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	2^338796+93	101988	Donovan Johnson	06/2008
3752	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
3753	25295^10744+10744^25295	101969	Hans Havermann	01/2019
3754	25712^9243+9243^25712	101969	Hans Havermann	01/2019
3755	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
3756	2^338682-19865	101954	Enzo Doria	06/2013
3757	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
3758	28594^3673+3673^28594	101939	Hans Havermann	02/2019
3759	2^338568+37	101920	Lelio R Paula	07/2011
3760	2^338559-1858777	101917	Enzo Doria	04/2016
3761	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
3762	24502^14419+14419^24502	101903	Hans Havermann	01/2019
3763	2^338497-17041	101898	Enzo Doria	05/2013
3764	2^338475+54615	101892	Lelio R Paula	10/2016
3765	2^338426-19797	101877	Enzo Doria	06/2013
3766	2^338368-20369	101859	Enzo Doria	06/2013
3767	2^338366+74179	101859	Enzo Doria	04/2016
3768	27088^5755+5755^27088	101853	Hans Havermann	01/2019
3769	2^338280-19745	101833	Enzo Doria	06/2013
3770	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
3771	6^130841+103	101815	Lelio R Paula	10/2016
3772	2^338122-20117	101785	Enzo Doria	06/2013
3773	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
3774	35^65917-7092	101781	Enzo Doria	03/2013
3775	2^338010-19833	101752	Enzo Doria	06/2013
3776	3^213215-76	101730	Lelio R Paula	09/2016
3777	23907^17998+17998^23907	101730	Hans Havermann	01/2019
3778	10^101728+154953	101729	Patrick De Geest	02/2020
3781	2^337930+63	101728	Lelio R Paula	07/2011
3779	10^101728-987654321	101728	Robert Price	12/2019
3780	10^101728-60741	101728	Patrick De Geest	02/2020
3782	2^337920+1869661	101725	Enzo Doria	05/2016
3783	24116^16509+16509^24116	101715	Hans Havermann	01/2019
3784	2^337859-19645	101706	Enzo Doria	05/2013
3785	2^337754+1869169	101675	Enzo Doria	05/2016
3786	3*10^101657-37	101658	Robert Price	07/2018
3787	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
3788	11^97605-24	101646	Lelio R Paula	10/2016
3789	8^112539-112539	101633	Robert Price	01/2014
3790	25694^9003+9003^25694	101605	Hans Havermann	12/2018
3791	2^337515-19869	101603	Enzo Doria	06/2013
3792	2^337473+719	101590	Lelio R Paula	08/2011
3793	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
3794	2^337452-108815	101584	Enzo Doria	03/2014
3795	2^337453+1185	101584	Lelio R Paula	09/2016
3796	2^337410-113561	101571	Enzo Doria	08/2014
3797	2^337387+855	101564	Lelio R Paula	09/2016
3798	2^337367-17295	101558	Lelio R Paula	09/2016
3799	2^337342-109035	101551	Enzo Doria	04/2014
3800	23703^19238+19238^23703	101548	Hans Havermann	12/2018
3801	(26*10^101537-167)/3	101538	Robert Price	10/2019
3802	2^337267-19	101528	Lelio R Paula	07/2011
3803	2^337183-19989	101503	Enzo Doria	06/2013
3804	2^337149+72425	101492	Enzo Doria	04/2016
3805	24041^16642+16642^24041	101483	Hans Havermann	12/2018
3806	33982^969+969^33982	101482	Hans Havermann	12/2018
3807	2^337101-20241	101478	Enzo Doria	06/2013
3808	2^337035-20001	101458	Enzo Doria	06/2013
3809	2^337017-16995	101453	Lelio R Paula	09/2016
3810	2^336979-115315	101441	Enzo Doria	06/2015
3811	2^336970-20885	101439	Enzo Doria	06/2013
3812	2^336958+79	101435	Lelio R Paula	10/2009
3813	2^336942+169	101430	Lelio R Paula	10/2009
3814	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
3815	4*10^101415-89	101416	Robert Price	11/2018
3816	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
3817	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
3818	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
3819	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
3820	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
3821	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
3822	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
3823	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
3824	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
3825	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
3826	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
3827	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
3828	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
3829	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
3830	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
3831	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
3832	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
3833	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
