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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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*10^132493-43	132494	Robert Price	04/2018
3752	31352^16809+16809^31352	132480	Hans Havermann	04/2021
3753	(418*10^132441+23)/9	132443	Robert Price	02/2020
3754	2^439931-21	132433	Lelio R Paula	08/2017
3755	47^79201-46^79201	132432	Robert Price	10/2012
3756	2^439897-113653	132423	Enzo Doria	08/2014
3757	35505^5362+5362^35505	132410	Hans Havermann	03/2021
3758	30079^25222+25222^30079	132402	Hans Havermann	04/2021
3759	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
3760	(695*10^132356+7)/9	132358	Robert Price	12/2021
3761	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
3762	2^439576-113247	132326	Enzo Doria	07/2014
3763	30059^25230+25230^30059	132318	Hans Havermann	04/2021
3764	2^439497-29143	132302	Enzo Doria	07/2015
3765	2^439409-114193	132276	Enzo Doria	12/2014
3766	(44*10^132233-233)/9	132234	Robert Price	01/2019
3767	9*10^132148-7	132149	Robert Price	09/2015
3768	(47*10^132125-119)/9	132126	Robert Price	05/2019
3769	2^438845+1870217	132106	Enzo Doria	05/2016
3770	2^438789+87855	132089	Lelio R Paula	01/2016
3771	2^438774-2786411	132085	Enzo Doria	03/2016
3772	2^438755-1848205	132079	Enzo Doria	07/2015
3773	30502^21381+21381^30502	132075	Hans Havermann	04/2021
3774	2^438739-112087	132074	Enzo Doria	06/2014
3775	(2^438438+100280245065)	131983	Paul Bourdelais	05/2022
3776	35872^4777+4777^35872	131979	Hans Havermann	04/2021
3777	31198^16945+16945^31198	131938	Hans Havermann	03/2021
3778	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
3779	L(631181)	131910	Henri Lifchitz	09/2008
3780	(47*10^131886-119)/9	131887	Robert Price	05/2019
3781	5*2^438096-3	131881	Jon Grantham	07/2023
3782	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
3783	2^438079-1863877	131875	Enzo Doria	03/2016
3784	(16*10^131872-37)/3	131873	Robert Price	05/2021
3785	(2^438067+5)/329	131869	Lelio R Paula	06/2015
3786	2^437908-113855	131824	Enzo Doria	09/2014
3787	2^437884-286349	131817	Enzo Doria	07/2015
3788	5^188558+4	131797	Tyler NeSmith	05/2021
3789	(11*10^131784-17)/3	131785	Robert Price	06/2018
3791	4*10^131719-93	131720	Robert Price	07/2020
3790	31629^14606+14606^31629	131720	Hans Havermann	04/2021
3792	3^276062-112292	131716	Enzo Doria	07/2014
3793	(7*10^131682+89)/3	131683	Robert Price	08/2020
3794	29512^28969+28969^29512	131681	Hans Havermann	03/2021
3795	2^437343+75953	131654	Enzo Doria	04/2016
3796	35^85243-34^85243	131621	Robert Price	05/2012
3797	(28*10^131586+59)/3	131587	Robert Price	05/2021
3798	(59*10^131575+391)/9	131576	Robert Price	03/2021
3799	39984^1945+1945^39984	131505	Hans Havermann	03/2021
3800	(203*10^131457+1)/3	131459	Robert Price	03/2020
3801	7*10^131421-41	131422	Robert Price	08/2021
3802	87309^32+32^87309	131414	Hans Havermann	03/2021
3803	(68^71713+1)/69	131413	Paul Bourdelais	09/2017
3804	(650*10^131391+43)/9	131393	Tyler Busby	01/2023
3805	2^436451+1884713	131385	Enzo Doria	03/2017
3806	2^436365+35	131359	Robert Price	11/2015
3807	2^436300+1866871	131340	Enzo Doria	03/2016
3808	(7*10^131339+179)/3	131340	Robert Price	09/2018
3809	14^114592-3	131338	Paul Bourdelais	12/2020
3810	36197^4236+4236^36197	131285	Hans Havermann	04/2021
3811	(37*10^131270+341)/9	131271	Robert Price	08/2018
3812	29863^24790+24790^29863	131227	Hans Havermann	03/2021
