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 (> 30000)	Who ?	When ?
3751	(1000547^15749+1)/1000548	94492	Faysal YAtim	12/2008
3752	(F(375345)^2+L(375345)^2)/4	94477	Henri Lifchitz	10/2017
3753	7^111792-32	94476	Lelio R Paula	04/2016
3754	11^90680-5850	94434	Enzo Doria	01/2013
3755	2^313675-110125	94426	Enzo Doria	04/2014
3756	(2999*29^64556-2427)/4	94410	Curtis Bright	05/2015
3757	2^313609-112225	94406	Enzo Doria	06/2014
3758	2^313584+72901	94399	Enzo Doria	04/2016
3759	2^313510-112865	94376	Enzo Doria	06/2014
3760	7*10^94373+87	94374	Robert Price	11/2016
3761	(9^98897+8^98897)/17	94371	Robert Price	12/2012
3762	2^313453-114703	94359	Enzo Doria	04/2015
3763	8*10^94357-51	94358	Robert Price	10/2017
3764	(379*10^94337-1)/9	94339	Robert Price	08/2017
3765	2^313344-313344+1	94326	Robert Price	10/2014
3766	20^72481-49	94300	Lelio R Paula	05/2016
3767	44725!2+128	94289	Robert Price	03/2015
3768	4*10^94286+9	94287	Robert Price	05/2015
3769	17^76621+24	94279	Lelio R Paula	07/2016
3770	2^313156-112859	94270	Enzo Doria	06/2014
3771	6^121130-59	94258	Lelio R Paula	05/2016
3772	3^197542+28	94252	Robert Price	11/2013
3773	(3^197521+2)/51655	94237	Lelio R Paula	04/2013
3774	2^313045-5955	94236	Lelio R Paula	03/2016
3775	(67*10^94212+23)/9	94213	Ray Chandler	02/2011
3776	2^312909-1865203	94195	Enzo Doria	03/2016
3777	2^312848-149	94177	Lelio R Paula	11/2012
3778	4^156403-77597	94164	Mike Oakes	04/2011
3779	18^75004-85	94151	Lelio R Paula	06/2016
3780	19^73622-48	94145	Lelio R Paula	06/2016
3781	(11^90397-3^90397)/8	94138	Robert Price	04/2011
3782	(3^197287+5)/16	94129	Lelio R Paula	04/2013
3783	12^87212-37	94118	Lelio R Paula	06/2016
3784	11^90376+76	94117	Lelio R Paula	05/2016
3785	(6^120946-11)/5	94114	Paul Bourdelais	11/2011
3786	(10^94096+191)/3	94096	Robert Price	11/2017
3787	2^312562-112685	94091	Enzo Doria	06/2014
3788	137^44026-2	94072	Lelio R Paula	10/2017
3789	2^312404-869688105	94043	Lelio R Paula	09/2016
3790	2^312387+2793533	94038	Enzo Doria	03/2016
3792	10^94016+91	94017	Robert Price	04/2011
3791	(15*2^312325-1)/7201	94017	Lelio R Paula	02/2014
3793	10^94016-188963	94016	Patrick De Geest	08/2013
3794	(17*2^312315-1)/45	94016	Lelio R Paula	02/2014
3795	6^120802+7661	94003	Mike Oakes	04/2011
3796	(67607*2^312254+1)/177	94001	Lelio R Paula	06/2014
3797	(11*2^312207+1)/19	93984	Lelio R Paula	09/2013
3798	2^312201+51	93982	Lelio R Paula	11/2012
3799	(4*6^120749+1)/5	93961	Serge Batalov	10/2014
3800	3^196892+58	93942	Lelio R Paula	05/2016
3801	2^312060+18915	93940	Lelio R Paula	03/2016
3802	2^311992-16209	93919	Enzo Doria	04/2013
3803	(85^48677+1)/86	93917	Paul Bourdelais	08/2017
3804	2^311965-39	93911	Lelio R Paula	11/2012
3805	2^311920-111689	93898	Enzo Doria	05/2014
3806	7*10^93887-47	93888	Robert Price	02/2017
3807	12^86965-13	93851	Lelio R Paula	06/2016
3808	2^311705+16095	93833	Lelio R Paula	03/2016
3809	2^311665-81	93821	Lelio R Paula	11/2012
3810	730^32761+32761^730	93806	Norbert Schneider	09/2017
3811	11^90073+92	93802	Lelio R Paula	05/2016
3812	6*10^93792+41	93793	Robert Price	01/2017
