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	(25*10^141366-331)/9	141367	Robert Price	08/2018
3752	36986^6639+6639^36986	141365	Hans Havermann	06/2021
3753	34572^12271+12271^34572	141361	Hans Havermann	06/2021
3754	37179^6338+6338^37179	141353	Hans Havermann	05/2021
3755	(2^469564-3)/611	141351	Lelio R Paula	08/2015
3756	197^61601+2	141342	Lelio R Paula	08/2017
3757	33420^16951+16951^33420	141340	Hans Havermann	05/2021
3758	31623^29458+29458^31623	141330	Hans Havermann	05/2021
3759	48112^865+865^48112	141306	Hans Havermann	05/2021
3760	2^469372-112949	141296	Enzo Doria	07/2014
3761	5*10^141294-63	141295	Robert Price	04/2021
3762	3^296115+4	141283	Tyler NeSmith	01/2021
3763	(64*10^141256+161)/9	141257	Robert Price	08/2022
3764	143^(2^16)+106^(2^16)	141253	Valeryi Kuryshev	02/2011
3765	143^65536+106^65536	141253	Serge Batalov	03/2018
3766	(11*10^141243-23)/3	141244	Robert Price	09/2021
3768	2^469198+782569	141243	Enzo Doria	10/2016
3767	38129^5062+5062^38129	141243	Hans Havermann	05/2021
3769	2^469076-2786939	141206	Enzo Doria	11/2015
3770	38630^4521+4521^38630	141202	Hans Havermann	05/2021
3771	31755^27836+27836^31755	141139	Hans Havermann	05/2021
3772	35554^9325+9325^35554	141137	Hans Havermann	05/2021
3773	2^468804+1874941	141125	Enzo Doria	06/2016
3774	2^468787+81353	141119	Enzo Doria	08/2016
3775	2^468595-350407	141062	Enzo Doria	06/2015
3776	2^468564+87855	141052	Lelio R Paula	01/2016
3777	2^468551-21987	141048	Enzo Doria	07/2013
3778	2^468523-7	141040	Lelio R Paula	08/2015
3779	(25*10^141019-13)/3	141020	Robert Price	09/2019
3780	2^468405+87855	141004	Lelio R Paula	01/2016
3781	39338^3831+3831^39338	140961	Hans Havermann	05/2021
3782	31458^30239+30239^31458	140950	Hans Havermann	05/2021
3783	8*10^140932+29	140933	Robert Price	11/2021
3784	33166^17691+17691^33166	140881	Hans Havermann	06/2021
3785	2^467978-113051	140876	Enzo Doria	07/2014
3786	2^467780-344429	140816	Enzo Doria	07/2015
3787	9*10^140802-89	140803	Robert Price	04/2020
3788	2^467605-1855603	140764	Enzo Doria	09/2015
3789	(9^147503-5^147503)/4	140754	Jon Grantham	07/2023
3790	5*10^140744-7	140745	Robert Price	09/2015
3791	(5^201359-1)/4	140744	Paul Bourdelais	12/2008
3792	2^467401-1850023	140702	Enzo Doria	08/2015
3793	(14*10^140693+13)/9	140694	Tyler Busby	02/2023
3794	(266*10^140681-17)/3	140683	Robert Price	07/2020
3795	(2^467270+78557)/23247	140658	Lelio R Paula	07/2015
3796	32138^23781+23781^32138	140644	Hans Havermann	05/2021
3797	31654^27735+27735^31654	140640	Hans Havermann	05/2021
3798	(29*2^467205+1)/2780517107	140635	Lelio R Paula	08/2015
3799	2^467166-1854941	140631	Enzo Doria	09/2015
3800	(203*10^140615-11)/3	140617	Robert Price	12/2020
3801	(85*10^140609+473)/9	140610	Robert Price	01/2020
3802	39231^3836+3836^39231	140600	Hans Havermann	06/2021
3803	5*3^294676+2^294676	140597	Jon Grantham	08/2023
3804	2^466866-1840571	140541	Enzo Doria	06/2015
3805	2^466829-459523	140530	Enzo Doria	05/2015
3806	2^466692-113213	140489	Enzo Doria	07/2014
3807	23*10^140464-3	140466	Robert Price	10/2021
3808	(2*10^140461-17)/3	140461	Serge Batalov	11/2022
3809	31335^30364+30364^31335	140455	Hans Havermann	05/2021
3810	32795^19126+19126^32795	140416	Hans Havermann	05/2021
3811	(44*10^140410-503)/9	140411	Robert Price	12/2018
3812	153^64265-2	140400	Lelio R Paula	11/2017
3813	(112*10^140357-1)/3	140359	Serge Batalov	12/2014
3814	(29*10^140337-17)/3	140338	Robert Price	09/2019
