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 ?
3501	10^100001+314199	100002	Patrick De Geest	07/2018
3549	25206!+p(4114)	100001	Henri Lifchitz	09/2005
3550	25206!-p(5447)	100001	Henri Lifchitz	10/2005
3551	25206!-p(12402)	100001	Henri Lifchitz	04/2006
3552	25206!-p(16290)	100001	Henri Lifchitz	09/2006
3553	25206!-p(19647)	100001	Henri Lifchitz	02/2007
3554	2^332194+11473	100001	Henri Lifchitz	03/2007
3526	10^100000+342909	100001	Milton L. Brown	12/2007
3527	10^100000+346579	100001	Robert Price	04/2012
3528	10^100000+829767	100001	Robert Price	05/2012
3529	10^100000+871899	100001	Robert Price	05/2012
3530	10^100000+1475997	100001	Robert Price	07/2012
3539	10^100000+1751769	100001	Robert Price	08/2012
3540	10^100000+2155489	100001	Robert Price	10/2012
3541	10^100000+2483527	100001	Robert Price	12/2012
3542	10^100000+2503087	100001	Robert Price	12/2012
3543	10^100000+2686179	100001	Robert Price	12/2012
3544	10^100000+2688933	100001	Robert Price	12/2012
3545	10^100000+3667159	100001	Robert Price	08/2013
3510	10^100000+3938473	100001	Robert Price	05/2015
3511	10^100000+3979761	100001	Robert Price	05/2015
3512	10^100000+4293973	100001	Robert Price	09/2015
3556	10^100000+4858267	100001	Robert Price	12/2015
3557	10^100000+5113299	100001	Robert Price	02/2016
3558	10^100000+5169411	100001	Robert Price	02/2016
3531	10^100000+5354043	100001	Robert Price	05/2016
3532	10^100000+5717979	100001	Robert Price	05/2016
3533	10^100000+6080631	100001	Robert Price	07/2016
3534	10^100000+6308469	100001	Robert Price	07/2016
3535	10^100000+6512023	100001	Robert Price	08/2016
3536	10^100000+6596557	100001	Robert Price	08/2016
3537	10^100000+7115409	100001	Robert Price	10/2016
3538	10^100000+7235803	100001	Robert Price	10/2016
3513	10^100000+7867333	100001	Robert Price	12/2016
3514	10^100000+8743093	100001	Robert Price	02/2017
3515	10^100000+8955391	100001	Robert Price	03/2017
3516	10^100000+9180019	100001	Robert Price	03/2017
3517	10^100000+9225987	100001	Robert Price	04/2017
3518	10^100000+9265587	100001	Robert Price	04/2017
3519	10^100000+9287049	100001	Robert Price	04/2017
3520	10^100000+9425053	100001	Robert Price	05/2017
3521	10^100000+9450769	100001	Robert Price	05/2017
3522	10^100000+9528747	100001	Robert Smith	05/2017
3523	10^100000+9548071	100001	Robert Price	06/2017
3524	10^100000+10064287	100001	Robert Price	08/2017
3525	10^100000+10229569	100001	Robert Price	10/2017
3502	10^100000+11187931	100001	Robert Price	03/2018
3503	10^100000+11264721	100001	Robert Price	04/2018
3504	10^100000+11477661	100001	Robert Price	05/2018
3505	10^100000+11644653	100001	Robert Price	07/2018
3506	10^100001-431439	100001	Patrick De Geest	07/2018
3507	10^100000+11769399	100001	Robert Price	08/2018
3508	10^100000+11848159	100001	Robert Price	08/2018
3509	10^100000+11863467	100001	Robert Price	08/2018
3546	10^100000+11992051	100001	Robert Price	09/2018
3547	2^332196-1-2*29696	100001	Matt Stath	11/2018
3548	10^100000+12363957	100001	Robert Price	11/2018
3555	2^332196+1+2*17152	100001	Matt Stath	12/2018
3560	10^99999+309403	100000	Daniel Heuer	01/2004
3559	10^100000-260199	100000	Patrick De Geest	01/2010
3561	10^99999-59511	99999	Patrick De Geest	07/2009
3562	2^332141-113073	99985	Enzo Doria	07/2014
3564	(3^209561+2)/728101255	99978	Lelio R Paula	09/2013
3563	23827^15702+15702^23827	99978	Hans Havermann	04/2018
3565	2^332085+1865897	99968	Enzo Doria	03/2016
3566	(9787*2^332070-1)/936402369	99959	Lelio R Paula	05/2015
3567	2^332023+191	99949	Lelio R Paula	02/2011
3568	2^331938+71149	99924	Enzo Doria	04/2016
3569	2^331932-78795	99922	Lelio R Paula	09/2016
3570	2^331921+771	99919	Lelio R Paula	01/2013
3571	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
