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	2^564561+225	169950	Henri Lifchitz	11/2024
3752	(7*10^169944+23)/3	169945	Robert Price	06/2020
3753	(37*10^169943+251)/9	169944	Robert Price	09/2021
3754	2^564526-351401	169940	Enzo Doria	07/2015
3755	3^355902+4	169809	Aurel Gibier	10/2024
3756	4*10^169759+19	169760	Robert Price	10/2018
3757	(2^563903-13)/5	169752	Stefano Morozzi	08/2022
3758	21^128327-20^128327	169677	Jean-Louis Charton	11/2014
3759	2^563583+89	169656	Stefano Morozzi	04/2021
3760	2^563311+215813	169574	Enzo Doria	11/2023
3761	(4*10^169559+83)/3	169560	Robert Price	02/2018
3762	(194*10^169461-17)/3	169463	Robert Price	09/2020
3763	2^562749+2793047	169405	Enzo Doria	02/2016
3764	(154*10^169337-1)/9	169339	Serge Batalov	12/2014
3765	(109*10^169337+11)/3	169339	Robert Price	06/2022
3766	(56*10^169311+691)/9	169312	Robert Price	05/2019
3767	2^562369-29503	169290	Enzo Doria	08/2015
3768	(17*10^169283+19)/9	169284	Robert Price	03/2021
3769	390151#-2322911	169082	Hayden Chesnut	07/2024
3770	10^169074-5000000001	169074	Robert Price	09/2022
3771	8*10^169071+59	169072	Robert Price	11/2021
3772	(10^169044+173)/3	169044	Robert Price	05/2021
3773	(22*10^169019+383)/9	169020	Robert Price	05/2018
3774	(64*10^168935+143)/9	168936	Robert Price	05/2021
3775	(22*10^168906+47)/3	168907	Robert Price	06/2021
3776	5*10^168807+87	168808	Robert Price	02/2019
3777	(77*10^168803-149)/9	168804	Robert Price	03/2022
3778	4*10^168788-47	168789	Robert Price	10/2021
3779	(154*10^168781+17)/9	168783	Robert Price	06/2022
3780	(418*10^168751-31)/9	168753	Robert Price	05/2022
3781	(29*10^168711+691)/9	168712	Robert Price	08/2021
3782	2^560405-39943	168699	Enzo Doria	09/2015
3783	(397*10^168634+17)/9	168636	Robert Price	03/2022
3784	2^560189+36587	168634	Enzo Doria	09/2024
3785	89*10^168614-7	168616	Robert Price	04/2020
3786	(23*10^168608-83)/3	168609	Robert Price	08/2019
3787	(94*10^168541+11)/3	168543	Robert Price	04/2020
3788	2^559686-350471	168483	Enzo Doria	06/2015
3789	2^559672-1855889	168479	Enzo Doria	09/2015
3790	(5*10^168379-473)/9	168379	Robert Price	01/2018
3791	2024^50920+3	168353	Martin Hopf	01/2024
3792	2^559000-59939	168276	Enzo Doria	11/2015
3793	2^558830+25009	168225	Enzo Doria	11/2023
3794	(16*10^168181+41)/3	168182	Robert Price	03/2019
3795	(19*10^168173+77)/3	168174	Robert Price	05/2019
3796	(74*10^168170+529)/9	168171	Robert Price	02/2022
3797	2^558640-114149	168168	Enzo Doria	12/2014
3798	2^558498-1849277	168125	Enzo Doria	08/2015
3799	2^558476-1850249	168119	Enzo Doria	08/2015
3800	(7*10^168067+71)/3	168068	Robert Price	05/2018
3801	2^558150-1852211	168020	Enzo Doria	08/2015
3802	2^558125-113661	168013	Enzo Doria	09/2014
3803	393^64747-392^64747	167980	Jean-Louis Charton	08/2012
3804	(8*10^167965-11)/3	167966	Robert Price	07/2023
3805	2^557916+216151	167950	Enzo Doria	12/2023
3806	(13*10^167911+179)/3	167912	Robert Price	11/2018
3807	(26*10^167861-167)/3	167862	Robert Price	10/2019
3808	36^107827-107827	167812	Kellen Shenton	06/2023
3809	32027^37242-37242^32027	167795	Frank Doornink	01/2024
3810	39^105456+2	167788	Robert Price	04/2015
3811	2^557322+217519	167771	Enzo Doria	01/2024
3812	(28^115877-1)/27	167691	Paul Bourdelais	12/2017
3813	6*10^167662-13	167663	Robert Price	07/2022
3814	10^167639+121911	167640	Patrick De Geest	07/2018