3815	2^466181-112735	140335	Enzo Doria	07/2014
3816	(16*10^140290-37)/3	140291	Robert Price	05/2021
3817	(5*10^140281-119)/3	140282	Robert Price	03/2018
3818	34568^11415+11415^34568	140259	Hans Havermann	05/2021
3819	(27*2^465872+1)/691	140241	Lelio R Paula	08/2015
3820	33632^14781+14781^33632	140236	Hans Havermann	05/2021
3821	31803^25670+25670^31803	140233	Hans Havermann	05/2021
3822	2^465803-114817	140221	Enzo Doria	05/2015
3823	floor(Pi*10^140344)%10^140165	140165	Serge Batalov	08/2012
3824	2^465503-112735	140131	Enzo Doria	07/2014
3825	(16*10^140091+167)/3	140092	Robert Price	06/2019
3826	(8*10^140087-137)/3	140088	Robert Price	03/2022
3827	6^179964+179964^6-1	140040	Robert Price	04/2014
3828	(89*10^140008-179)/9	140009	Robert Price	12/2019
3829	(29*2^465077-1)/9	140003	Lelio R Paula	08/2015
3830	2^465072-344789	140001	Enzo Doria	07/2015
3831	34742^10683+10683^34742	139965	Hans Havermann	05/2021
3832	5*10^139945+81	139946	Robert Price	03/2019
3833	32648^19335+19335^32648	139941	Hans Havermann	05/2021
3834	2^464864-17	139939	Lelio R Paula	09/2017
3835	8*10^139920+51	139921	Robert Price	08/2019
3836	(85*10^139913-1)/3	139915	Robert Price	02/2020
3837	31203^30436+30436^31203	139896	Hans Havermann	04/2021
3838	2^464642+22189	139872	Enzo Doria	09/2023
3839	26138^31663-31663^26138	139865	Frank Doornink	03/2024
3840	(16^116139+619)/5	139845	Anonymous	08/2022
3841	(2^464556+619)/5	139845	Eric Chen	10/2023
3842	4*10^139839-27	139840	Robert Price	08/2021
3843	33582^14573+14573^33582	139821	Hans Havermann	05/2021
3844	(17^113621+1)/18	139804	Paul Bourdelais	09/2011
3846	2*10^139800-21	139801	Robert Price	09/2020
3845	32628^19261+19261^32628	139801	Hans Havermann	04/2021
3847	(13*10^139782+191)/3	139783	Robert Price	11/2018
3848	(64*10^139776+791)/9	139777	Robert Price	01/2022
3849	(695*10^139772+7)/9	139774	Robert Price	12/2021
3850	(19*2^464312-1)/3	139773	Lelio R Paula	08/2015
3851	(74*10^139723+133)/9	139724	Robert Price	06/2019
3852	3*10^139722+13	139723	Robert Price	07/2018
3853	31577^26592+26592^31577	139721	Hans Havermann	05/2021
3854	77*10^139692+3	139694	Robert Price	06/2020
3855	(31*2^463970+1)/5	139670	Lelio R Paula	08/2015
3856	(18203^(2^15)+(18201)^(2^15))/2	139597	Robert Price	05/2018
3857	39640^3321+3321^39640	139584	Hans Havermann	05/2021
3858	36663^6410+6410^36663	139571	Hans Havermann	05/2021
3859	2^463633-2788423	139568	Enzo Doria	11/2015
3860	33659^13978+13978^33659	139532	Hans Havermann	05/2021
3861	31811^24318+24318^31811	139521	Hans Havermann	04/2021
3862	34149^12172+12172^34149	139512	Hans Havermann	04/2021
3863	(29*10^139476+313)/9	139477	Robert Price	04/2021
3864	31721^24940+24940^31721	139474	Hans Havermann	05/2021
3865	32833^17698+17698^32833	139473	Hans Havermann	05/2021
3866	2^463271-109501	139459	Enzo Doria	04/2014
3867	(5*10^139457+79)/3	139458	Robert Price	03/2018
3868	2^463237-99	139449	Lelio R Paula	09/2017
3869	(49*10^139442+383)/9	139443	Robert Price	04/2019
3870	31155^29902+29902^31155	139441	Hans Havermann	05/2021
3871	(7*10^139417-547)/9	139417	Robert Price	01/2018
3872	(10^139398+191)/3	139398	Robert Price	02/2018
3873	23*10^139386-3	139388	Robert Price	10/2021
3874	2^463019+79463	139383	Enzo Doria	06/2016
3875	3^292129-112756	139381	Enzo Doria	07/2014
3876	(15*2^462951+1)/527	139361	Lelio R Paula	08/2015
3877	31922^23205+23205^31922	139359	Hans Havermann	05/2021
