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	(23*10^163523+301)/9	163524	Robert Price	06/2021
3752	(68*10^163521-329)/9	163522	Robert Price	03/2021
3753	35820^35899+35899^35820	163489	Norbert Schneider	11/2021
3754	2^542870-69551	163421	Enzo Doria	12/2015
3755	2^542502+24799	163310	Enzo Doria	10/2023
3756	2^542395+72533	163278	Enzo Doria	04/2016
3757	2^542258+216949	163236	Enzo Doria	12/2023
3758	2^542072-3683	163180	Yves Minet	03/2017
3759	fibonacci(780566)-4	163129	Jon Grantham	08/2023
3760	(682*10^163106-7)/9	163108	Robert Price	08/2021
3761	2^541779-1867357	163092	Enzo Doria	04/2016
3762	(29*10^163056+313)/9	163057	Robert Price	04/2021
3763	2^541476+214743	163001	Enzo Doria	11/2023
3764	13^142159+14^142159-2	162933	Harsh Aggarwal	05/2024
3765	8*10^162924+9	162925	Robert Price	12/2015
3766	2^540905+81557	162829	Enzo Doria	08/2016
3767	2^540628-2939	162746	Yves Minet	09/2014
3768	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
3769	(203*10^162689+1)/3	162691	Robert Price	03/2020
3770	3*10^162620-59	162621	Robert Price	09/2018
3771	2^540180+26791	162611	Enzo Doria	12/2023
3772	3^340694-112960	162553	Enzo Doria	07/2014
3773	2^539925+81	162534	Henri Lifchitz	11/2024
3774	2^539807-114081	162499	Enzo Doria	12/2014
3775	414^62093+62093^414	162498	Norbert Schneider	03/2022
3776	2^539654-114893	162453	Enzo Doria	05/2015
3777	9*10^162449-71	162450	Robert Price	11/2020
3778	2^539617-1851583	162441	Enzo Doria	08/2015
3779	(509*10^162422+31)/9	162424	Robert Price	08/2022
3780	(91*10^162410+11)/3	162412	Robert Price	02/2020
3781	2^539346+81049	162360	Enzo Doria	07/2016
3782	2^539220-115499	162322	Enzo Doria	07/2015
3783	2^539217-113713	162321	Enzo Doria	09/2014
3784	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
3785	4*10^162263-39	162264	Robert Price	09/2020
3786	31243^36098-36098^31243	162252	Frank Doornink	01/2024
3787	31987^36000-36000^31987	162180	Frank Doornink	01/2024
3788	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
3789	(10^162138+11)/3	162138	Serge Batalov	07/2015
3790	(61*10^162100-403)/9	162101	Robert Price	10/2021
3791	2^538473-112723	162097	Enzo Doria	06/2014
3792	2^538157+79337	162002	Enzo Doria	06/2016
3793	2^538136-114749	161996	Enzo Doria	05/2015
3794	2^538104+1531	161986	Lelio R Paula	01/2013
3795	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
3796	((2^179294-1)^3+2)/11	161918	Serge Batalov	03/2023
3797	31198^36027-36027^31198	161910	Frank Doornink	01/2024
3798	2^537815-22737	161899	Enzo Doria	07/2013
3799	2^537804-39839	161896	Enzo Doria	09/2015
3800	(754*10^161816-7)/9	161818	Robert Price	05/2020
3801	2^537461+29867	161792	Enzo Doria	03/2024
3802	2^537458-59201	161791	Enzo Doria	10/2015
3803	2*10^161766+51	161767	Robert Price	05/2018
3804	(7*10^161760+131)/3	161761	Robert Price	06/2020
3805	2^537209-49849	161717	Enzo Doria	10/2015
3806	(58*10^161691+329)/9	161692	Robert Price	05/2019
3807	23*10^161668-3	161670	Robert Price	10/2021
3808	2^536937+1879397	161635	Enzo Doria	09/2016
3809	3*2^536868-5	161614	Jon Grantham	07/2023
3810	34*10^161593-9	161595	Robert Price	06/2020
3811	(31*10^161582-1)/3	161584	Robert Price	02/2020
3812	24494^36813+36813^24494	161575	Norbert Schneider	11/2023
3813	2^536569-22881	161524	Enzo Doria	07/2013