3815	10^167639-8001	167639	Robert Price	03/2018
3816	2^556504-462059	167525	Enzo Doria	07/2015
3817	(88*10^167522-637)/9	167523	Robert Price	11/2020
3818	5*10^167510+9	167511	Robert Price	08/2015
3819	7*10^167437-93	167438	Robert Price	08/2020
3820	(43^102451-1)/7138097213378082	167335	Paul Vanderveen	05/2025
3821	25455^37978-37978^25455	167323	Frank Doornink	01/2024
3822	11^160663+6	167314	Paul Bourdelais	02/2021
3823	(7*10^167308-493)/9	167308	Robert Price	04/2021
3824	2^555759+74333	167301	Enzo Doria	07/2023
3825	26084^37871-37871^26084	167253	Frank Doornink	03/2024
3826	2^555343+1874333	167175	Enzo Doria	06/2016
3827	2^555210-461261	167135	Enzo Doria	07/2015
3828	9*10^166996+59	166997	Robert Price	01/2020
3829	(68*10^166976-329)/9	166977	Robert Price	03/2021
3830	(64*10^166901+683)/9	166902	Robert Price	06/2022
3831	2^554372+1880527	166883	Enzo Doria	11/2016
3832	2^554299+72173	166861	Enzo Doria	04/2016
3833	(185*10^166837+7)/3	166839	Robert Price	03/2020
3834	(14*10^166813+139)/9	166814	Robert Price	11/2021
3835	26084^37767-37767^26084	166794	Frank Doornink	03/2024
3836	2^554037-2797063	166782	Enzo Doria	03/2016
3837	31861^37028-37028^31861	166747	Frank Doornink	01/2024
3838	Phi(276951,2^3)	166740	Henri Lifchitz	12/2025
3839	(49*10^166721-139)/9	166722	Robert Price	03/2019
3840	2*10^166646+69	166647	Robert Price	06/2020
3841	2^553484-29819	166616	Enzo Doria	08/2015
3842	(188*10^166611+7)/3	166613	Robert Price	03/2020
3843	2^553383-2784217	166585	Enzo Doria	10/2015
3844	2^553069+76427	166491	Enzo Doria	05/2016
3845	2^553020+1152921504606846975	166476	Alfred Reich	05/2026
3846	25218^37819-37819^25218	166469	Frank Doornink	12/2023
3847	2*10^166458+51	166459	Robert Price	05/2018
3848	589^60089-588^60089	166454	Jean-Louis Charton	09/2012
3849	Phi(556277,2)	166404	Henri Lifchitz	12/2025
3850	25214^37799-37799^25214	166378	Frank Doornink	11/2023
3851	11^159756-2424	166369	Mike Oakes	06/2010
3852	2^552649-361275	166364	Enzo Doria	05/2014
3853	2^552628-113669	166358	Enzo Doria	09/2014
3854	(19*10^166325+137)/3	166326	Robert Price	03/2022
3855	10^166324+550603	166325	Patrick De Geest	07/2018
3856	10^166324-801	166324	Robert Price	02/2018
3857	(85*10^166297-1)/3	166299	Robert Price	02/2020
3858	(19*10^166280-7)/3	166281	Robert Price	12/2023
3859	25533^37726-37726^25533	166263	Frank Doornink	02/2024
3860	8*10^166227+87	166228	Robert Price	10/2019
3861	2^552137+1879397	166210	Enzo Doria	09/2016
3862	262273205671539190984629()252475512364409752762433	166141	Anonymous	01/2025
3863	490079063773165613318095()218182139934160868002603	166141	Anonymous	01/2025
3864	140717254840416411192803()712689271538459396766869	166140	Anonymous	01/2025
3865	122398296040696255481419()271117913237372866926417	166140	Anonymous	01/2025
3866	(103*10^166126+11)/3	166128	Robert Price	01/2021
3867	(22*10^166077+179)/3	166078	Robert Price	02/2022
3868	(23^121949-1)/22	166061	Paul Bourdelais	10/2017
3869	2^551576+236221	166041	Enzo Doria	05/2025
3870	2^551542+19249	166031	Payam Samidoost	08/2002
3871	2^551535-23821	166029	Enzo Doria	08/2013
3872	2^551507-23557	166021	Enzo Doria	08/2013
3873	32030^36841-36841^32030	165990	Frank Doornink	01/2024
3874	10^165947-7000000001	165947	Robert Price	12/2021
3875	4*10^165938-47	165939	Robert Price	10/2021
