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	(2^352136+2638)/2	106004	Stefano Morozzi	09/2020
3752	2^352107+1872533	105995	Enzo Doria	05/2016
3753	(2^352096+2086)/2	105992	Stefano Morozzi	09/2020
3754	2^352066-2591	105983	Yves Minet	07/2014
3755	2^352030+715	105972	Lelio R Paula	10/2011
3756	9*6^136176-5	105967	Lelio R Paula	11/2014
3757	17099*2^351991+58329	105965	Paul Vanderveen	12/2017
3758	28582^5097+5097^28582	105963	Hans Havermann	09/2020
3759	155^48377+2	105962	Lelio R Paula	08/2013
3760	2^351865+1869707	105922	Enzo Doria	05/2016
3761	24974^17427+17427^24974	105921	Hans Havermann	09/2020
3762	25163^16194+16194^25163	105920	Hans Havermann	09/2020
3763	2^351831+23	105912	Lelio R Paula	10/2011
3764	9*2^351784-5	105899	Lelio R Paula	09/2014
3765	(85*10^105881+203)/9	105882	Robert Price	09/2020
3766	2^351671-112387	105864	Enzo Doria	06/2014
3767	2^351669-109501	105863	Enzo Doria	04/2014
3768	2^351644+74731	105856	Enzo Doria	04/2016
3769	13^95025-42	105853	Lelio R Paula	12/2016
3770	2^351599+15015	105842	Lelio R Paula	01/2017
3771	19^82763+90	105834	Lelio R Paula	01/2017
3772	26050^11551+11551^26050	105832	Hans Havermann	09/2020
3773	(9179*2^351540-1)/221	105826	Lelio R Paula	05/2015
3774	20^81329-51	105812	Lelio R Paula	01/2017
3775	(5*10^105811+211)/9	105811	Robert Price	02/2018
3776	2^351483+28425	105807	Lelio R Paula	01/2017
3777	25231^15610+15610^25231	105804	Hans Havermann	09/2020
3778	15^89960+86	105802	Lelio R Paula	02/2017
3779	2^351460-17289	105801	Enzo Doria	05/2013
3780	19^82735+22	105798	Lelio R Paula	01/2017
3781	2^351435-109077	105793	Enzo Doria	04/2014
3782	2^351393+1089	105780	Lelio R Paula	01/2017
3783	2^351364+72631	105772	Enzo Doria	04/2016
3784	(2^351333+3626)/2	105762	Stefano Morozzi	09/2020
3785	26818^8783+8783^26818	105761	Hans Havermann	09/2020
3787	2^351305+1872467	105754	Enzo Doria	05/2016
3788	3^221649+16	105754	Lelio R Paula	11/2016
3786	32511^1790+1790^32511	105754	Hans Havermann	09/2020
3789	8*3^221637-5	105749	Lelio R Paula	09/2014
3790	2^351279-2780449	105746	Enzo Doria	03/2016
3791	(2^351263+3198)/2	105741	Stefano Morozzi	09/2020
3792	15^89903-26	105735	Lelio R Paula	02/2017
3794	2^351213-73	105726	Lelio R Paula	10/2011
3793	(2^351214+1210)/2	105726	Stefano Morozzi	09/2020
3795	2^351192-4589	105720	Yves Minet	07/2011
3796	20^81250-33	105709	Lelio R Paula	12/2016
3797	(2^351133+3530)/2	105702	Stefano Morozzi	09/2020
3798	(2^351103+534)/2	105693	Stefano Morozzi	09/2020
3799	2^351076-113159	105685	Enzo Doria	07/2014
3800	93^53688-2	105684	Lelio R Paula	09/2013
3801	2^351060-4559	105680	Yves Minet	07/2011
3802	((10^52836-1)10000/9+5927)10^52836+(10^52836-1)/9	105676	Hans Havermann	08/2019
3803	11^101473-750	105674	Enzo Doria	11/2012
3804	3*5^151181-8	105672	Lelio R Paula	11/2014
3805	15^89831-34	105650	Lelio R Paula	02/2017
3807	11^101448-360	105648	Enzo Doria	08/2012
3806	3*7^125011+4	105648	Lelio R Paula	11/2014
3808	2^350943-113269	105645	Enzo Doria	07/2014
3809	2*10^105636-91	105637	Robert Price	04/2020
3810	24231^22880+22880^24231	105634	Hans Havermann	09/2020
3811	35296^983+983^35296	105626	Hans Havermann	09/2020
3812	2^350868-19725	105622	Enzo Doria	06/2013
3813	2^350858-59291	105619	Enzo Doria	10/2015
