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 (> 30000)	Who ?	When ?
3751	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
3752	12^89153-43	96213	Lelio R Paula	06/2016
3753	(2*10^96195-59)/3	96195	Robert Price	05/2017
3754	2^319545+147	96193	Lelio R Paula	11/2012
3755	(50^56597+1)/51	96155	Robert Price	03/2014
3756	(41*10^96137-59)/9	96138	Robert Price	10/2017
3757	2^319353-110343	96135	Enzo Doria	05/2014
3758	11^92309-42	96130	Lelio R Paula	05/2016
3759	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
3760	(7*10^96112+143)/3	96113	Robert Price	04/2016
3761	2^319237+65835	96100	Lelio R Paula	03/2016
3762	2^319194-1841	96087	Yves Minet	03/2013
3763	20^73847-31	96078	Lelio R Paula	05/2016
3764	2^319107-109555	96061	Enzo Doria	04/2014
3765	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
3766	2^319098-112157	96059	Enzo Doria	06/2014
3767	15^81673+94	96055	Lelio R Paula	07/2016
3768	2^319074+1871749	96051	Enzo Doria	05/2016
3769	2^319007-112111	96031	Enzo Doria	06/2014
3770	2^318946-1421	96013	Yves Minet	01/2013
3771	2^318834-110411	95979	Enzo Doria	05/2014
3772	2^318831-1965	95978	Lelio R Paula	03/2016
3773	(5*10^95976+7)/3	95977	Erik Branger	03/2014
3774	5*3^201089-8	95945	Lelio R Paula	08/2014
3775	2^318711-139	95942	Lelio R Paula	11/2012
3776	2^318635-1167	95919	Lelio R Paula	03/2016
3777	15^81555+16	95917	Lelio R Paula	07/2016
3778	(37*10^95895+377)/9	95896	Robert Price	10/2017
3779	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
3780	2^318496-97305	95877	Lelio R Paula	03/2016
3781	2^318466+15015	95868	Lelio R Paula	03/2016
3782	6^123187-173129	95859	Mike Oakes	04/2011
3783	2^318423-487	95855	Yves Minet	03/2012
3784	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
3785	45369!2+1024	95787	Robert Price	02/2015
3786	3^200758-86	95786	Lelio R Paula	05/2016
3787	3*10^95776-59	95777	Robert Price	10/2017
3788	193^41901-2	95768	Lelio R Paula	10/2017
3789	4*10^95752-71	95753	Robert Price	11/2017
3790	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
3791	4*10^95672+91	95673	Robert Price	11/2017
3792	(11*10^95641-113)/3	95642	Robert Price	01/2017
3793	(13*10^95588+11)/3	95589	Robert Price	05/2015
3794	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
3795	3^200325+70	95580	Lelio R Paula	05/2016
3796	(25*10^95574-7)/9	95575	Robert Price	12/2014
3797	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
3798	2^317464+31	95567	Lelio R Paula	11/2012
3799	7^113073+82	95558	Lelio R Paula	04/2016
3800	2^317251+465	95503	Lelio R Paula	03/2016
3801	19^74684+58	95503	Lelio R Paula	06/2016
3802	(2^317250-7)/339	95500	Lelio R Paula	07/2013
3803	6^122718-79	95494	Lelio R Paula	05/2016
3804	2^317141-110491	95469	Enzo Doria	05/2014
3805	2^317094+76309	95455	Enzo Doria	05/2016
3806	2^317085+95	95453	Lelio R Paula	11/2012
3807	(17*10^95451-377)/9	95452	Robert Price	11/2017
3808	2^317057-109551	95444	Enzo Doria	04/2014
3809	3^200026+28	95437	Lelio R Paula	05/2016
3810	2^317024+93	95434	Donovan Johnson	06/2008
3811	2^316999+1605	95427	Lelio R Paula	03/2016
3812	2^316995-110427	95426	Enzo Doria	05/2014