3814	(46*10^161505+593)/9	161506	Robert Price	04/2022
3815	10^161253+573493	161254	Patrick De Geest	07/2018
3816	10^161253-8001	161253	Robert Price	03/2018
3817	97*10^161247-3	161249	Robert Price	05/2020
3818	7*10^161192-9	161193	Robert Price	10/2015
3819	2^535415-19	161176	Stefano Morozzi	07/2022
3820	2^535269-113803	161133	Enzo Doria	09/2014
3821	2^535205-23295	161113	Enzo Doria	08/2013
3822	(49*10^161105+437)/9	161106	Robert Price	09/2021
3823	2^534961+6561	161040	Henri Lifchitz	11/2024
3824	(89^82609+1)/90	161036	Paul Bourdelais	10/2017
3825	35385^35385-17692^17692	160960	Henri Lifchitz	10/2024
3826	2^534429-19	160880	Stefano Morozzi	07/2022
3827	2^534359-23229	160859	Enzo Doria	08/2013
3828	10^160836-1001	160836	Robert Price	10/2022
3829	457^60454+60454^457	160803	Norbert Schneider	07/2021
3830	8*10^160782+53	160783	Robert Price	08/2020
3831	67^88037-66^88037	160763	Robert Price	10/2013
3832	(88*10^160761-637)/9	160762	Robert Price	11/2020
3833	2^533981+81	160745	Henri Lifchitz	11/2024
3834	2^533948-1852559	160735	Enzo Doria	08/2015
3835	(2^769082)%F(769082)	160728	Henri Lifchitz	05/2025
3836	2^533665-23335	160650	Enzo Doria	08/2013
3837	2^533600+217981	160630	Enzo Doria	01/2024
3838	(19*10^160619+77)/3	160620	Robert Price	05/2019
3839	2^533350-5	160555	Stefano Morozzi	07/2022
3840	(38*10^160508+151)/9	160509	Robert Price	03/2022
3841	3^336353-2^336353	160482	Mike Oakes	10/2007
3842	26134^36315-36315^26134	160411	Frank Doornink	03/2024
3843	25821^36358-36358^25821	160411	Frank Doornink	03/2024
3844	2*10^160339-63	160340	Robert Price	01/2022
3845	24419^36532+36532^24419	160293	Norbert Schneider	10/2023
3846	(91*10^160249+11)/3	160251	Robert Price	02/2020
3847	(772*10^160239-7)/9	160241	Robert Price	06/2022
3848	(2*10^160226+187)/9	160226	Robert Price	06/2022
3849	2^532253+1868417	160225	Enzo Doria	04/2016
3850	2^532108-291989	160181	Enzo Doria	07/2015
3851	(28*10^160171-79)/3	160172	Robert Price	02/2021
3852	(26*10^160166-131)/3	160167	Robert Price	10/2019
3853	55*10^160145+9	160147	Robert Price	03/2022
3854	(17*10^160143+67)/3	160144	Robert Price	01/2019
3855	(394^61637-1)/393	159977	Jinyuan Wang	04/2023
3856	(3^765357)%F(765357)	159950	Henri Lifchitz	07/2025
3857	(19*10^159921-49)/3	159922	Robert Price	05/2019
3858	2^531110-1853771	159881	Enzo Doria	09/2015
3859	2^531088+48451	159874	Enzo Doria	07/2025
3860	(275^65536+53^65536)/2	159864	Kellen Shenton	11/2020
3861	2^530992-1845299	159845	Enzo Doria	07/2015
3862	2^530810+25	159790	Stefano Morozzi	04/2021
3863	25590^36241-36241^25590	159753	Frank Doornink	02/2024
3864	(136*10^159736-1)/9	159738	Serge Batalov	12/2014
3865	2^530417-113833	159672	Enzo Doria	09/2014
3866	2^530406-69701	159669	Enzo Doria	02/2016
3867	5*10^159656+41	159657	Robert Price	03/2019
3868	8*10^159614+29	159615	Robert Price	11/2021
3869	7^188858-188858^7	159604	Norbert Schneider	05/2018
3870	28^110278+27	159590	Alfred Reich	02/2024
3871	(45^96517-2^96517)/43	159562	Robert Price	11/2024
3872	7*10^159553-27	159554	Robert Price	11/2022
3873	3^334409-5*2^334409	159554	Jon Grantham	08/2023
3874	(24^115597-1)/23	159547	Paul Bourdelais	09/2017
3875	25472^36209-36209^25472	159540	Frank Doornink	01/2024
3876	(17*10^159438-377)/9	159439	Robert Price	03/2018
