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 (> 30000)	Who ?	When ?
3751	97*10^91205-3	91207	Robert Price	01/2017
3752	2^302979-161181	91206	Enzo Doria	04/2013
3753	2^302949+81	91197	Henri Lifchitz	02/2007
3754	4*6^117192-5	91194	Lelio R Paula	10/2014
3755	2^302918+99	91188	Lelio R Paula	11/2012
3756	2^302797+1869587	91151	Enzo Doria	05/2016
3757	265^37614+37614^265	91148	Norbert Schneider	01/2015
3758	7^107852+82	91146	Lelio R Paula	04/2016
3759	(38*10^91144-11)/9	91145	Robert Price	05/2015
3760	249^38030+38030^249	91128	Norbert Schneider	01/2015
3761	6^117094-211049	91117	Mike Oakes	05/2011
3762	2^302602-1867181	91093	Enzo Doria	03/2016
3763	(1017*2^302592-1)/53	91091	Lelio R Paula	04/2015
3764	15^77445-16	91083	Lelio R Paula	07/2016
3765	2^302505+81	91064	Henri Lifchitz	02/2007
3766	2^302496-112349	91061	Enzo Doria	06/2014
3767	17^73999-72	91052	Lelio R Paula	07/2016
3768	2^302332+577294575	91012	Lelio R Paula	08/2016
3769	2^302274+74209	90994	Enzo Doria	04/2016
3770	(3^190668+2)/89	90970	Lelio R Paula	04/2013
3771	2^302188+90195	90968	Lelio R Paula	02/2016
3772	(53*10^90965-71)/9	90966	Robert Price	09/2015
3773	2^302113+74105	90946	Enzo Doria	04/2016
3774	2^302102-6555	90942	Lelio R Paula	02/2016
3775	156(10^(422731)-1)/101-1	90925	Robert Price	05/2014
3776	3^190568+38	90925	Lelio R Paula	04/2016
3777	2^302009-16449	90914	Enzo Doria	04/2013
3778	(17*2^301951-1)/165	90896	Lelio R Paula	02/2014
3779	3^190497+74	90891	Lelio R Paula	04/2016
3780	(24737*2^301896+1)/399	90882	Lelio R Paula	06/2014
3781	18^72397+89	90878	Lelio R Paula	06/2016
3782	6^116769-47	90864	Lelio R Paula	05/2016
3783	2^301712-465	90825	Lelio R Paula	02/2016
3784	2^301693-69	90819	Lelio R Paula	11/2012
3785	2^301683-301683^2	90816	Henri Lifchitz	05/2005
3786	11^87187-1710	90796	Enzo Doria	12/2012
3787	5*10^90793+21	90794	Robert Price	01/2017
3788	(22*10^90792-13)/9	90793	Robert Price	03/2015
3789	2^301591-1615	90788	Lelio R Paula	02/2016
3790	2^301546-109037	90775	Enzo Doria	04/2014
3791	14^79195-3	90768	Lelio R Paula	06/2016
3792	2^301517-1861693	90766	Enzo Doria	11/2015
3793	2^301460-173	90749	Lelio R Paula	11/2012
3794	2^301312-89	90704	Lelio R Paula	11/2012
3795	2^301285-129	90696	Lelio R Paula	11/2012
3796	2^301282-109991	90695	Enzo Doria	04/2014
3797	2^301228-1854269	90679	Enzo Doria	09/2015
3798	(151*10^90669-1)/3	90671	Robert Price	04/2017
3799	(32*10^90669+13)/9	90670	Robert Price	04/2015
3800	3*5^129698+8	90656	Lelio R Paula	10/2014
3801	F(433781)	90655	Henri Lifchitz	09/2003
3802	19^70891+82	90653	Lelio R Paula	06/2016
3803	(29*2^301124-1)/13	90648	Lelio R Paula	02/2014
3804	7*3^189953-8	90632	Lelio R Paula	08/2014
3805	11^87022-1800	90625	Enzo Doria	12/2012
3806	(2^301042+47)/12036969	90616	Lelio R Paula	06/2013
3807	2^301004-2786939	90612	Enzo Doria	03/2016
3808	2^300980-27	90605	Lelio R Paula	11/2012
3809	2*10^90597-7	90598	Dmitry Domanov	11/2010
3810	197^39485+2	90597	Lelio R Paula	06/2013
3811	7^107198+48	90593	Lelio R Paula	04/2016
3812	(86*10^90588+121)/9	90589	Robert Price	03/2017
3813	2^300923+53	90587	Lelio R Paula	11/2012