3814	2^350851+135	105617	Lelio R Paula	10/2011
3815	2^350841-741	105614	Lelio R Paula	01/2017
3816	3*10^105582+77	105583	Robert Price	09/2018
3817	24915^17284+17284^24915	105581	Hans Havermann	09/2020
3818	(5*10^105576-53)/3	105577	Robert Price	09/2020
3819	8*10^105571+3	105572	Robert Price	08/2015
3820	2^350674-78557	105564	Jorge Menendez	03/2018
3821	2*5^151026-3	105563	Lelio R Paula	11/2014
3822	(2^350702+5)/34264674063	105562	Lelio R Paula	12/2013
3823	6^135647-5^135647	105554	Jean-Louis Charton	02/2009
3824	3^221211+236	105545	Lelio R Paula	11/2016
3825	(32*10^105530-77)/9	105531	Robert Price	06/2018
3826	10^105515+33	105516	Lelio R Paula	11/2016
3827	10^105515-41033	105515	Patrick De Geest	12/2016
3828	(29*2^350473-1)/267927	105499	Lelio R Paula	03/2014
3829	17^85732-72	105489	Lelio R Paula	01/2017
3830	(2^350399+3618)/2	105481	Stefano Morozzi	09/2020
3831	(2^350379+1010)/2	105475	Stefano Morozzi	09/2020
3832	25233^15118+15118^25233	105462	Hans Havermann	09/2020
3833	26261^10366+10366^26261	105454	Hans Havermann	09/2020
3834	2^350307-110329	105453	Enzo Doria	05/2014
3835	2^350253-20365	105437	Enzo Doria	06/2013
3836	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
3837	(2^350187+2658)/2	105417	Stefano Morozzi	09/2020
3838	2^350139-109009	105403	Enzo Doria	04/2014
3839	(2^350129+3026)/2	105400	Stefano Morozzi	09/2020
3840	(2^350097+2070)/2	105390	Stefano Morozzi	09/2020
3841	3*5^150763+4	105380	Lelio R Paula	11/2014
3842	12^97643+91	105375	Lelio R Paula	02/2017
3843	6*5^150744-7	105367	Lelio R Paula	11/2014
3844	(2^350018+2074)/2	105366	Stefano Morozzi	09/2020
3845	4*10^105364-39	105365	Robert Price	09/2020
3847	2^349996-112169	105360	Enzo Doria	06/2014
3846	(2^349997+3702)/2	105360	Stefano Morozzi	09/2020
3848	(418*10^105343+23)/9	105345	Robert Price	02/2020
3849	11^101142-1080	105329	Enzo Doria	12/2012
3850	(68*10^105320-41)/9	105321	Robert Price	10/2013
3851	24800^17649+17649^24800	105319	Hans Havermann	09/2020
3852	3^220712-9934	105307	Enzo Doria	05/2014
3853	7*10^105296+9	105297	Robert Price	09/2015
3854	89*10^105284-7	105286	Robert Price	04/2020
3855	2^349739+1873373	105282	Enzo Doria	06/2016
3856	7^124574+24	105278	Lelio R Paula	11/2016
3857	2^349708-20957	105273	Enzo Doria	06/2013
3858	34115^1218+1218^34115	105267	Hans Havermann	09/2020
3859	2^349649-20469	105255	Enzo Doria	06/2013
3860	2^349607-20109	105243	Enzo Doria	06/2013
3861	(85*10^105242+473)/9	105243	Robert Price	01/2020
3862	2^349594-19085	105239	Enzo Doria	05/2013
3863	2^349530+1874479	105220	Enzo Doria	06/2016
3864	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
3865	(2^349452+3570)/2	105196	Stefano Morozzi	09/2020
3866	3^220464-112852	105189	Enzo Doria	07/2014
3867	2^349419-17349	105186	Enzo Doria	05/2013
3868	2^349400-2579	105180	Yves Minet	07/2014
3869	8*5^150471+3	105176	Lelio R Paula	11/2014
3870	655^37342+37342^655	105165	Norbert Schneider	08/2018
3871	13^94403+94	105160	Lelio R Paula	12/2016
3872	2^349301-112309	105151	Enzo Doria	06/2014
3873	27350^6981+6981^27350	105132	Hans Havermann	09/2020
3875	9*2^349220+5	105127	Lelio R Paula	09/2014
3874	(2^349225+3122)/2	105127	Stefano Morozzi	09/2020
3876	7*3^220317+8	105119	Lelio R Paula	09/2014