3834	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3835	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
3836	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3837	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
3838	24097^16150+16150^24097	101405	Hans Havermann	12/2018
3839	2^336842+94065	101400	Lelio R Paula	09/2016
3840	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
3841	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
3842	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
3843	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
3844	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
3845	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
3846	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
3847	10^101369+203811	101370	Patrick De Geest	11/2016
3848	10^101369-99	101369	Lelio R Paula	09/2016
3849	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
3850	2^336701-113563	101358	Enzo Doria	08/2014
3851	89717!4-512	101351	Robert Price	11/2019
3852	2^336644-109023	101340	Enzo Doria	04/2014
3853	2^336601-21081	101327	Enzo Doria	06/2013
3854	20^77869+63	101310	Lelio R Paula	09/2016
3855	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
3856	6^130179-137	101299	Lelio R Paula	10/2016
3857	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
3858	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
3859	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
3860	2^336369-19753	101258	Enzo Doria	05/2013
3861	23842^17653+17653^23842	101253	Hans Havermann	11/2018
3862	2^336350-344291	101252	Enzo Doria	07/2015
3863	(56*10^101222-47)/9	101223	Robert Price	02/2019
3864	2^336243-108777	101220	Enzo Doria	03/2014
3865	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
3866	23535^19954+19954^23535	101202	Hans Havermann	11/2018
3867	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
3868	2^336150-20393	101192	Enzo Doria	06/2013
3869	23996^16473+16473^23996	101186	Hans Havermann	11/2018
3870	2^336112-1865249	101180	Enzo Doria	03/2016
3871	2^336103-109015	101178	Enzo Doria	04/2014
3872	13^90809-96	101157	Lelio R Paula	10/2016
3873	26199^7258+7258^26199	101150	Hans Havermann	11/2018
3874	19^79098-30	101147	Lelio R Paula	10/2016
3875	19^79095+88	101144	Lelio R Paula	10/2016
3876	15^85976+32	101116	Lelio R Paula	10/2016
3877	2^335872-2776215	101108	Tony Prest / Never Odd Or Even	01/2019
3878	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
3879	(4^167933+17)/3	101106	Robert Price	02/2017
3881	2^335858+153	101104	Lelio R Paula	10/2009
3880	(2^335872-2776871)/5/5/479	101104	Tony Prest / Never Odd Or Even	01/2019
3882	(2^335872-2758787)/23/31/20809	101101	Tony Prest / Never Odd Or Even	01/2019
3883	(2^335872-2795083)/3/3/113/283/148367	101097	Tony Prest / Never Odd Or Even	01/2019
3884	6^129918-35	101096	Lelio R Paula	10/2016
3885	3^211885-70	101095	Lelio R Paula	09/2016
3887	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
3886	(2^335872-2794771)/3/5/5/61/232312440293	101093	Tony Prest / Never Odd Or Even	01/2019
3888	2^335818-20033	101092	Enzo Doria	06/2013
3889	2^335813-110083	101090	Enzo Doria	04/2014
3890	2^335804+2155	101088	Lelio R Paula	09/2016
3891	(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021	101087	Tony Prest / Never Odd Or Even	01/2019
3892	2^335784-16145	101082	Enzo Doria	04/2013
3893	11^97051+62	101069	Lelio R Paula	10/2016
3894	3*10^101065+11	101066	Robert Price	07/2018
3895	27820^4293+4293^27820	101064	Hans Havermann	10/2018
3896	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
3897	2^335658-94395	101044	Lelio R Paula	09/2016
3898	24514^13215+13215^24514	101024	Hans Havermann	11/2018
3899	2^335586+169	101022	Lelio R Paula	10/2009
3900	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
3901	(19*10^100997+737)/9	100998	Robert Price	07/2018
3902	47599!2+1024	100991	Robert Price	02/2015
3903	2^335468-18629	100986	Enzo Doria	05/2013
3904	2^335454-20961	100982	Enzo Doria	06/2013
3905	10^100978+61	100979	Lelio R Paula	09/2016
3906	10^100978-156437	100978	Patrick De Geest	11/2016
3907	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
3908	2^335403-1859167	100967	Enzo Doria	03/2016
3909	23599^18976+18976^23599	100962	Hans Havermann	10/2018
3910	9*2^335364-5	100956	Lelio R Paula	08/2014
3911	2^335349+72287	100951	Enzo Doria	04/2016
3912	2^335329+16095	100945	Lelio R Paula	09/2016
3913	232823#+233663	100937	Makoto Morimoto	10/2017
3914	(232823#+10141)/(10141*1674461)	100927	Makoto Morimoto	06/2019
3915	2^335237-20893	100917	Enzo Doria	06/2013