3813	2^316937+177	95408	Lelio R Paula	11/2012
3814	4*10^95407+91	95408	Robert Price	11/2017
3815	2^316908+1915	95399	Lelio R Paula	03/2016
3816	2^316894+99	95395	Lelio R Paula	11/2012
3817	6^122547+11	95361	Lelio R Paula	05/2016
3818	2^316771+82875	95358	Lelio R Paula	03/2016
3820	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
3819	1*10^95326+57	95327	Robert Price	03/2011
3821	10^95326-393687	95326	Patrick De Geest	09/2013
3822	(3^199803+4)/479539	95325	Lelio R Paula	04/2013
3823	2^316654-109481	95323	Enzo Doria	04/2014
3824	8*10^95316+51	95317	Robert Price	05/2017
3825	(50^56099+43^56099)/93	95309	Serge Batalov	12/2016
3826	(23*2^316559+1)/3925	95292	Lelio R Paula	09/2013
3827	(71*10^95277-539)/9	95278	Robert Price	11/2017
3828	19^74503-56	95271	Lelio R Paula	06/2016
3829	11^91475-4380	95262	Enzo Doria	01/2013
3830	(62*10^95251-611)/9	95252	Robert Price	05/2017
3831	(2^316321-509203)/69377	95218	Lelio R Paula	06/2013
3832	(79*10^95214-43)/9	95215	Erik Branger	11/2013
3833	(9*2^316233-1)/1751	95194	Lelio R Paula	02/2014
3834	5*2^316213+9	95191	Lelio R Paula	08/2014
3835	2^316205-1848163	95188	Enzo Doria	07/2015
3836	2^316185-2787913	95182	Enzo Doria	04/2016
3837	(9787*2^316142-1)/3	95172	Lelio R Paula	04/2015
3838	2^316140-5	95168	Henri Lifchitz	02/2006
3839	(15185*2^316117-1)/3	95165	Lelio R Paula	04/2015
3840	(34*10^95153-7)/9/19/19157	95149	Makoto Morimoto	05/2016
3841	2^316069+76817	95147	Enzo Doria	05/2016
3842	(199*10^95134-7)/3	95136	Robert Price	02/2017
3843	2^316027-97305	95134	Lelio R Paula	03/2016
3844	2^316006-2798051	95128	Enzo Doria	04/2016
3845	2^315921-2797603	95102	Enzo Doria	04/2016
3846	2*10^95095+63	95096	Robert Price	10/2017
3847	2^315857+1299	95083	Lelio R Paula	03/2016
3848	14^82955-43	95078	Lelio R Paula	06/2016
3849	(2*10^95072-17)/3	95072	Robert Price	08/2014
3850	2^315727+65	95044	Lelio R Paula	11/2012
3851	2^315725+1885757	95043	Enzo Doria	03/2017
3852	1*10^94983+21	94984	Robert Price	03/2011
3853	10^94983-717	94983	Patrick De Geest	08/2013
3854	17^77187-82	94975	Lelio R Paula	07/2016
3855	3*10^94964+37	94965	Robert Price	10/2017
3856	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
3857	2^315423-110329	94952	Enzo Doria	05/2014
3858	11^91169-7230	94943	Enzo Doria	02/2013
3859	7*10^94938+61	94939	Robert Price	02/2017
3860	2^315351+1025	94931	Lelio R Paula	03/2016
3861	2^315350-112253	94930	Enzo Doria	06/2014
3863	((1001327^(15817)+1)/1001328)	94906	Faysal YAtim	10/2010
3862	2^315268+7	94906	Lelio R Paula	10/2012
3864	11^91133+62	94906	Lelio R Paula	05/2016
3865	30^64244+41	94897	Lelio R Paula	08/2012
3866	(151*10^94885-7)/9	94887	Robert Price	07/2017
3867	4^157583+22147	94875	Mike Oakes	01/2011
3868	2^315098+123	94854	Lelio R Paula	11/2012
3869	3^198791-34	94848	Robert Price	11/2013
3870	3*2^315067+7	94846	Lelio R Paula	08/2014
3871	(9*2^315057+1)/73	94841	Lelio R Paula	09/2013
3872	(16*10^94822+53)/3	94823	Robert Price	12/2016
3873	8*6^121849-7	94818	Lelio R Paula	10/2014
3874	(85*10^94802+473)/9	94803	Robert Price	03/2017
3875	2^314870-108761	94786	Enzo Doria	03/2014