3814	2^300874+7	90573	Lelio R Paula	10/2012
3815	5^129568-56	90565	Lelio R Paula	04/2016
3816	2^300847-112831	90564	Enzo Doria	06/2014
3817	2^300718+255255	90526	Lelio R Paula	02/2016
3818	2^300637+95	90501	Lelio R Paula	11/2012
3819	7^107087-24	90500	Lelio R Paula	04/2016
3820	(10^90499+3^90499)/13	90498	Robert Price	01/2013
3821	13^81241+90	90498	Lelio R Paula	06/2016
3822	6^116273-85	90478	Lelio R Paula	05/2016
3823	6^116256-17573	90465	Enzo Doria	02/2013
3824	2^300502+54615	90461	Lelio R Paula	02/2016
3825	(13*2^300487+1)/45	90456	Lelio R Paula	09/2013
3826	(3^189545-8)/5	90436	Lelio R Paula	01/2013
3827	(7*2^300406-1)/3	90432	Lelio R Paula	02/2014
3828	4*5^129332+3	90400	Lelio R Paula	10/2014
3829	2^300249-16245	90384	Enzo Doria	04/2013
3830	(7*10^90371-313)/9	90371	Robert Price	11/2016
3831	2*6^116118+7	90358	Lelio R Paula	10/2014
3832	(24737*2^300101+1)/25	90343	Lelio R Paula	06/2014
3833	4*10^90334-21	90335	Robert Price	04/2016
3834	2^300019-110335	90315	Enzo Doria	05/2014
3835	2^299949-1005	90294	Lelio R Paula	11/2013
3836	2^299868-109613	90270	Enzo Doria	04/2014
3837	5*2^299799-3	90250	Lelio R Paula	08/2014
3838	13^81008-2	90239	Lelio R Paula	09/2013
3839	64^49957-63^49957	90232	Robert Price	07/2013
3840	10^90227+56281	90228	Patrick De Geest	06/2016
3843	2^299725+315	90227	Lelio R Paula	11/2013
3841	10^90227-1000000001	90227	Robert Price	05/2016
3842	10^90227-68763	90227	Patrick De Geest	06/2016
3844	5^129082+48	90225	Lelio R Paula	03/2016
3845	2^299699+195	90219	Lelio R Paula	10/2012
3846	(55*10^90211-1)/9	90212	Ray Chandler	02/2012
3847	3^189053+280	90202	Lelio R Paula	04/2016
3848	2^299639-187	90201	Lelio R Paula	10/2012
3849	2^299631+183	90198	Lelio R Paula	10/2012
3850	(21*2^299611-1)/29	90192	Lelio R Paula	02/2014
3851	2^299567+113	90179	Lelio R Paula	10/2012
3852	2^299550+189	90174	Lelio R Paula	10/2012
3853	(2^299535+3)/29	90168	Lelio R Paula	01/2013
3854	(97*10^90155-1)/3	90157	Serge Batalov	12/2014
3855	3^188938+8680	90147	Lelio R Paula	04/2016
3856	6^115840-55	90142	Lelio R Paula	05/2016
3857	8*7^106659+5	90139	Lelio R Paula	10/2014
3858	2^299406-16653	90131	Enzo Doria	05/2013
3859	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
3860	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
3861	6^115819-53	90125	Lelio R Paula	05/2016
3862	6^115816-16853	90123	Enzo Doria	02/2013
3863	6^115813-23	90121	Lelio R Paula	05/2016
3864	(22*10^90110+161)/3	90111	Robert Price	02/2017
3865	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
3866	(29*10^90096-17)/3	90097	Erik Branger	09/2014
3867	2^299247+1870529	90083	Enzo Doria	05/2016
3868	2^299229-2797783	90077	Enzo Doria	04/2016
3869	2^299220-16317	90075	Enzo Doria	04/2013
3870	11^86491-1350	90072	Enzo Doria	12/2012
3871	(31*10^90064-1)/3	90066	Robert Price	03/2017
3872	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
3873	2^299112+73951	90042	Enzo Doria	04/2016
3874	8^99702+7^(99702-1)	90040	Robert Price	02/2016
3875	5*10^90033+3	90034	Dmitry Domanov	11/2010
3876	243^37738+37738^243	90029	Norbert Schneider	01/2015