3877	(49^94321+2^94321)/51	159420	Robert Price	06/2025
3878	(203*10^159381+1)/3	159383	Robert Price	03/2020
3879	32282^35343-35343^32282	159361	Frank Doornink	02/2024
3880	2^529215+219383	159310	Enzo Doria	02/2024
3881	89*10^159258-9	159260	Robert Price	05/2020
3882	2^528944-461315	159229	Enzo Doria	07/2015
3883	(13*10^159147+161)/3	159148	Robert Price	11/2018
3884	2^528620-113879	159131	Enzo Doria	10/2014
3885	32125^35306-35306^32125	159119	Frank Doornink	02/2024
3886	(47*10^159083+259)/9	159084	Robert Price	03/2022
3887	(861^54181-1)/860	159019	Jinyuan Wang	11/2023
3888	2^528000-23307	158944	Enzo Doria	08/2013
3889	(29*10^158909+61)/9	158910	Robert Price	08/2018
3890	2^527817+1876817	158889	Enzo Doria	07/2016
3891	2^527774-49451	158876	Enzo Doria	10/2015
3892	2^527745-291553	158868	Enzo Doria	07/2015
3893	(91*10^158862+11)/3	158864	Robert Price	02/2020
3894	2^527644-1856999	158837	Enzo Doria	10/2015
3895	(37200^37199-37198^37199)/(2^37199)	158822	Henri Lifchitz	06/2013
3896	(17*10^158819+7)/3	158820	Robert Price	06/2023
3897	2^527573-1863253	158816	Enzo Doria	12/2015
3898	2^527553-23401	158810	Enzo Doria	08/2013
3899	(49*10^158783+437)/9	158784	Robert Price	09/2021
3900	10^158755+310207	158756	Patrick De Geest	08/2021
3901	10^158755-50001	158755	Robert Price	08/2020
3902	(61*10^158748-619)/9	158749	Robert Price	03/2022
3903	11^152420-210	158730	Enzo Doria	09/2012
3904	(13*10^158694+401)/9	158695	Robert Price	01/2018
3905	2^527052-69059	158659	Enzo Doria	11/2015
3906	2^526849-113233	158598	Enzo Doria	07/2014
3907	24286^36161+36161^24286	158579	Norbert Schneider	08/2023
3908	(2^526763-lucasV(1,2,526763)+1)/2	158572	Mike Oakes	11/2016
3909	(299*10^158544-17)/3	158546	Robert Price	04/2020
3910	2^526658-3551	158540	Yves Minet	03/2017
3911	7*10^158465-11	158466	Robert Price	06/2019
3912	(7^187507-3^187507)/4	158462	Jon Grantham	08/2023
3913	2^526375-23115	158455	Enzo Doria	08/2013
3914	(77*10^158407-293)/9	158408	Robert Price	09/2019
3915	31209^35242-35242^31209	158388	Frank Doornink	01/2024
3916	32071^35144-35144^32071	158363	Frank Doornink	01/2024
3917	2^526028-112793	158351	Enzo Doria	07/2014
3918	(229*10^158339-1)/3	158341	Robert Price	07/2020
3919	32042^35123-35123^32042	158255	Frank Doornink	01/2024
3920	2^525690-9221	158249	Lelio R Paula	01/2013
3921	2*10^158242-7	158243	Robert Price	10/2015
3922	2^525667-525667^2	158242	Henri Lifchitz	12/2017
3923	(56*10^158230+187)/9	158231	Robert Price	10/2021
3924	10^158209-7000000001	158209	Robert Price	12/2021
3925	31050^35207-35207^31050	158153	Frank Doornink	01/2024
3926	2^525186-1857431	158097	Enzo Doria	10/2015
3927	31527^35108-35108^31527	157940	Frank Doornink	01/2024
3928	2^524515-23245	157895	Enzo Doria	08/2013
3929	2^524499-109087	157890	Enzo Doria	04/2014
3930	2^524384-219533	157856	Enzo Doria	03/2024
3932	2^18067*(2^506221+1)-1	157827	Makoto Morimoto	05/2014
3933	2^524288+189093	157827	Makoto Morimoto	01/2016
3931	2^524288-164073	157827	Matthias Baur	03/2020
3934	(2^(2^19)-9333)/(1923463121331973)	157814	Makoto Morimoto	09/2017
3935	(10^157792+359)/9	157792	Serge Batalov	12/2014
3936	2^524154+25	157787	Stefano Morozzi	04/2021
3937	2^523924+1876591	157717	Enzo Doria	07/2016
3938	(17*10^157705+67)/3	157706	Robert Price	01/2019
3939	(46^94841+1)/47	157696	Robert Price	01/2014