3876	5*2^314841-3	94778	Lelio R Paula	08/2014
3877	6^121772+113	94758	Lelio R Paula	05/2016
3878	6^121756-16253	94745	Enzo Doria	02/2013
3879	2^314718-112793	94740	Enzo Doria	06/2014
3880	2^314697-1847293	94734	Enzo Doria	07/2015
3881	2^314548-249	94689	Yves Minet	02/2012
3882	5^135469+42	94689	Lelio R Paula	04/2016
3883	gcd(V(1137755),5F(227551)(F(227551)-1)+1)	94676	Serge Batalov	04/2015
3884	(2*10^94604+547)/9	94604	Robert Price	10/2017
3885	3*2^314152+5	94570	Lelio R Paula	08/2014
3886	2*6^121530-5	94570	Lelio R Paula	10/2014
3887	7*10^94563+87	94564	Robert Price	11/2016
3888	2^314114-109677	94558	Enzo Doria	04/2014
3889	(218389#+240867)/(311811)	94557	Makoto Morimoto	10/2017
3890	2^314059+76583	94542	Enzo Doria	05/2016
3891	2^314041-4035	94536	Lelio R Paula	03/2016
3892	(7*2^314003-11)/15	94524	Renaud Lifchitz	03/2011
3893	11^90760-4710	94517	Enzo Doria	01/2013
3894	(7*2^313926-1)/148821	94497	Lelio R Paula	02/2014
3895	94*10^94493-3	94495	Robert Price	11/2016
3896	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
3897	(F(375345)^2+L(375345)^2)/4	94477	Henri Lifchitz	10/2017
3898	7^111792-32	94476	Lelio R Paula	04/2016
3899	11^90680-5850	94434	Enzo Doria	01/2013
3900	2^313675-110125	94426	Enzo Doria	04/2014
3901	(2999*29^64556-2427)/4	94410	Curtis Bright	05/2015
3902	2^313609-112225	94406	Enzo Doria	06/2014
3903	2^313584+72901	94399	Enzo Doria	04/2016
3904	2^313510-112865	94376	Enzo Doria	06/2014
3905	7*10^94373+87	94374	Robert Price	11/2016
3906	(9^98897+8^98897)/17	94371	Robert Price	12/2012
3907	2^313453-114703	94359	Enzo Doria	04/2015
3908	8*10^94357-51	94358	Robert Price	10/2017
3909	(379*10^94337-1)/9	94339	Robert Price	08/2017
3910	2^313344-313344+1	94326	Robert Price	10/2014
3911	20^72481-49	94300	Lelio R Paula	05/2016
3912	44725!2+128	94289	Robert Price	03/2015
3913	4*10^94286+9	94287	Robert Price	05/2015
3914	17^76621+24	94279	Lelio R Paula	07/2016
3915	2^313156-112859	94270	Enzo Doria	06/2014
3916	6^121130-59	94258	Lelio R Paula	05/2016
3917	3^197542+28	94252	Robert Price	11/2013
3918	(3^197521+2)/51655	94237	Lelio R Paula	04/2013
3919	2^313045-5955	94236	Lelio R Paula	03/2016
3920	(67*10^94212+23)/9	94213	Ray Chandler	02/2011
3921	2^312909-1865203	94195	Enzo Doria	03/2016
3922	2^312848-149	94177	Lelio R Paula	11/2012
3923	4^156403-77597	94164	Mike Oakes	04/2011
3924	18^75004-85	94151	Lelio R Paula	06/2016
3925	19^73622-48	94145	Lelio R Paula	06/2016
3926	(11^90397-3^90397)/8	94138	Robert Price	04/2011
3927	(3^197287+5)/16	94129	Lelio R Paula	04/2013
3928	12^87212-37	94118	Lelio R Paula	06/2016
3929	11^90376+76	94117	Lelio R Paula	05/2016
3930	(6^120946-11)/5	94114	Paul Bourdelais	11/2011
3931	(10^94096+191)/3	94096	Robert Price	11/2017
3932	2^312562-112685	94091	Enzo Doria	06/2014
3933	137^44026-2	94072	Lelio R Paula	10/2017
3934	2^312404-869688105	94043	Lelio R Paula	09/2016
3935	2^312387+2793533	94038	Enzo Doria	03/2016
3936	10^94016+91	94017	Robert Price	04/2011
3937	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
3939	10^94016-188963	94016	Patrick De Geest	08/2013