3877	2^299048-113297	90023	Enzo Doria	07/2014
3878	3^188648+92	90008	Lelio R Paula	12/2015
3879	5*2^298991+7	90006	Lelio R Paula	08/2014
3880	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
3881	10^90000+8869	90001	Patrick De Geest	12/2009
3883	10^89999+82939	90000	Dirk Augustin	04/2007
3882	10^90000-140343	90000	Patrick De Geest	12/2009
3884	10^89999-194891	89999	Patrick De Geest	11/2009
3885	19^70365-78	89980	Lelio R Paula	12/2015
3886	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
3887	2^298852-64875	89964	Lelio R Paula	11/2013
3888	18^71659+37	89952	Lelio R Paula	12/2015
3889	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
3890	17^73067+20	89906	Lelio R Paula	11/2015
3891	2^298637-99	89899	Lelio R Paula	10/2012
3892	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
3893	9*10^89858+19	89859	Robert Price	05/2016
3894	2^298501+1870067	89858	Enzo Doria	05/2016
3895	11^86280-98	89852	Lelio R Paula	11/2015
3896	2^298473-110059	89850	Enzo Doria	04/2014
3897	19^70263-32	89850	Lelio R Paula	12/2015
3898	(299*10^89836-17)/3	89838	Robert Price	01/2017
3899	3^188286+14	89836	Robert Price	09/2013
3900	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
3901	2^298367+58905	89818	Lelio R Paula	11/2013
3902	2^298319-109657	89803	Enzo Doria	04/2014
3903	8*10^89800+81	89801	Robert Price	05/2017
3904	18^71505-91	89759	Lelio R Paula	12/2015
3905	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
3906	2^298079-109531	89731	Enzo Doria	04/2014
3907	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
3908	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
3909	2^298003-66945	89708	Lelio R Paula	11/2013
3910	17^72900-54	89700	Lelio R Paula	11/2015
3911	3*2^297956+5	89695	Lelio R Paula	08/2014
3912	20^68938-11	89691	Lelio R Paula	01/2016
3913	89*10^89687-7	89689	Robert Price	03/2017
3914	2^297923+77783	89684	Enzo Doria	05/2016
3915	11^86107-24576000	89672	Enzo Doria	02/2013
3916	2^297878-111911	89671	Enzo Doria	05/2014
3917	7^106084+40	89652	Lelio R Paula	10/2015
3918	3^187780-11038	89594	Enzo Doria	05/2014
3919	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
3920	5^128141-36	89567	Lelio R Paula	10/2015
3921	4*7^105951+9	89540	Lelio R Paula	10/2014
3922	2^297397+177257	89526	Enzo Doria	05/2016
3923	2^297346-16241	89511	Enzo Doria	04/2013
3925	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
3924	2^297328-869688105	89505	Lelio R Paula	07/2016
3926	2^297325-459043	89504	Enzo Doria	05/2015
3927	2^297310-112391	89500	Enzo Doria	06/2014
3928	2^297296-112157	89496	Enzo Doria	06/2014
3929	57^50966-2	89490	Lelio R Paula	08/2013
3930	(266*10^89482+1)/3	89484	Robert Price	02/2016
3931	(14*10^89480-101)/3	89481	Robert Price	04/2017
3932	2^297122+99	89443	Lelio R Paula	10/2012
3933	(3^187435-5)/1286	89427	Lelio R Paula	01/2013
3934	(25*10^89413+161)/3	89414	Robert Price	01/2017
3935	2^296990+1870699	89403	Enzo Doria	05/2016
3936	2^296972-1017	89398	Lelio R Paula	11/2013
3937	(85*10^89375-31)/9	89376	Robert Price	11/2015
3938	9*2^296870+7	89368	Lelio R Paula	08/2014
3939	100^44683-99^44683	89366	Robert Price	07/2013