3813	(2^311580+7)/591329	93790	Lelio R Paula	06/2013
3814	12^86900-77	93781	Lelio R Paula	06/2016
3815	2^311508-109769	93774	Enzo Doria	04/2014
3816	2^311486-1859621	93767	Enzo Doria	03/2016
3817	Phi(93811,10)/968129521/2109997013/3280113810431/639637782545831	93765	Kurt Beschorner	04/2015
3818	2^311471+311469	93763	Renaud Lifchitz	01/2003
3819	(88*10^93760-1)/3	93762	Robert Price	10/2017
3820	2^311426+79459	93749	Enzo Doria	06/2016
3821	2^311294+5775	93709	Lelio R Paula	03/2016
3822	2^311252-1017	93697	Lelio R Paula	03/2016
3823	2^311247-112041	93695	Enzo Doria	06/2014
3824	7*10^93692-83	93693	Robert Price	09/2017
3825	2^311205-109645	93683	Enzo Doria	04/2014
3826	5^134027-84	93681	Lelio R Paula	04/2016
3827	(2^311148-1017)/557	93663	Lelio R Paula	06/2013
3828	(2^311027-2^155514+1)/5	93628		11/2006
3829	3^196192-28	93608	Robert Price	12/2013
3830	216091#+261433	93606	Makoto Morimoto	12/2015
3831	5^133917+68	93604	Lelio R Paula	04/2016
3832	2^310924-1709	93598	Yves Minet	03/2013
3833	(266*10^93577-11)/3	93579	Robert Price	09/2016
3834	(16*10^93577+161)/3	93578	Robert Price	05/2016
3835	3^196113-56	93570	Lelio R Paula	04/2016
3836	2^310806-110345	93562	Enzo Doria	05/2014
3837	3^196093+86	93561	Lelio R Paula	04/2016
3838	2^310780-2327	93555	Yves Minet	10/2013
3839	30^63332+41	93550	Lelio R Paula	08/2012
3840	(21181*2^310707+1)/21	93536	Lelio R Paula	06/2014
3841	8*5^133807+7	93528	Lelio R Paula	10/2014
3842	2^310686+8193	93526	Lelio R Paula	03/2016
3843	2^310646+63	93514	Lelio R Paula	11/2012
3844	(77*10^93508+31)/9	93509	Robert Price	10/2015
3845	(1000907^15583+1)/1000908	93499	Faysal YAtim	04/2009
3846	(2*10^93497+7)/9	93497	Erik Branger	03/2011
3847	3^195958-112852	93496	Enzo Doria	07/2014
3848	2^310583+16385	93495	Lelio R Paula	03/2016
3849	(9913*2^310557-1)/35	93490	Lelio R Paula	04/2015
3850	9*7^110614+2	93481	Lelio R Paula	11/2014
3851	2^310469-8295	93461	Lelio R Paula	03/2016
3852	2^310459-1159	93458	Yves Minet	11/2012
3853	6^120075-95	93437	Lelio R Paula	05/2016
3854	2^310289+98327	93407	Yves Minet	11/2010
3855	2^310217-113143	93385	Enzo Doria	07/2014
3856	7^110494-68	93379	Lelio R Paula	04/2016
3857	2^310184-113093	93375	Enzo Doria	07/2014
3858	2^310180-110417	93374	Enzo Doria	05/2014
3859	gcd(V(1124905),5F(224981)(F(224981)-1)+1)	93372	Serge Batalov	04/2015
3860	3^195669+68	93358	Lelio R Paula	04/2016
3861	10^93356+91	93357	Robert Price	04/2011
3862	10^93356-28313	93356	Patrick De Geest	08/2013
3863	(85*10^93346+23)/9	93347	Robert Price	11/2015
3864	(3^195648-5)/3158276	93342	Lelio R Paula	04/2013
3865	3^195556+8680	93304	Lelio R Paula	04/2016
3866	2^309942-109991	93302	Enzo Doria	04/2014
3867	2^309926-1867301	93298	Enzo Doria	03/2016
3868	2^309924+85951	93297	Yves Minet	03/2011
3869	(86*10^93263-77)/9	93264	Robert Price	05/2016
3870	6^119836-125	93251	Lelio R Paula	05/2016
3871	(77*10^93249-257)/9	93250	Robert Price	10/2017
3872	3^195430-2	93244	Theodore Burton	02/2007
3873	(13*10^93236+47)/3	93237	Robert Price	01/2017
3874	(67*10^93226-7)/3	93228	Robert Price	10/2017
3875	(86*10^93217-221)/9	93218	Robert Price	06/2017