3876	7*10^165916-3	165917	Robert Price	08/2015
3877	(29*10^165796+67)/3	165797	Robert Price	12/2019
3878	81^86837-80^86837	165728	Robert Price	01/2015
3879	(71*10^165716-17)/9	165717	Serge Batalov	01/2023
3880	fibonacci(792909)+3	165708	Jon Grantham	08/2023
3881	(71*10^165663-539)/9	165664	Robert Price	07/2019
3882	25682^37567-37567^25682	165657	Frank Doornink	02/2024
3883	2^550270-69551	165648	Enzo Doria	12/2015
3884	2^550250+29329	165642	Enzo Doria	03/2024
3885	(202*10^165569-13)/9	165571	Robert Price	01/2020
3886	2^550000-23625	165567	Enzo Doria	08/2013
3887	31688^36783-36783^31688	165557	Frank Doornink	01/2024
3888	2^549675-1852057	165469	Enzo Doria	08/2015
3889	2^549663+212543	165466	Enzo Doria	08/2023
3890	(3^549633)%(2^549633)	165456	Henri Lifchitz	06/2025
3891	Phi(125543,5#)	165438	Henri Lifchitz	12/2025
3892	(529*10^165394-7)/9	165396	Robert Price	08/2021
3893	26253^37424-37424^26253	165384	Frank Doornink	03/2024
3894	-tau(103^14938)	165374	Nik Lygeros / Olivier Rozier	10/2013
3895	(28*10^165358-1)/9	165359	Serge Batalov	10/2014
3896	2^549278+1879669	165350	Enzo Doria	09/2016
3897	(7*10^165350-439)/9	165350	Robert Price	02/2018
3898	2^549252-351269	165342	Enzo Doria	06/2015
3899	2^549221+335931	165332	Enzo Doria	09/2024
3900	67*10^165327-9	165329	Robert Price	03/2021
3901	(14*10^165282+73)/3	165283	Robert Price	12/2018
3902	(8*10^165283-629)/9	165283	Robert Price	01/2022
3903	2^549049+2797607	165281	Enzo Doria	04/2016
3904	(218*10^165258+7)/9	165260	Robert Price	06/2022
3905	(7*10^165239+107)/3	165240	Robert Price	02/2018
3906	2^548880+23961	165230	Enzo Doria	10/2023
3907	5*2^548778+3	165200	Jon Grantham	07/2023
3908	(44^100511-1)/43	165184	Paul Bourdelais	11/2017
3909	(7*10^165134+107)/3	165135	Robert Price	02/2018
3910	(301*10^165082+23)/9	165084	Robert Price	06/2021
3911	(23*10^165060-83)/3	165061	Robert Price	08/2019
3912	7*10^165023-27	165024	Robert Price	11/2022
3913	(76*10^164984+77)/9	164985	Robert Price	10/2019
3914	31058^36715-36715^31058	164931	Frank Doornink	01/2024
3915	(4*10^164929-211)/9	164929	Robert Price	03/2022
3916	10^164878-500001	164878	Robert Price	03/2022
3917	Phi(175151,10)/25997097796891253	164816	Anonymous	02/2026
3918	9*10^164791-89	164792	Robert Price	04/2020
3919	(2^788414)%F(788414)	164769	Henri Lifchitz	05/2025
3920	2^547178-1856501	164717	Enzo Doria	10/2015
3921	11^158160-60	164707	Enzo Doria	07/2012
3922	(26*10^164643-167)/3	164644	Robert Price	10/2019
3923	(10^164643+83)/3	164643	Robert Price	08/2021
3924	2^546398-59201	164483	Enzo Doria	10/2015
3925	2^546332-114893	164463	Enzo Doria	05/2015
3926	36087^36087-36080^36080	164462	Henri Lifchitz	08/2024
3927	32003^36504-36504^32003	164458	Frank Doornink	01/2024
3928	(65*10^164427+277)/9	164428	Robert Price	08/2021
3929	2^545958+1876189	164350	Enzo Doria	07/2016
3930	2^545878-49841	164326	Enzo Doria	10/2015
3931	(10^164284+77)/3	164284	Robert Price	01/2018
3932	2^545668-4019	164263	Yves Minet	04/2017
3933	10^164216+780639	164217	Patrick De Geest	08/2021
3935	10^164216-50000000001	164216	Robert Price	12/2020
3934	10^164216-891051	164216	Patrick De Geest	08/2021
3936	(1353^238539617^9)/10^247183	164151	Hans Havermann	07/2017
3937	(16*10^164122+197)/3	164123	Robert Price	04/2019
3938	2^545185+76757	164118	Enzo Doria	05/2016