3877	7^124386+88	105119	Lelio R Paula	11/2016
3878	(2^349197+570)/2	105119	Stefano Morozzi	09/2020
3879	2^349171-19657	105111	Enzo Doria	06/2013
3880	(2^349115+590)/2	105094	Stefano Morozzi	09/2020
3881	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
3882	(2^349111-5)/3	105093	Lelio R Paula	12/2013
3883	675^37142+37142^675	105087	Norbert Schneider	08/2018
3884	2^348981-2797573	105054	Enzo Doria	04/2016
3885	2^348869-6555	105021	Lelio R Paula	01/2017
3886	5^150217+78	104998	Lelio R Paula	11/2016
3887	(88*10^104989-1)/3	104991	Robert Price	04/2020
3888	(28*10^104972+149)/3	104973	Robert Price	12/2019
3889	2^348703-113005	104971	Enzo Doria	06/2014
3891	2^348612-809	104943	Yves Minet	05/2013
3890	(73*10^104942-1)/9	104943	Robert Price	01/2015
3892	2^348583-350407	104934	Enzo Doria	06/2015
3893	2^348531-949	104919	Yves Minet	05/2012
3894	20^80636-59	104910	Lelio R Paula	12/2016
3895	8*10^104893-13	104894	Robert Price	08/2019
3897	2^348437+35	104890	Lelio R Paula	09/2011
3896	25208^14487+14487^25208	104890	Hans Havermann	09/2020
3898	2^348348+135	104864	Lelio R Paula	09/2011
3899	6*10^104852-31	104853	Robert Price	07/2020
3901	(2^348284+9)/25	104843	Lelio R Paula	12/2013
3900	75^55914-74	104843	Norbert Schneider	01/2015
3902	2^348268+255255	104840	Lelio R Paula	01/2017
3903	35540^891+891^35540	104839	Hans Havermann	09/2020
3904	5^149985-52	104836	Lelio R Paula	11/2016
3905	2^348224-20249	104826	Enzo Doria	06/2013
3906	(2^348217+2522)/2	104824	Stefano Morozzi	09/2020
3907	2^348212-20105	104823	Enzo Doria	06/2013
3908	20^80562+19	104814	Lelio R Paula	12/2016
3909	2*10^104811-87	104812	Robert Price	04/2018
3910	2^348149-20053	104804	Enzo Doria	06/2013
3911	2^348095-171	104788	Lelio R Paula	09/2011
3912	25383^13412+13412^25383	104769	Hans Havermann	09/2020
3913	2^348003-20377	104760	Enzo Doria	06/2013
3914	2^347994-741	104757	Lelio R Paula	12/2016
3915	(2^347990+790)/2	104756	Stefano Morozzi	09/2020
3916	25137^14702+14702^25137	104756	Hans Havermann	09/2020
3917	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
3918	2^347910-109937	104732	Enzo Doria	04/2014
3919	5^149794+28	104702	Lelio R Paula	11/2016
3920	105^51800-2	104698	Lelio R Paula	10/2017
3921	(16^86939+3^86939)/19	104684	Robert Price	06/2013
3922	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
3923	2^347731-18609	104678	Enzo Doria	05/2013
3924	4*6^134519+7	104677	Lelio R Paula	11/2014
3925	25321^13588+13588^25321	104656	Hans Havermann	09/2020
3926	2^347612-18545	104642	Enzo Doria	05/2013
3928	6^134465+95	104635	Lelio R Paula	11/2016
3927	(2^347588+3718)/2	104635	Stefano Morozzi	09/2020
3929	2^347517-17301	104614	Enzo Doria	05/2013
3930	(2^347493+3186)/2	104606	Stefano Morozzi	09/2020
3931	(2^347490+2574)/2	104605	Stefano Morozzi	09/2020
3932	3^219222-310	104596	Lelio R Paula	11/2016
3933	25993^10554+10554^25993	104581	Hans Havermann	09/2020
3934	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
3935	2^347372-17853	104570	Enzo Doria	05/2013
3936	2^347314+99	104552	Lelio R Paula	09/2011
3937	2^347300-22233	104548	Enzo Doria	06/2013
3938	2^347287-19845	104544	Enzo Doria	06/2013
3939	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
3940	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