3813	(5*10^131223-29)/3	131224	Robert Price	03/2018
3814	29524^27825+27825^29524	131218	Hans Havermann	03/2021
3815	(23*2^435891-1)/699	131215	Lelio R Paula	07/2015
3816	(11*2^435879+1)/3337	131211	Lelio R Paula	06/2015
3817	30639^19136+19136^30639	131192	Hans Havermann	04/2021
3818	(2^435808+1)/641/6700417	131182	Lelio R Paula	02/2012
3819	(2^435808+1)/4294967297	131182	Serge Batalov	12/2016
3820	2^435773+1875557	131181	Enzo Doria	06/2016
3822	(16*10^131180+167)/3	131181	Robert Price	06/2019
3821	(26*10^131180-77)/3	131181	Robert Price	11/2019
3823	(25*10^131144-7)/9	131145	Robert Price	05/2018
3824	29299^29358-29358^29299	131138	Norbert Schneider	03/2022
3825	2^435612-2789939	131133	Enzo Doria	12/2015
3826	33976^7231+7231^33976	131121	Hans Havermann	03/2021
3827	33715^7746+7746^33715	131121	Hans Havermann	03/2021
3828	66^72047-65^72047	131093	Robert Price	09/2013
3829	(5*10^131090+37)/3	131091	Robert Price	03/2018
3830	2^435468+75631	131089	Enzo Doria	04/2016
3831	37^83588-2	131083	Lelio R Paula	08/2015
3832	(4^217720+11)/3	131081	Robert Price	02/2017
3833	30407^20448+20448^30407	131074	Hans Havermann	04/2021
3834	(22*10^131070+179)/3	131071	Robert Price	02/2022
3835	29487^27836+27836^29487	131059	Hans Havermann	04/2021
3836	29962^23615+23615^29962	131030	Hans Havermann	03/2021
3837	2^435202-113193	131009	Enzo Doria	07/2014
3838	41705^1384+1384^41705	131002	Hans Havermann	04/2021
3839	9*10^130998-19	130999	Robert Price	07/2019
3840	36243^4108+4108^36243	130969	Hans Havermann	04/2021
3841	floor((sqrt(5)-1)/2*10^130911)	130911	Serge Batalov	06/2017
3842	2^434835-111937	130899	Enzo Doria	05/2014
3843	(62*10^130895-629)/9	130896	Robert Price	07/2021
3844	2^434685+72257	130854	Enzo Doria	04/2016
3845	(7*10^130825+113)/3	130826	Robert Price	02/2018
3846	2^434539-29317	130810	Enzo Doria	07/2015
3847	(74*10^130791+637)/9	130792	Robert Price	01/2022
3848	2^434469-114259	130789	Enzo Doria	01/2015
3849	(5*10^130763+103)/9	130763	Robert Price	04/2022
3850	2^434246+33	130722	Robert Price	11/2015
3851	30156^21599+21599^30156	130710	Hans Havermann	04/2021
3852	(17*10^130695-161)/9	130695	Robert Price	02/2021
3853	30513^19148+19148^30513	130661	Hans Havermann	03/2021
3854	29736^24761+24761^29736	130654	Hans Havermann	04/2021
3855	9*10^130638+41	130639	Robert Price	08/2020
3856	2^433911-91	130621	Lelio R Paula	06/2017
3857	30786^17449+17449^30786	130588	Hans Havermann	03/2021
3858	2^433744-114419	130570	Enzo Doria	02/2015
3860	2^433708+1869451	130560	Enzo Doria	05/2016
3859	2^433710+93	130560	Lelio R Paula	06/2017
3861	7*10^130535-27	130536	Robert Price	11/2022
3862	(9629^32768+1)/120501441265666	130520	Kellen Shenton	05/2021
3863	804*34^85220+713	130516	Eric Chen	08/2023
3864	(29*2^433547-1)/27	130511	Lelio R Paula	06/2015
3865	3^273521+10	130503	Tyler NeSmith	01/2021
3866	41659^1356+1356^41659	130487	Hans Havermann	03/2021
3867	4*10^130480+9	130481	Robert Price	05/2015
3868	(23*2^433449-1)/75	130481	Lelio R Paula	06/2015
3869	3*2^433422+5	130474	Jon Grantham	07/2023
3870	(23*2^433334-1)/3731	130445	Lelio R Paula	06/2015
3871	(31*10^130414-49)/9	130415	Robert Price	11/2021
3872	33481^7848+7848^33481	130401	Hans Havermann	03/2021
3873	(17*10^130393+7)/3	130394	Robert Price	06/2023
3874	(22*10^130392+203)/9	130393	Robert Price	10/2021
3875	29773^23950+23950^29773	130386	Hans Havermann	04/2021