3876	2^309637-16329	93211	Enzo Doria	04/2013
3877	(41*10^93207+49)/9	93208	Robert Price	04/2016
3878	14^81312-57	93194	Lelio R Paula	06/2016
3879	41^57783-40	93192	Theodore Burton	02/2007
3880	3*10^93179-97	93180	Robert Price	08/2017
3881	5*7^110252-4	93175	Lelio R Paula	11/2014
3882	2^309380-27	93133	Lelio R Paula	11/2012
3883	23*10^93116-7	93118	Robert Price	03/2016
3884	(29*10^93082+1)/3	93083	Robert Price	11/2015
3885	(58*10^93062-13)/9	93063	Robert Price	09/2015
3886	2^309131+1869383	93058	Enzo Doria	05/2016
3887	2^309066-93	93039	Lelio R Paula	11/2012
3888	2^309063-113269	93038	Enzo Doria	07/2014
3889	3^194965+16	93022	Robert Price	10/2013
3890	2^308979+1869143	93012	Enzo Doria	05/2016
3891	5^133064+54	93008	Lelio R Paula	04/2016
3892	(2^308905-509203)/119	92988	Lelio R Paula	06/2013
3893	(94*10^92981-49)/99	92981	Ray Chandler	07/2011
3894	(2*10^92976-17)/3	92976	Robert Price	08/2014
3895	2^308809+37967	92961	Phil Moore	03/2008
3896	(3^194825+5)/11656	92952	Lelio R Paula	04/2013
3897	(2^308679+5)/1573	92919	Lelio R Paula	06/2013
3898	2^308650+513	92913	Lelio R Paula	02/2016
3899	5*7^109936+6	92908	Lelio R Paula	10/2014
3900	2*10^92897+89	92898	Robert Price	07/2016
3901	12^86073-29	92889	Lelio R Paula	06/2016
3902	2^308566-117	92888	Lelio R Paula	11/2012
3903	(17*10^92869-11)/3	92870	Robert Price	07/2015
3904	2^308459+75431	92856	Enzo Doria	04/2016
3905	2^308426-1866377	92846	Enzo Doria	03/2016
3906	(96^46831-1)/95	92830	Paul Bourdelais	09/2017
3907	2^308349-112111	92823	Enzo Doria	06/2014
3908	9*10^92821+19	92822	Robert Price	05/2016
3909	2^308337-75	92819	Lelio R Paula	11/2012
3910	4*3^194508+7	92805	Lelio R Paula	08/2014
3911	22*25^66379-113	92796	Curtis Bright	05/2015
3912	11^89101-1080	92790	Enzo Doria	12/2012
3913	2^308236-1867859	92789	Enzo Doria	04/2016
3914	12^85963+25	92770	Lelio R Paula	06/2016
3915	7^109750-66	92750	Lelio R Paula	04/2016
3916	9*10^92742+11	92743	Robert Kinser	01/2017
3917	(21*2^308046-1)/8857	92729	Lelio R Paula	02/2014
3918	2^307997-110655	92717	Enzo Doria	05/2014
3919	L(443609)	92709	Renaud Lifchitz	11/2003
3920	10^92691+9	92692	Robert Price	03/2011
3921	10^92691-252291	92691	Patrick De Geest	08/2013
3922	2^307879-2521	92681	Yves Minet	07/2014
3923	(2^307780-7)/19959669	92644	Lelio R Paula	06/2013
3924	14^80831+47	92643	Lelio R Paula	06/2016
3925	15^78744+92	92611	Lelio R Paula	07/2016
3926	65^51083-64	92610	Norbert Schneider	11/2014
3927	6^118996-16943	92597	Enzo Doria	02/2013
3928	(16*10^92591+41)/3	92592	Robert Price	10/2017
3929	(3^194014-7)/2	92568	Lelio R Paula	04/2013
3930	(63^51439+1)/64	92555	Paul Bourdelais	08/2017
3931	(26*10^92546-77)/3	92547	Robert Price	02/2017
3932	3^193954+340	92540	Lelio R Paula	04/2016
3933	2^307407-307407^2	92539	Henri Lifchitz	05/2005
3934	(17*10^92513-11)/3	92514	Robert Price	07/2015
3935	2^307318-4211	92512	Yves Minet	06/2011
3936	2^307280+193	92501	Lelio R Paula	11/2012
3937	20^71075-33	92471	Lelio R Paula	05/2016
3938	2^307126-78795	92455	Lelio R Paula	02/2016
3939	2^307125-49789	92454	Henri Lifchitz	08/2005