3938	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
3940	6^120802+7661	94003	Mike Oakes	04/2011
3941	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
3942	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
3943	2^312201+51	93982	Lelio R Paula	11/2012
3944	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
3945	3^196892+58	93942	Lelio R Paula	05/2016
3946	2^312060+18915	93940	Lelio R Paula	03/2016
3947	2^311992-16209	93919	Enzo Doria	04/2013
3948	(85^48677+1)/86	93917	Paul Bourdelais	08/2017
3949	2^311965-39	93911	Lelio R Paula	11/2012
3950	2^311920-111689	93898	Enzo Doria	05/2014
3951	7*10^93887-47	93888	Robert Price	02/2017
3952	12^86965-13	93851	Lelio R Paula	06/2016
3953	2^311705+16095	93833	Lelio R Paula	03/2016
3954	2^311665-81	93821	Lelio R Paula	11/2012
3955	730^32761+32761^730	93806	Norbert Schneider	09/2017
3956	11^90073+92	93802	Lelio R Paula	05/2016
3957	6*10^93792+41	93793	Robert Price	01/2017
3958	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
3959	12^86900-77	93781	Lelio R Paula	06/2016
3960	2^311508-109769	93774	Enzo Doria	04/2014
3961	2^311486-1859621	93767	Enzo Doria	03/2016
3962	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
3963	2^311471+311469	93763	Renaud Lifchitz	01/2003
3964	(88*10^93760-1)/3	93762	Robert Price	10/2017
3965	2^311426+79459	93749	Enzo Doria	06/2016
3966	2^311294+5775	93709	Lelio R Paula	03/2016
3967	2^311252-1017	93697	Lelio R Paula	03/2016
3968	2^311247-112041	93695	Enzo Doria	06/2014
3969	7*10^93692-83	93693	Robert Price	09/2017
3970	2^311205-109645	93683	Enzo Doria	04/2014
3971	5^134027-84	93681	Lelio R Paula	04/2016
3972	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
3973	(2^311027-2^155514+1)/5	93628		11/2006
3974	3^196192-28	93608	Robert Price	12/2013
3975	216091#+261433	93606	Makoto Morimoto	12/2015
3976	5^133917+68	93604	Lelio R Paula	04/2016
3977	2^310924-1709	93598	Yves Minet	03/2013
3978	(266*10^93577-11)/3	93579	Robert Price	09/2016
3979	(16*10^93577+161)/3	93578	Robert Price	05/2016
3980	3^196113-56	93570	Lelio R Paula	04/2016
3981	2^310806-110345	93562	Enzo Doria	05/2014
3982	3^196093+86	93561	Lelio R Paula	04/2016
3983	2^310780-2327	93555	Yves Minet	10/2013
3984	30^63332+41	93550	Lelio R Paula	08/2012
3985	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
3986	8*5^133807+7	93528	Lelio R Paula	10/2014
3987	2^310686+8193	93526	Lelio R Paula	03/2016
3988	2^310646+63	93514	Lelio R Paula	11/2012
3989	(77*10^93508+31)/9	93509	Robert Price	10/2015
3990	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
3991	(2*10^93497+7)/9	93497	Erik Branger	03/2011
3992	3^195958-112852	93496	Enzo Doria	07/2014
3993	2^310583+16385	93495	Lelio R Paula	03/2016
3994	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
3995	9*7^110614+2	93481	Lelio R Paula	11/2014
3996	2^310469-8295	93461	Lelio R Paula	03/2016
3997	2^310459-1159	93458	Yves Minet	11/2012
3998	6^120075-95	93437	Lelio R Paula	05/2016
3999	2^310289+98327	93407	Yves Minet	11/2010
4000	2^310217-113143	93385	Enzo Doria	07/2014

Find by discoverer :

PRP Records

Probable Primes Top 10000

(218736 PRPs in the top)