3878	(19*10^139336+503)/9	139337	Alfred Reich	11/2023
3880	2^462855-1865707	139334	Enzo Doria	02/2016
3879	31237^28876+28876^31237	139334	Hans Havermann	05/2021
3881	(86*10^139315+121)/9	139316	Robert Price	08/2019
3882	2^462786-292043	139313	Enzo Doria	08/2015
3883	38915^3798+3798^38915	139299	Hans Havermann	05/2021
3885	(26*10^139289+1)/9	139290	Serge Batalov	05/2010
3884	(17*10^139289+7)/3	139290	Robert Price	06/2023
3886	34065^12248+12248^34065	139260	Hans Havermann	05/2021
3887	36425^6654+6654^36425	139256	Hans Havermann	05/2021
3888	39252^3527+3527^39252	139243	Hans Havermann	05/2021
3889	(17*10^139239+67)/3	139240	Robert Price	01/2019
3890	31887^23248+23248^31887	139231	Hans Havermann	05/2021
3891	(25*10^139210-97)/9	139211	Robert Price	01/2022
3892	2^462238-935	139148	Yves Minet	02/2014
3893	(29*10^139134-119)/9	139135	Robert Price	12/2021
3894	(109*10^139100-7)/3	139102	Robert Price	03/2021
3895	38744^3885+3885^38744	139068	Hans Havermann	05/2021
3896	31112^29499+29499^31112	139065	Hans Havermann	05/2021
3897	2*10^139043-63	139044	Robert Price	01/2022
3898	36390^6613+6613^36390	139025	Hans Havermann	04/2021
3899	2*10^138975+33	138976	Robert Price	11/2021
3900	42437^1882+1882^42437	138966	Hans Havermann	05/2021
3901	32151^20990+20990^32151	138958	Hans Havermann	05/2021
3902	32154^20933+20933^32154	138933	Hans Havermann	04/2021
3903	31082^29499+29499^31082	138931	Hans Havermann	04/2021
3904	2^461228+1870441	138844	Enzo Doria	05/2016
3905	2^461204-113675	138837	Enzo Doria	08/2014
3906	(2^461139-7)/47	138815	Lelio R Paula	08/2015
3907	(17*10^138812-521)/9	138813	Robert Price	04/2018
3908	3*10^138811-11	138812	Robert Price	07/2018
3909	(28*10^138768+173)/3	138769	Robert Price	12/2019
3910	(17*2^460963+1)/124051613	138757	Lelio R Paula	08/2015
3911	(379*10^138737-1)/9	138739	Robert Price	02/2020
3912	(43*10^138648+101)/9	138649	Robert Price	11/2018
3913	2^460567-113541	138645	Enzo Doria	08/2014
3914	(10^138622+161)/9	138622	Robert Price	09/2021
3915	7*10^138604+3	138605	Robert Price	08/2015
3916	(133*10^138600+17)/3	138602	Robert Price	11/2021
3917	33912^12203+12203^33912	138581	Hans Havermann	05/2021
3918	2^460330+69	138574	Lelio R Paula	09/2017
3919	(17*10^138569-77)/3	138570	Robert Price	08/2019
3920	31186^27725+27725^31186	138556	Hans Havermann	05/2021
3921	(16*10^138545+89)/3	138546	Robert Price	03/2021
3922	39753^3056+3056^39753	138546	Hans Havermann	05/2021
3923	31282^26847+26847^31282	138545	Hans Havermann	05/2021
3924	6*10^138520-37	138521	Robert Price	02/2021
3926	2^460078-69581	138498	Enzo Doria	12/2015
3925	31830^22447+22447^31830	138498	Hans Havermann	05/2021
3927	37384^5065+5065^37384	138492	Hans Havermann	05/2021
3928	34774^9585+9585^34774	138456	Hans Havermann	05/2021
3929	10^138444-5001	138444	Robert Price	12/2021
3930	2^459768+1531	138404	Lelio R Paula	06/2012
3931	(266*10^138328-17)/3	138330	Robert Price	07/2020
3932	27200^31193-31193^27200	138328	Frank Doornink	01/2024
3933	32963^15696+15696^32963	138306	Hans Havermann	05/2021
3934	2^459343-113611	138277	Enzo Doria	08/2014
3935	(28*10^138240+113)/3	138241	Robert Price	03/2020
3936	2^459199+1874393	138233	Enzo Doria	06/2016
3937	33339^14002+14002^33339	138230	Hans Havermann	05/2021
3938	2^459063-345307	138192	Enzo Doria	06/2015
3939	2*10^138162-43	138163	Robert Price	04/2018
3940	2^458927-112747	138151	Enzo Doria	06/2014
3941	2^458927-69217	138151	Enzo Doria	11/2015