3876	2^433023-113497	130353	Enzo Doria	08/2014
3877	31175^15178+15178^31175	130350	Hans Havermann	04/2021
3878	2^433002+1179379	130347	Enzo Doria	06/2016
3879	2^432974+19	130339	Robert Price	08/2015
3880	31903^12168+12168^31903	130331	Hans Havermann	04/2021
3881	2^432917+22217	130322	Enzo Doria	09/2023
3882	29387^27112+27112^29387	130278	Hans Havermann	04/2021
3883	2^432768+213181	130277	Enzo Doria	09/2023
3884	29577^25370+25370^29577	130267	Hans Havermann	04/2021
3885	31738^12685+12685^31738	130231	Hans Havermann	03/2021
3886	44235^878+878^44235	130206	Hans Havermann	04/2021
3887	32160^11171+11171^32160	130187	Hans Havermann	04/2021
3888	29489^25956+25956^29489	130172	Hans Havermann	04/2021
3889	(2^432457-1)/1672739247834685086279697	130159	Tony Prest / Never Odd Or Even	09/2013
3890	33005^8766+8766^33005	130133	Hans Havermann	04/2021
3891	(35*10^130132-611)/9	130133	Robert Price	02/2022
3892	2^432217+41	130111	Lelio R Paula	06/2017
3893	(2^216089*(2^216091-1)-339)/25	130098	Makoto Morimoto	03/2017
3894	((2^216091+1066)^2+(2^216091+1066)+41)/47/2069	130095	Makoto Morimoto	05/2016
3895	97^65480-2	130094	Lelio R Paula	05/2017
3896	36007^4102+4102^36007	130094	Hans Havermann	04/2021
3897	4*10^130088-89	130089	Robert Price	11/2018
3898	2^432117-113215	130081	Enzo Doria	07/2014
3899	(4*10^130080+41)/9	130080	Serge Batalov	11/2022
3900	2^431804+72511	129986	Enzo Doria	04/2016
3901	(13*10^129896+137)/3	129897	Robert Price	06/2021
3902	(13*10^129890+71)/3	129891	Robert Price	06/2021
3903	29048^29101-29101^29048	129882	Norbert Schneider	03/2022
3904	37832^2709+2709^37832	129871	Hans Havermann	04/2021
3905	31055^15184+15184^31055	129853	Hans Havermann	04/2021
3906	(3^272141-3^136071+1)/7	129844	Serge Batalov	03/2014
3907	31385^13702+13702^31385	129833	Hans Havermann	04/2021
3908	(13*10^129826+41)/9	129827	Tyler Busby	02/2023
3909	28901^29102-29102^28901	129822	Norbert Schneider	03/2022
3910	(47*10^129789-119)/9	129790	Robert Price	05/2019
3911	(9*2^431141+1)/17	129787	Lelio R Paula	06/2015
3912	(166*10^129712+17)/3	129714	Robert Price	07/2022
3913	(29*2^430881-1)/21	129709	Lelio R Paula	06/2015
3914	2^430807+1869563	129686	Enzo Doria	05/2016
3915	2^430721-21429	129660	Enzo Doria	07/2013
3916	(4*10^129618+89)/3	129619	Robert Price	08/2021
3917	(10^129587-7^129587)/3	129587	Jon Grantham	07/2023
3918	2^430415-276271	129568	Enzo Doria	07/2015
3919	32282^10311+10311^32282	129558	Hans Havermann	04/2021
3920	29486^24741+24741^29486	129545	Hans Havermann	04/2021
3921	(29*10^129543+313)/9	129544	Robert Price	04/2021
3922	37095^3104+3104^37095	129533	Hans Havermann	04/2021
3923	31132^14459+14459^31132	129514	Hans Havermann	04/2021
3924	32582^9435+9435^32582	129506	Hans Havermann	03/2021
3925	30442^17953+17953^30442	129505	Hans Havermann	03/2021
3926	(199*10^129487-7)/3	129489	Robert Price	05/2020
3927	2^430142-2791721	129486	Enzo Doria	03/2016
3928	(7*10^129472-13)/3	129473	Robert Price	07/2018
3929	(8*10^129469+79)/3	129470	Robert Price	10/2020
3930	31678^12213+12213^31678	129463	Hans Havermann	04/2021
3931	10620^32143-10619^32143	129412	Norbert Schneider	08/2023
3932	(772*10^129406-7)/9	129408	Robert Price	06/2022
3933	31100^14439+14439^31100	129362	Hans Havermann	04/2021
3934	33009^8288+8288^33009	129345	Hans Havermann	04/2021
3935	29675^22804+22804^29675	129324	Hans Havermann	04/2021
3936	29068^28099+28099^29068	129315	Hans Havermann	04/2021