3940	2^307099+23	92447	Lelio R Paula	11/2012
3941	7*10^92414-69	92415	Robert Price	01/2017
3942	(9787*2^306975-1)/2129155	92407	Lelio R Paula	04/2015
3943	2^306915+1873373	92391	Enzo Doria	06/2016
3944	2^306908+12915	92389	Lelio R Paula	02/2016
3945	19^72244-80	92383	Lelio R Paula	06/2016
3947	2^306849+75	92371	Lelio R Paula	11/2012
3946	(397*10^92369+53)/9	92371	Robert Price	11/2017
3948	2^306813-869688105	92360	Lelio R Paula	08/2016
3949	2^306672-109059	92318	Enzo Doria	04/2014
3950	6^118604-17063	92292	Enzo Doria	02/2013
3951	(31*2^306487-1)/2291	92260	Lelio R Paula	02/2014
3952	2^306467-1835611	92256	Enzo Doria	04/2015
3953	2^306433+76427	92246	Enzo Doria	05/2016
3955	2^306430-113313	92245	Enzo Doria	07/2014
3954	(23*10^92244-59)/9	92245	Robert Price	03/2017
3956	(47*2^306398+1)/1384803	92231	Lelio R Paula	04/2015
3957	(25*10^92186+59)/3	92187	Robert Price	05/2016
3958	2^306213-286183	92180	Enzo Doria	06/2015
3959	10^92178+61	92179	Robert Price	04/2011
3960	10^92178-175509	92178	Patrick De Geest	07/2013
3961	2^306200+1185	92176	Lelio R Paula	02/2016
3962	2^306153+11	92162	Lelio R Paula	11/2012
3963	(2^306141-7)/5	92157	Lelio R Paula	06/2013
3964	(26*10^92152-23)/3	92153	Robert Price	08/2016
3965	(2*10^92152+67)/3	92152	Robert Price	04/2017
3966	410^92099+37^92099	92100	Mike Oakes	12/2010
3967	(2^305867-2^152934+1)/5	92075		11/2006
3968	2^305851-109495	92071	Enzo Doria	04/2014
3969	12^85300+35	92055	Lelio R Paula	06/2016
3970	3^192911+92	92042	Lelio R Paula	04/2016
3971	2^305723-276271	92032	Enzo Doria	07/2015
3972	2^305676+93	92018	Donovan Johnson	06/2008
3973	3^192819+4	91999	Lelio R Paula	04/2013
3974	(38*10^91997-83)/99	91997	Ray Chandler	07/2011
3975	2^305539+72911	91977	Enzo Doria	04/2016
3976	(2^305427-5)/1297998213	91934	Lelio R Paula	06/2013
3977	85^47642+84	91922	Norbert Schneider	10/2015
3978	10^91920+187651	91921	Patrick De Geest	07/2013
3979	10^91920-39	91920	Robert Price	05/2011
3980	(22*10^91903+41)/9	91904	Robert Price	02/2015
3982	2^305275-27	91897	Lelio R Paula	11/2012
3981	3^192607-7726	91897	Enzo Doria	05/2014
3983	(7*10^91856-61)/9	91856	Erik Branger	12/2009
3984	(89*10^91839-53)/9	91840	Robert Price	11/2015
3985	8*5^131351+7	91812	Lelio R Paula	10/2014
3986	3^192426-68	91811	Lelio R Paula	04/2016
3987	2^304973+117	91807	Lelio R Paula	11/2012
3988	2^304939-1863727	91796	Enzo Doria	03/2016
3989	2^304902+8415	91785	Lelio R Paula	02/2016
3990	18^73119+61	91785	Lelio R Paula	06/2016
3991	(78557*2^304740+1)/159	91739	Lelio R Paula	06/2014
3992	2^304747+71355	91738	Lelio R Paula	02/2016
3993	8*3^192251+5	91728	Lelio R Paula	08/2014
3994	2^304674-87	91717	Lelio R Paula	11/2012
3995	(28*10^91715+701)/9	91716	Robert Price	11/2017
3996	(2^304698+9)/1362809953	91715	Lelio R Paula	06/2013
3997	(5*10^91707-119)/3	91708	Robert Price	04/2016
3998	2^304633-112771	91704	Enzo Doria	06/2014
3999	9*10^91693+23	91694	Robert Price	11/2017
4000	2^304578-16713	91688	Enzo Doria	05/2013

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PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)