3940	2^296810+76519	89349	Enzo Doria	05/2016
3941	8^98928+7^(98928+1)	89341	Robert Price	06/2016
3942	(3^187247+4)/1027	89337	Lelio R Paula	01/2013
3943	(3^187235-2)/2045	89331	Lelio R Paula	01/2013
3945	2^296736-432149	89327	Paul Bourdelais	05/2013
3944	2^296737-112519	89327	Enzo Doria	06/2014
3946	2^296718-3645	89322	Lelio R Paula	11/2013
3947	2^296681-16221	89310	Enzo Doria	04/2013
3948	2^296669-16513	89307	Enzo Doria	04/2013
3949	2^296619-16357	89292	Enzo Doria	04/2013
3950	2^296614-110051	89290	Enzo Doria	04/2014
3951	(3^187138+8)/83147	89283	Lelio R Paula	01/2013
3952	(2*10^89279+457)/9	89279	Robert Price	01/2017
3953	15^75907-28	89274	Lelio R Paula	11/2015
3954	2^296547-37	89270	Yves Minet	01/2012
3955	2^296485+191	89251	Lelio R Paula	10/2012
3956	2^296467-75	89246	Lelio R Paula	10/2012
3957	2^296416-109535	89231	Enzo Doria	04/2014
3958	(23*2^296406+1)/3	89228	Lelio R Paula	01/2013
3959	66^49037-65	89225	Norbert Schneider	11/2014
3960	2^296377-16245	89219	Enzo Doria	04/2013
3961	2^296372-64875	89217	Lelio R Paula	11/2013
3962	5*6^114648-7	89215	Lelio R Paula	10/2014
3963	3*10^89206+13	89207	Robert Price	08/2017
3964	7*3^186960-4	89204	Lelio R Paula	08/2014
3965	2^296290-112133	89193	Enzo Doria	06/2014
3966	6^114620-17003	89192	Enzo Doria	02/2013
3967	(4*10^89189+41)/9	89189	Robert Price	11/2014
3968	2^296261-161181	89184	Enzo Doria	04/2013
3969	(19*2^296269-1)/530623	89182	Lelio R Paula	02/2014
3970	3^186903-10	89176	Robert Price	09/2013
3972	7*10^89169-3	89170	Dmitry Domanov	11/2010
3971	(2^296221-1017)/35	89170	Lelio R Paula	01/2013
3973	(10^89160+29)/3	89160	Serge Batalov	12/2014
3974	(28*10^89141-97)/3	89142	Robert Price	07/2016
3975	2^296116-734639	89140	Paul Bourdelais	04/2013
3976	6^114544-133	89133	Lelio R Paula	12/2015
3977	2^296076-113297	89128	Enzo Doria	07/2014
3978	(11*2^296060-1)/215	89122	Lelio R Paula	02/2014
3979	2^296037-1411	89117	Yves Minet	01/2013
3980	2^296020-2604809	89111	Enzo Doria	05/2015
3981	2^296016+81	89110	Henri Lifchitz	02/2007
3982	2^296010-11	89108	Lelio R Paula	10/2012
3983	2^295998-111911	89105	Enzo Doria	05/2014
3984	(2^296014+47)/93991149	89102	Lelio R Paula	01/2013
3985	2^295939-16621	89087	Enzo Doria	04/2013
3986	2^295934-109691	89086	Enzo Doria	04/2014
3987	(185*10^89063+7)/3	89065	Robert Price	02/2017
3988	2^295831+143	89055	Lelio R Paula	10/2012
3989	31^59713-30	89054	Theodore Burton	02/2007
3990	(7*2^295834-1)/27663	89052	Lelio R Paula	02/2014
3992	123^42608+2	89047	Lelio R Paula	05/2013
3991	6^114433-114433^6	89047	Norbert Schneider	04/2017
3993	2^295800-459659	89045	Enzo Doria	05/2015
3994	(52*10^89037-1)/3	89039	Robert Price	02/2017
3995	(6^114398-11)/5	89019	Paul Bourdelais	11/2011
3996	11^85470-5850	89008	Enzo Doria	02/2013
3997	(27*2^295634+1)/4687	88993	Lelio R Paula	01/2013
3998	2^295564-189	88974	Lelio R Paula	10/2012
3999	2^295557+73097	88972	Enzo Doria	04/2016
4000	11^85433-5760	88970	Enzo Doria	01/2013

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PRP Records

Probable Primes Top 10000

(180278 PRPs in the top)