3572	2^331860-114989	99900	Enzo Doria	05/2015
3573	2^331746-11655	99866	Lelio R Paula	09/2016
3574	11^95891-28	99861	Lelio R Paula	08/2016
3575	(2^331694-5)/11	99849	Lelio R Paula	10/2013
3576	(3^209246+7)/64	99834	Lelio R Paula	09/2013
3577	25062^9617+9617^25062	99823	Hans Havermann	04/2018
3578	15^84866-52	99811	Lelio R Paula	08/2016
3579	13^89600+30	99810	Lelio R Paula	08/2016
3580	22950^22309+22309^22950	99798	Hans Havermann	03/2018
3581	5^142772-38	99794	Lelio R Paula	08/2016
3582	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
3583	2^331416-331416+1	99767	Robert Price	10/2014
3584	2^331256-57	99718	Lelio R Paula	12/2012
3585	28192^3443+3443^28192	99714	Hans Havermann	03/2018
3586	2^331185+737	99697	Lelio R Paula	01/2013
3587	(4*10^99693+149)/9	99693	Robert Price	03/2017
3588	2^331154+1880527	99688	Enzo Doria	10/2016
3590	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
3589	24354^12385+12385^24354	99679	Hans Havermann	03/2018
3591	2^331110+1870459	99675	Enzo Doria	05/2016
3592	5*2^331075+7	99665	Lelio R Paula	08/2014
3593	25776^7351+7351^25776	99659	Hans Havermann	02/2018
3594	(16*10^99656-31)/3	99657	Robert Price	03/2016
3595	2^330968+345	99632	Lelio R Paula	09/2016
3597	2*5^142528-7	99624	Lelio R Paula	11/2014
3596	2^330942+77329	99624	Enzo Doria	05/2016
3598	14^86914-99	99615	Lelio R Paula	08/2016
3599	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
3600	22971^21692+21692^22971	99610	Hans Havermann	03/2018
3601	2^330845+71687	99595	Enzo Doria	04/2016
3602	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
3603	24494^11613+11613^24494	99567	Hans Havermann	03/2018
3604	2^330735+8415	99562	Lelio R Paula	09/2016
3605	2^330720+74071	99557	Enzo Doria	04/2016
3606	31^66738-2	99531	Lelio R Paula	09/2013
3607	7*3^208567+4	99513	Lelio R Paula	08/2014
3608	(13*10^99508+47)/3	99509	Robert Price	01/2017
3609	2^330553+779	99507	Lelio R Paula	01/2013
3610	15^84606-94	99505	Lelio R Paula	08/2016
3611	6^127858+47	99493	Lelio R Paula	08/2016
3612	5^142337+48	99490	Lelio R Paula	08/2016
3613	7^117724-20	99489	Lelio R Paula	08/2016
3614	(29*10^99474-17)/3	99475	Erik Branger	09/2014
3615	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
3616	(68*10^99441+7)/3	99443	Robert Price	03/2016
3617	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
3618	23839^14802+14802^23839	99417	Hans Havermann	02/2018
3619	(2*10^99408+529)/9	99408	Robert Price	01/2017
3620	53^57646-2	99398	Lelio R Paula	09/2013
3621	2^330165+1870025	99390	Enzo Doria	05/2016
3622	2^330142-155	99383	Lelio R Paula	12/2012
3623	2^330088-115259	99367	Enzo Doria	06/2015
3624	24216^12671+12671^24216	99354	Hans Havermann	01/2018
3625	(746*10^99303+1)/9	99305	Robert Price	02/2017
3626	3^208107+40	99293	Lelio R Paula	08/2016
3627	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
3628	8*3^208093+5	99287	Lelio R Paula	08/2014
3629	5^142043+56	99284	Lelio R Paula	08/2016
3630	22*10^99275+7	99277	Robert Price	04/2016
3631	2^329778+1876189	99274	Enzo Doria	07/2016
3632	(10^99239-13)/3	99239	Robert Price	02/2017
3633	3^207987+62	99236	Lelio R Paula	08/2016
3634	2^329638+49	99231	Lelio R Paula	12/2012
3635	7^117413-18	99226	Lelio R Paula	08/2016
3636	2^329586-458903	99216	Enzo Doria	04/2015
3637	2^329553+101	99206	Lelio R Paula	12/2012
3638	2^329551-112897	99205	Enzo Doria	06/2014
3639	(3^207925+7)/50	99204	Lelio R Paula	09/2013
3640	6^127458-17993	99182	Enzo Doria	03/2013
3641	27197^4428+4428^27197	99166	Hans Havermann	10/2017
3642	(46*10^99143-1)/9	99144	Robert Price	12/2014
3643	7*10^99133+69	99134	Robert Price	10/2017
3644	18^78968-3065	99127	Enzo Doria	03/2013
3645	25927^6654+6654^25927	99122	Hans Havermann	10/2017
3646	2^329259+189	99117	Lelio R Paula	12/2012
3647	8*10^99113+39	99114	Robert Price	01/2017