3941	7*2^347239-3	104531	Lelio R Paula	09/2014
3942	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
3943	5*3^219047+8	104513	Lelio R Paula	09/2014
3944	2^347148-109073	104502	Enzo Doria	04/2014
3945	2^347129-20145	104497	Enzo Doria	06/2013
3946	4*10^104461-57	104462	Robert Price	10/2018
3947	(2^346989+590)/2	104454	Stefano Morozzi	09/2020
3948	2^346923-19585	104435	Enzo Doria	05/2013
3949	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
3950	2^346854+346854^2+1	104414	Robert Price	06/2014
3951	2^346834+11715	104408	Lelio R Paula	04/2015
3952	24276^19961+19961^24276	104392	Hans Havermann	09/2020
3953	79^55009+78	104387	Norbert Schneider	02/2015
3954	3^218744+58	104368	Lelio R Paula	11/2016
3955	9*10^104361+89	104362	Robert Price	11/2019
3956	25048^14665+14665^25048	104358	Hans Havermann	09/2020
3957	2^346649+65	104352	Lelio R Paula	09/2011
3958	2^346638-17265	104349	Enzo Doria	05/2013
3959	(2^346606+2082)/2	104339	Stefano Morozzi	09/2020
3960	(2^346607+2070)/2	104339	Stefano Morozzi	09/2020
3961	(2^346582+3202)/2	104332	Stefano Morozzi	09/2020
3962	26092^9967+9967^26092	104331	Hans Havermann	09/2020
3963	5*10^104326+77	104327	Robert Price	12/2018
3964	(2^346564+2026)/2	104326	Stefano Morozzi	09/2020
3966	2^346527-111817	104316	Enzo Doria	05/2014
3965	6^134055+101	104316	Lelio R Paula	11/2016
3967	92105!4+8	104312	Robert Price	09/2019
3968	6^134013+163	104283	Lelio R Paula	11/2016
3969	18^83049-89	104250	Lelio R Paula	01/2017
3970	(2^346311+606)/2	104250	Stefano Morozzi	09/2020
3971	2^346213+484049	104221	Enzo Doria	04/2017
3972	18^83021-91	104214	Lelio R Paula	01/2017
3973	10^104212+128779	104213	Patrick De Geest	05/2016
3974	10^104212+237447	104213	Patrick De Geest	05/2016
3975	10^104212+242139	104213	Patrick De Geest	05/2016
3976	10^104212+269199	104213	Patrick De Geest	05/2016
3977	24254^19803+19803^24254	104213	Hans Havermann	09/2020
3978	(10^104212-71)/1	104212	Serge Batalov	12/2014
3979	23678^23821-23821^23678	104202	Norbert Schneider	01/2020
3980	2^346078+7695	104180	Lelio R Paula	12/2016
3981	2^346055-19537	104173	Enzo Doria	05/2013
3982	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
3983	2^346037-20125	104168	Enzo Doria	06/2013
3984	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
3985	6^133854-17993	104159	Enzo Doria	03/2013
3986	2^345990+1874239	104154	Enzo Doria	06/2016
3987	2^345988-20373	104153	Enzo Doria	06/2013
3988	(2^345965+2214)/2	104146	Stefano Morozzi	09/2020
3989	(26*10^104132-503)/9	104133	Robert Price	07/2018
3990	3*5^148968+8	104125	Lelio R Paula	11/2014
3991	(7*10^104113+53)/3	104114	Robert Price	05/2018
3992	p(21253)#/2+8	104113	Robert Price	01/2017
3993	33582^1259+1259^33582	104106	Hans Havermann	09/2020
3994	32958^1441+1441^32958	104104	Hans Havermann	09/2020
3995	29127^3748+3748^29127	104095	Hans Havermann	09/2020
3996	322^41507+41507^322	104094	Norbert Schneider	12/2014
3997	6^133768-17423	104092	Enzo Doria	03/2013
3998	2^345786-19557	104092	Enzo Doria	05/2013
4000	171^46606-2	104072	Lelio R Paula	10/2017
3999	(29*10^104071+91)/3	104072	Robert Price	04/2020

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Probable Primes Top 10000

(271067 PRPs in the top)