3940	2^523774+77839	157672	Enzo Doria	05/2016
3941	2^523587+2799143	157616	Enzo Doria	04/2016
3942	2^523496+220141	157588	Enzo Doria	03/2024
3943	2^523371+1872113	157551	Enzo Doria	05/2016
3944	8*10^157477+27	157478	Robert Price	09/2021
3945	p(30987)#-p(30987+1)	157417	Henri Lifchitz	11/2024
3946	32268^34909-34909^32268	157397	Frank Doornink	02/2024
3947	(8*10^157368+49)/3	157369	Robert Price	05/2020
3948	(82*10^157319+449)/9	157320	Robert Price	11/2019
3949	2^522535-351457	157299	Enzo Doria	07/2015
3950	25401^35704-35704^25401	157271	Frank Doornink	01/2024
3951	2^522226+2799079	157206	Enzo Doria	04/2016
3952	(134*10^157191-11)/3	157193	Robert Price	01/2022
3953	2^522134-1849451	157178	Enzo Doria	08/2015
3954	9*10^157152+71	157153	Robert Price	08/2020
3955	4*10^157150+93	157151	Robert Price	08/2018
3956	31227^34952-34952^31227	157093	Frank Doornink	01/2024
3957	(32^104347+5^104347)/37	157057	Anonymous	12/2023
3958	fibonacci(751442)-2	157042	Jon Grantham	08/2023
3959	2^521401-29593	156958	Enzo Doria	08/2015
3960	7*10^156956+87	156957	Robert Price	07/2019
3961	2^521348-23397	156942	Enzo Doria	08/2013
3962	10^156902+34509	156903	Patrick De Geest	08/2021
3964	10^156902-80000001	156902	Robert Price	04/2021
3963	10^156902-69789	156902	Patrick De Geest	08/2021
3965	(98^78797+1)/99	156901	Paul Bourdelais	12/2017
3966	65^86522+64	156857	Lelio R Paula	04/2016
3967	8^173687-7^173687	156855	Jean-Louis Charton	09/2004
3968	2^520977-1858183	156830	Enzo Doria	10/2015
3969	(8*10^156718-101)/3	156719	Robert Price	08/2018
3970	(10^156640+7)/53	156639	Alfred Reich	07/2021
3971	2^520314-1849481	156631	Enzo Doria	08/2015
3972	(16*10^156563-637)/9	156564	Robert Price	09/2022
3973	(13*10^156522+89)/3	156523	Robert Price	09/2018
3974	(2^(6*86654+1)-5)/3	156513	Kevin Acres	12/2013
3975	(2^519925-5)/3	156513	Stefano Morozzi	08/2022
3976	(4*10^156501+119)/3	156502	Robert Price	12/2021
3977	(83*10^156476-101)/9	156477	Robert Price	08/2021
3978	3*10^156435-97	156436	Robert Price	07/2018
3979	10^156428+111	156429	Boyan Hu	10/2024
3980	(8*10^156371-77)/3	156372	Robert Price	07/2018
3981	53^90679-52^90679	156356	Robert Price	01/2013
3982	31267^34782-34782^31267	156349	Frank Doornink	01/2024
3983	(418*10^156309-31)/9	156311	Robert Price	05/2022
3984	2^519106-59141	156267	Enzo Doria	10/2015
3985	25929^35404-35404^25929	156266	Frank Doornink	03/2024
3986	2^519053+6077	156251	Enzo Doria	02/2016
3987	31199^34764-34764^31199	156235	Frank Doornink	01/2024
3988	2^518968-1860989	156225	Enzo Doria	11/2015
3989	(25*10^156221-7)/9	156222	Robert Price	05/2018
3990	2^518931-2782297	156214	Enzo Doria	09/2015
3991	2^518608-2939	156117	Yves Minet	09/2014
3992	10*27^109005+697	156027	Curtis Bright	05/2015
3993	(49*10^155933-319)/9	155934	Robert Price	10/2021
3994	2^517967-113485	155924	Enzo Doria	08/2014
3995	(103*10^155904+17)/3	155906	Robert Price	08/2020
3996	(8*10^155887-719)/9	155887	Robert Price	03/2021
3997	2^517789+29231	155871	Enzo Doria	02/2024
3998	4*10^155853-39	155854	Robert Price	09/2020
3999	2^517698+4429	155843	Lelio R Paula	01/2013
4000	32015^34584-34584^32015	155814	Frank Doornink	01/2024

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Probable Primes Top 10000

(301979 PRPs in the top)