737#+393581	97389	Nicolas PALAU	12/2016
3885	(26*10^97353+31)/3	97354	Robert Price	07/2016
3886	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
3887	(38*10^97329+187)/9	97330	Robert Price	11/2017
3888	p(19982)#/2-1024	97293	Robert Price	09/2017
3889	6^125021-85	97286	Lelio R Paula	08/2016
3890	2^323164-47355	97283	Lelio R Paula	07/2016
3891	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
3892	2^323054-6555	97249	Lelio R Paula	07/2016
3893	9*10^97247-29	97248	Robert Price	05/2017
3894	(31*10^97242+41)/9	97243	Robert Price	04/2015
3895	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
3896	12^90098-41	97233	Lelio R Paula	07/2016
3897	2^322928-216929	97212	Enzo Doria	05/2014
3898	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
3899	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
3900	2^322725+75761	97150	Enzo Doria	04/2016
3901	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
3902	(41*10^97085+373)/9	97086	Robert Price	04/2017
3903	2^322413+77	97056	Lelio R Paula	12/2012
3904	2^322406+177	97054	Lelio R Paula	12/2012
3905	(14*10^97044+31)/9	97045	Robert Price	02/2015
3906	2^322302+255255	97023	Lelio R Paula	07/2016
3907	2^322196-113093	96991	Enzo Doria	07/2014
3908	2^322000-1861469	96932	Enzo Doria	03/2016
3909	2^321971-112747	96923	Enzo Doria	06/2014
3910	11^93062-92	96915	Lelio R Paula	06/2016
3911	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
3912	3^203051+34	96880	Lelio R Paula	05/2016
3913	2*10^96867-51	96868	Robert Price	11/2017
3914	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
3915	2^321716-2786939	96847	Enzo Doria	03/2016
3916	2^321701-113053	96842	Enzo Doria	07/2014
3917	2^321700-28635	96842	Lelio R Paula	06/2016
3918	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
3919	6^124433-124433	96828	Robert Price	01/2014
3920	2^321631+69	96821	Lelio R Paula	12/2012
3921	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
3922	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
3923	(59*10^96798+31)/9	96799	Robert Price	09/2015
3924	223319#+231223	96790	Makoto Morimoto	02/2016
3925	2^321519-28635	96787	Lelio R Paula	06/2016
3926	2^321487-1867237	96778	Enzo Doria	03/2016
3927	2^321461-63	96770	Lelio R Paula	12/2012
3928	2^321439+123	96763	Lelio R Paula	12/2012
3929	2^321434+709	96762	Lelio R Paula	02/2013
3930	14^84413+89	96749	Lelio R Paula	07/2016
3931	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
3932	13^86847+96	96743	Lelio R Paula	06/2016
3933	9*2^321336-7	96733	Lelio R Paula	08/2014
3934	(209*10^96722-17)/3	96724	Robert Price	05/2017
3935	2^321187-1159	96687	Yves Minet	11/2012
3936	2^321182-1850081	96686	Enzo Doria	08/2015
3937	2^321116-112829	96666	Enzo Doria	06/2014
3938	2^321108-109499	96664	Enzo Doria	04/2014
3939	2^321098+2793859	96661	Enzo Doria	03/2016
3940	2^321057+4097	96648	Lelio R Paula	06/2016
3941	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
3942	p(19849)#/2-64	96581	Robert Price	04/2017
3943	2^320817+189	96576	Lelio R Paula	12/2012
3944	(361*10^96567-163)/9	96569	Robert Price	10/2017
3945	2^320788-110327	96567	Enzo Doria	05/2014
3946	2^320764+793	96560	Lelio R Paula	02/2013
3947	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
3948	2^320616-78795	96516	Lelio R Paula	03/2016
3949	2^320612-461939	96514	Enzo Doria	07/2015
3950	5*2^320431+7	96461	Lelio R Paula	08/2014
3951	19^75431-90	96458	Lelio R Paula	06/2016
3952	(2^320370+3)/67	96440	Lelio R Paula	10/2013
3953	2^320309+1871477	96423	Enzo Doria	05/2016
3954	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
3955	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
3956	2^320232-173	96400	Lelio R Paula	12/2012
3957	175^42975-2	96395	Lelio R Paula	10/2017
3958	10^96377+199911	96378	Patrick De Geest	12/2016
3959	10^96377-20001	96377	Robert Price	11/2016
3960	2^320124-2790449	96367	Enzo Doria	03/2016
3961	2^320043-108775	96343	Enzo Doria	04/2014
3962	10^96338+424939	96339	Patrick De Geest	03/2016
3963	10^96338-9281	96338	Robert Price	09/2015
3964	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
3965	2^319838+4257	96281	Lelio R Paula	03/2016
3966	2^319830-16995	96279	Lelio R Paula	03/2016
3967	6^123713+143	96268	Lelio R Paula	05/2016
3968	(28*10^96265-97)/3	96266	Robert Price	07/2016
3969	103^47825-102	96264	Norbert Schneider	10/2016
3970	2^319713-81	96244	Lelio R Paula	11/2012
3971	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
3972	12^89153-43	96213	Lelio R Paula	06/2016
3973	(2*10^96195-59)/3	96195	Robert Price	05/2017
3974	2^319545+147	96193	Lelio R Paula	11/2012
3975	(50^56597+1)/51	96155	Robert Price	03/2014
3976	(41*10^96137-59)/9	96138	Robert Price	10/2017
3977	2^319353-110343	96135	Enzo Doria	05/2014
3978	11^92309-42	96130	Lelio R Paula	05/2016
3979	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
3980	(7*10^96112+143)/3	96113	Robert Price	04/2016
3981	2^319237+65835	96100	Lelio R Paula	03/2016
3982	2^319194-1841	96087	Yves Minet	03/2013
3983	20^73847-31	96078	Lelio R Paula	05/2016
3984	50^56543-49	96065	Norbert Schneider	09/2018
3985	2^319107-109555	96061	Enzo Doria	04/2014
3986	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
3987	2^319098-112157	96059	Enzo Doria	06/2014
3988	15^81673+94	96055	Lelio R Paula	07/2016
3989	2^319074+1871749	96051	Enzo Doria	05/2016
3990	2^319007-112111	96031	Enzo Doria	06/2014
3991	2^318946-1421	96013	Yves Minet	01/2013
3992	2^318834-110411	95979	Enzo Doria	05/2014
3993	2^318831-1965	95978	Lelio R Paula	03/2016
3994	(5*10^95976+7)/3	95977	Erik Branger	03/2014
3995	5*3^201089-8	95945	Lelio R Paula	08/2014
3996	2^318711-139	95942	Lelio R Paula	11/2012
3997	2^318635-1167	95919	Lelio R Paula	03/2016
3998	15^81555+16	95917	Lelio R Paula	07/2016
3999	(37*10^95895+377)/9	95896	Robert Price	10/2017
4000	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014

Find by discoverer :

PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)