3939	2^545076-114329	164085	Enzo Doria	01/2015
3940	(2*10^164043-143)/3	164043	Robert Price	03/2018
3941	(33085^36481-1)/(33085^191-1)	164018	Ryan Propper	11/2023
3942	(29^112153+1)/30	164011	Lelio R Paula	03/2017
3943	2^544757+1874777	163989	Enzo Doria	06/2016
3944	2^544723+211193	163978	Enzo Doria	08/2023
3945	2^544444-457199	163894	Enzo Doria	01/2015
3946	(32804^36481-1)/(32804^191-1)	163883	Ryan Propper	11/2023
3947	2^544264-343529	163840	Enzo Doria	07/2015
3948	7*10^163780+9	163781	Robert Price	09/2015
3949	(2^783598)%L(783598)	163761	Henri Lifchitz	05/2025
3950	2^543989+2793047	163758	Enzo Doria	02/2016
3951	(28*10^163709+113)/3	163710	Robert Price	03/2020
3952	(2^543398)/(543398^2)	163568	Henri Lifchitz	05/2025
3953	(2013^49729-1)/(2013^223-1)	163561	Ryan Propper	11/2023
3954	L(2*543272)%(2^543272)	163541	Henri Lifchitz	07/2025
3955	(23*10^163523+301)/9	163524	Robert Price	06/2021
3956	(68*10^163521-329)/9	163522	Robert Price	03/2021
3957	35820^35899+35899^35820	163489	Norbert Schneider	11/2021
3958	2^542870-69551	163421	Enzo Doria	12/2015
3959	2^542502+24799	163310	Enzo Doria	10/2023
3960	2^542395+72533	163278	Enzo Doria	04/2016
3961	2^542258+216949	163236	Enzo Doria	12/2023
3962	2^542072-3683	163180	Yves Minet	03/2017
3963	fibonacci(780566)-4	163129	Jon Grantham	08/2023
3964	(682*10^163106-7)/9	163108	Robert Price	08/2021
3965	2^541779-1867357	163092	Enzo Doria	04/2016
3966	(29*10^163056+313)/9	163057	Robert Price	04/2021
3967	2^541476+214743	163001	Enzo Doria	11/2023
3968	13^142159+14^142159-2	162933	Harsh Aggarwal	05/2024
3969	8*10^162924+9	162925	Robert Price	12/2015
3970	2^540905+81557	162829	Enzo Doria	08/2016
3971	2^540628-2939	162746	Yves Minet	09/2014
3972	919^54919-918^54919	162743	Jean-Louis Charton	01/2013
3973	(203*10^162689+1)/3	162691	Robert Price	03/2020
3974	3*10^162620-59	162621	Robert Price	09/2018
3975	2^540180+26791	162611	Enzo Doria	12/2023
3976	3^340694-112960	162553	Enzo Doria	07/2014
3977	2^539925+81	162534	Henri Lifchitz	11/2024
3978	2^539807-114081	162499	Enzo Doria	12/2014
3979	414^62093+62093^414	162498	Norbert Schneider	03/2022
3980	2^539654-114893	162453	Enzo Doria	05/2015
3981	9*10^162449-71	162450	Robert Price	11/2020
3982	2^539617-1851583	162441	Enzo Doria	08/2015
3983	(509*10^162422+31)/9	162424	Robert Price	08/2022
3984	(91*10^162410+11)/3	162412	Robert Price	02/2020
3985	2^539346+81049	162360	Enzo Doria	07/2016
3986	2^539220-115499	162322	Enzo Doria	07/2015
3987	2^539217-113713	162321	Enzo Doria	09/2014
3988	9^170099-8^170099	162316	Jean-Louis Charton	05/2005
3989	4*10^162263-39	162264	Robert Price	09/2020
3990	31243^36098-36098^31243	162252	Frank Doornink	01/2024
3991	31987^36000-36000^31987	162180	Frank Doornink	01/2024
3992	(115*10^162153-1)/3	162155	Serge Batalov	12/2014
3993	(10^162138+11)/3	162138	Serge Batalov	07/2015
3994	(61*10^162100-403)/9	162101	Robert Price	10/2021
3995	2^538473-112723	162097	Enzo Doria	06/2014
3996	2^538157+79337	162002	Enzo Doria	06/2016
3997	2^538136-114749	161996	Enzo Doria	05/2015
3998	2^538104+1531	161986	Lelio R Paula	01/2013
3999	(9*29^110727-1199)/14	161927	Curtis Bright	05/2015
4000	((2^179294-1)^3+2)/11	161918	Serge Batalov	03/2023

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Probable Primes Top 10000

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