3937	2^429568-21017	129313	Enzo Doria	07/2013
3938	(10^129295+83)/3	129295	Robert Price	08/2021
3939	(853*10^129274-7)/9	129276	Robert Price	07/2021
3940	30958^14961+14961^30958	129249	Hans Havermann	04/2021
3941	(11*10^129239-179)/3	129240	Robert Price	09/2018
3942	28659^28988+28988^28659	129208	Norbert Schneider	02/2021
3943	29423^24616+24616^29423	129203	Hans Havermann	03/2021
3944	2^429194-112685	129201	Enzo Doria	06/2014
3945	2^429145-2780449	129186	Enzo Doria	04/2016
3946	32500^9427+9427^32500	129168	Hans Havermann	04/2021
3947	33577^7014+7014^33577	129136	Hans Havermann	03/2021
3948	2^428892-113453	129110	Enzo Doria	07/2014
3949	(11*2^428881-7)/15	129106	Renaud Lifchitz	03/2011
3950	2^428727-113959	129060	Enzo Doria	10/2014
3951	(7*2^428725-1)/13	129059	Lelio R Paula	05/2014
3952	(10^129051-31)/3	129051	Serge Batalov	12/2014
3953	(134*10^129038+7)/3	129040	Robert Price	02/2020
3954	2^428564+71161	129011	Enzo Doria	04/2016
3955	28781^28930+28930^28781	129002	Norbert Schneider	02/2021
3956	29065^27424+27424^29065	128995	Hans Havermann	04/2021
3957	2^428502-113285	128992	Enzo Doria	07/2014
3958	2^428421-21373	128968	Enzo Doria	06/2013
3959	L(616787)	128901	Henri Lifchitz	09/2008
3960	20^99055-3	128874	Paul Bourdelais	12/2020
3961	91^65772-2	128851	Lelio R Paula	05/2017
3962	2^428022+43	128848	Lelio R Paula	05/2017
3963	2^427999-459397	128841	Enzo Doria	05/2015
3964	2^427993+76847	128839	Enzo Doria	05/2016
3965	31059^14060+14060^31059	128833	Hans Havermann	03/2021
3966	10^128805+152871	128806	Patrick De Geest	05/2021
3967	10^128805-10001	128805	Robert Price	02/2021
3968	2^427824-1851507	128788	Enzo Doria	08/2015
3969	2^427807-21469	128783	Enzo Doria	07/2013
3970	29082^26783+26783^29082	128772	Hans Havermann	04/2021
3971	40055^1638+1638^40055	128750	Hans Havermann	04/2021
3972	11^123594-240	128710	Enzo Doria	09/2012
3973	2^427504-21503	128692	Enzo Doria	07/2013
3974	37727^2574+2574^37727	128673	Hans Havermann	04/2021
3975	29686^21591+21591^29686	128668	Hans Havermann	04/2021
3976	10^128668-70000000001	128668	Robert Price	08/2021
3977	2^427420+91	128667	Lelio R Paula	05/2017
3978	8*10^128651-37	128652	Robert Price	03/2022
3979	(68*10^128645-257)/9	128646	Robert Price	07/2019
3980	2^427269-113635	128621	Enzo Doria	08/2014
3981	2^427130+1877569	128579	Enzo Doria	08/2016
3982	2^427068+20011	128561	Enzo Doria	06/2023
3983	2^427016-115349	128545	Enzo Doria	07/2015
3984	(4*10^128510+137)/3	128511	Robert Price	03/2018
3985	2^426889-112879	128507	Enzo Doria	06/2014
3986	2^426804+1869931	128481	Enzo Doria	05/2016
3987	2^426750+77635	128465	Enzo Doria	05/2016
3988	36988^2969+2969^36988	128445	Hans Havermann	03/2021
3989	36664^3185+3185^36664	128439	Hans Havermann	03/2021
3990	32618^8649+8649^32618	128416	Hans Havermann	04/2021
3991	28883^27874+27874^28883	128391	Hans Havermann	04/2021
3992	2^426425-91	128367	Lelio R Paula	05/2017
3993	(15*2^426398-1)/11	128359	Lelio R Paula	05/2014
3994	2^426352+74971	128345	Enzo Doria	04/2016
3995	(199*10^128343-7)/3	128345	Robert Price	05/2020
3996	4*10^128343-21	128344	Robert Price	09/2018
3997	(65*10^128338+493)/9	128339	Robert Price	08/2021
3998	35632^3997+3997^35632	128337	Hans Havermann	04/2021
3999	2^426300-1863689	128330	Enzo Doria	03/2016
4000	2^426293+1881017	128327	Enzo Doria	11/2016

Find by discoverer :

PRP Records

Probable Primes Top 10000

(293510 PRPs in the top)