3916	2^335222-19337	100912	Enzo Doria	05/2013
3917	2^335222-109985	100912	Enzo Doria	04/2014
3918	2^335182-17237	100900	Enzo Doria	05/2013
3919	2^335043-16737	100858	Enzo Doria	05/2013
3920	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
3921	2^335038-20633	100857	Enzo Doria	06/2013
3922	2^335031+1873373	100855	Enzo Doria	06/2016
3923	23489^19650+19650^23489	100847	Hans Havermann	10/2018
3924	3^211354-8816	100842	Enzo Doria	05/2014
3925	2^334984-112757	100841	Enzo Doria	06/2014
3926	(746*10^100827+1)/9	100829	Robert Price	03/2020
3927	29451^2648+2648^29451	100809	Hans Havermann	09/2018
3928	25583^8716+8716^25583	100806	Hans Havermann	08/2018
3930	2^334857+48527	100803	Lelio R Paula	08/2011
3929	12^93406+29	100803	Lelio R Paula	10/2016
3931	28780^3179+3179^28780	100796	Hans Havermann	09/2018
3932	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
3933	2^334809-13	100788	Lelio R Paula	04/2011
3934	(82*10^100780-1)/9	100781	Robert Price	12/2014
3935	31395^1622+1622^31395	100780	Hans Havermann	09/2018
3936	(2^334779+47)/5	100778	Lelio R Paula	12/2013
3937	2^334751+2049	100771	Lelio R Paula	09/2016
3938	13^90443-98	100749	Lelio R Paula	10/2016
3939	(7*10^100737+71)/3	100738	Robert Price	05/2018
3940	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
3941	15^85639-28	100720	Lelio R Paula	10/2016
3942	27068^5259+5259^27068	100718	Hans Havermann	08/2018
3943	2^334562+577294575	100711	Lelio R Paula	09/2016
3944	4*3^211077-5	100710	Lelio R Paula	08/2014
3945	2^334524+145	100702	Lelio R Paula	07/2009
3946	27648^4375+4375^27648	100666	Hans Havermann	09/2018
3947	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
3948	2^334294-113111	100633	Enzo Doria	07/2014
3949	25581^8582+8582^25581	100626	Hans Havermann	08/2018
3950	6^129308-17723	100622	Enzo Doria	03/2013
3951	6^129305+95	100619	Lelio R Paula	10/2016
3952	2^334244-1167	100618	Lelio R Paula	09/2016
3953	(76*10^100611+77)/9	100612	Robert Price	10/2019
3954	(26*10^100566+49)/3	100567	Robert Price	08/2019
3955	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
3956	24885^10984+10984^24885	100555	Hans Havermann	07/2018
3957	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
3958	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
3959	23578^18367+18367^23578	100538	Hans Havermann	07/2018
3960	13^90251+24	100535	Lelio R Paula	10/2016
3961	2^333963+789	100533	Lelio R Paula	08/2011
3962	2^333919-1840087	100520	Enzo Doria	06/2015
3963	2^333911+72623	100518	Enzo Doria	04/2016
3964	24605^12168+12168^24605	100517	Hans Havermann	08/2018
3965	18^80064-67	100503	Lelio R Paula	10/2016
3966	5^143742-48	100472	Lelio R Paula	10/2016
3967	24095^14784+14784^24095	100472	Hans Havermann	08/2018
3968	2^333757-112123	100471	Enzo Doria	06/2014
3969	27358^4693+4693^27358	100444	Hans Havermann	07/2018
3970	8*10^100439-51	100440	Robert Price	08/2019
3971	2^333603-108861	100425	Enzo Doria	03/2014
3972	9*7^118818-2	100414	Lelio R Paula	11/2014
3973	2^333546-17097	100408	Enzo Doria	05/2013
3974	17^81597+72	100401	Lelio R Paula	10/2016
3975	p(20559)#/2+8	100384	Robert Price	01/2017
3976	11^96390-24	100380	Lelio R Paula	10/2016
3978	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
3977	23565^18136+18136^23565	100353	Hans Havermann	07/2018
3979	2^333354+763	100350	Lelio R Paula	08/2011
3980	(25*10^100343-67)/3	100344	Robert Price	06/2019
3981	2^333289-109483	100330	Enzo Doria	04/2014
3982	2^333240-2790209	100316	Enzo Doria	03/2016
3983	23601^17798+17798^23601	100314	Hans Havermann	05/2018
3985	(2^333227-2^166614+1)/5	100311		11/2006
3984	2^333225+719	100311	Lelio R Paula	08/2011
3986	2^333221-2785333	100310	Enzo Doria	10/2015
3987	76^53332-75	100308	Norbert Schneider	02/2015
3988	6^128892-17573	100298	Enzo Doria	03/2013
3989	(47*10^100283-119)/9	100284	Robert Price	05/2019
3990	2^333105-113215	100275	Enzo Doria	07/2014
3991	(31*2^333102+1)/2375	100272	Lelio R Paula	11/2013
3992	4*10^100257-83	100258	Robert Price	10/2018
3993	17^81476-74	100253	Lelio R Paula	10/2016
3994	23392^19207+19207^23392	100199	Hans Havermann	06/2018
3995	(206*10^100189-17)/9	100191	Robert Price	01/2020
3996	17^81417-16	100180	Theodore Burton	11/2005
3997	2^332739-113215	100165	Enzo Doria	07/2014
3998	2^332730-1865621	100162	Enzo Doria	03/2016
3999	91^51127-2	100160	Lelio R Paula	09/2013
4000	15^85159-32	100155	Lelio R Paula	10/2016

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Probable Primes Top 10000

(259919 PRPs in the top)