3942	30907^29458+29458^30907	138130	Hans Havermann	05/2021
3943	32882^15837+15837^32882	138094	Hans Havermann	05/2021
3944	39252^3295+3295^39252	138083	Hans Havermann	05/2021
3945	33789^12190+12190^33789	138062	Hans Havermann	06/2021
3946	555555*2^458524+1513	138036	Darren Bedwell	08/2009
3947	30931^29002+29002^30931	138028	Hans Havermann	05/2021
3948	2^458465+2^32+1	138012	T. D. Noe	06/2007
3949	32206^19275+19275^32206	138003	Hans Havermann	05/2021
3950	2^458321-113053	137969	Enzo Doria	07/2014
3951	6^177298+323	137965	Riley Fisher	03/2023
3952	2^458298+79459	137962	Enzo Doria	06/2016
3953	2^458248-21815	137947	Enzo Doria	07/2013
3954	2^458194+1876549	137931	Enzo Doria	07/2016
3955	(318259#+325270)/(2^2511*2957)	137907	Makoto Morimoto	10/2017
3956	(318259#+2625)/(3^257^5*22965193)	137899	Makoto Morimoto	06/2019
3957	(793*10^137887+53)/9	137889	Robert Price	01/2022
3958	2^457937+57	137853	Lelio R Paula	09/2017
3959	(8*10^137845+13)/3	137846	Robert Price	06/2018
3960	2^457822+105	137819	Donovan Johnson	06/2006
3961	2^457754-113711	137798	Enzo Doria	09/2014
3962	11^132315-360	137792	Enzo Doria	09/2012
3963	32072^19689+19689^32072	137725	Hans Havermann	06/2021
3964	26529^31132-31132^26529	137720	Frank Doornink	03/2024
3965	44592^1225+1225^44592	137707	Hans Havermann	05/2021
3966	2^457347-37	137676	Lelio R Paula	09/2017
3967	2^457322-2786393	137668	Enzo Doria	10/2015
3968	gcd(Phi(699340,10),(10^34967+1)^3(10^34967+1+10^17484)-(10^69934+10^34967)(10^17484-1)+10^104901)	137664	Serge Batalov	04/2015
3969	34015^11134+11134^34015	137647	Hans Havermann	06/2021
3970	2^457240-59939	137643	Enzo Doria	10/2015
3971	(856*10^137633-1)/9	137635	Robert Price	03/2020
3972	36232^6289+6289^36232	137631	Hans Havermann	05/2021
3973	2^457120-21575	137607	Enzo Doria	07/2013
3975	(11*2^456978+1)/15	137564	Lelio R Paula	07/2015
3974	30963^27722+27722^30963	137564	Hans Havermann	04/2021
3976	33722^12003+12003^33722	137562	Hans Havermann	06/2021
3977	(7*25^98399+10613)/12	137556	Curtis Bright	05/2015
3978	41901^1918+1918^41901	137555	Hans Havermann	06/2021
3979	(7*10^137551-1)/3	137552	Robert Price	08/2022
3980	32930^15021+15021^32930	137539	Hans Havermann	05/2021
3981	31178^25785+25785^31178	137538	Hans Havermann	05/2021
3982	419^52446+52446^419	137525	Norbert Schneider	11/2020
3983	2^456813+214175	137515	Enzo Doria	10/2023
3984	2^456796-113513	137510	Enzo Doria	08/2014
3985	31788^21137+21137^31788	137485	Hans Havermann	04/2021
3986	(7*2^456655+1)/39	137467	Lelio R Paula	07/2015
3987	27151^31004-31004^27151	137466	Frank Doornink	01/2024
3988	2^456503-114361	137422	Enzo Doria	01/2015
3989	(11*2^456387+1)/19	137386	Lelio R Paula	07/2015
3990	30618^30618-5^5	137352	Serge Batalov	04/2024
3991	36248^6147+6147^36248	137332	Hans Havermann	05/2021
3992	31986^19651+19651^31986	137329	Hans Havermann	05/2021
3993	2^456167+22313	137320	Enzo Doria	09/2023
3994	31817^20656+20656^31817	137292	Hans Havermann	05/2021
3995	(71*10^137250+1)/9	137251	Serge Batalov	05/2010
3996	2^455922+76249	137247	Enzo Doria	05/2016
3997	31310^24171+24171^31310	137241	Hans Havermann	05/2021
3998	14^119741-119741^14	137239	Serge Batalov	04/2016
3999	35014^8297+8297^35014	137218	Hans Havermann	05/2021
4000	(19*2^455760+1)/3455	137196	Lelio R Paula	07/2015

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Probable Primes Top 10000

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