3648	6^127364+77	99109	Lelio R Paula	08/2016
3649	6^127285+13	99047	Lelio R Paula	08/2016
3650	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
3651	2^329007+73283	99041	Enzo Doria	04/2016
3652	5*3^207543-8	99024	Lelio R Paula	08/2014
3653	2^328885+149	99005	Lelio R Paula	12/2012
3654	23392^17075+17075^23392	99004	Hans Havermann	09/2017
3655	(2^328879-9)/119	99001	Lelio R Paula	10/2013
3656	5^141618+54	98987	Lelio R Paula	08/2016
3657	8*10^98982+51	98983	Robert Price	05/2017
3658	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
3659	2^328794-2797601	98977	Enzo Doria	04/2016
3660	6^127176+5	98963	Lelio R Paula	11/2014
3661	24262^11989+11989^24262	98960	Hans Havermann	09/2017
3662	2^328700-109709	98949	Enzo Doria	04/2014
3663	46711!2-2^46711	98916	Robert Price	09/2015
3664	9*7^117037+4	98909	Lelio R Paula	11/2014
3665	(10^98890+149)/3	98890	Serge Batalov	12/2014
3666	22775^21978+21978^22775	98889	Hans Havermann	08/2017
3667	2^328497-216933	98888	Enzo Doria	05/2014
3668	2^328487+32769	98885	Lelio R Paula	08/2016
3669	3^207250-112358	98884	Enzo Doria	06/2014
3670	13^88754-90	98867	Lelio R Paula	08/2016
3671	2^328406+709	98861	Lelio R Paula	02/2013
3672	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
3673	7^116976+76	98857	Lelio R Paula	08/2016
3674	2^328335+1155	98839	Lelio R Paula	08/2016
3675	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
3676	287^40210+40210^287	98832	Norbert Schneider	11/2014
3677	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
3678	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
3679	65^54491+48	98788	Lelio R Paula	04/2016
3680	3^207042+98	98785	Lelio R Paula	08/2016
3681	3^206977-112756	98754	Enzo Doria	07/2014
3682	7^116846-50	98747	Lelio R Paula	08/2016
3683	2^327967-28635	98728	Lelio R Paula	08/2016
3684	707^34642+34642^707	98710	Norbert Schneider	12/2017
3685	6^126850-47	98709	Lelio R Paula	08/2016
3686	8*6^126830-7	98694	Lelio R Paula	11/2014
3687	11^94770-270	98693	Enzo Doria	08/2012
3688	2^327832+43	98688	Lelio R Paula	12/2012
3689	2^327795+761	98677	Lelio R Paula	02/2013
3690	10^98669+147411	98670	Patrick De Geest	11/2016
3692	10^98669-9^(98669-1)	98669	Robert Price	05/2016
3691	10^98669-105249	98669	Patrick De Geest	11/2016
3693	2^327671-109801	98639	Enzo Doria	04/2014
3694	5^141090-14	98618	Lelio R Paula	08/2016
3695	20^75799+47	98617	Lelio R Paula	08/2016
3696	2^327515-1017	98592	Lelio R Paula	08/2016
3697	6^126692+97681	98586	Mike Oakes	04/2011
3698	2^327467-741	98578	Lelio R Paula	08/2016
3699	(2^327329+9)/19	98535	Lelio R Paula	10/2013
3700	7^116577-66	98519	Lelio R Paula	08/2016
3701	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
3702	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
3703	2^327162-66945	98486	Lelio R Paula	08/2016
3704	4*10^98472-3	98473	Erik Branger	11/2013
3705	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
3706	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
3707	13^88363+94	98432	Lelio R Paula	08/2016
3708	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
3709	6^126481+41	98422	Lelio R Paula	08/2016
3710	78*10^98413-7	98415	Robert Price	05/2017
3711	7^116416+46	98383	Lelio R Paula	08/2016
3712	7^116407-24	98376	Lelio R Paula	07/2016
3713	439^37228+37228^439	98374	Norbert Schneider	08/2018
3714	2^326782-1860671	98372	Enzo Doria	03/2016
3715	17^79948+58	98372	Lelio R Paula	08/2016
3716	3^206143-98	98356	Lelio R Paula	08/2016
3717	8*5^140705+7	98350	Lelio R Paula	11/2014
3718	2^326585+11	98312	Lelio R Paula	12/2012
3719	2^326582-459161	98311	Enzo Doria	05/2015
3720	(2^326548+9)/5	98301	Lelio R Paula	10/2013
3721	2^326538+71659	98298	Enzo Doria	04/2016
3722	15^83575-58	98292	Lelio R Paula	08/2016
3723	10^98288+3	98289	Robert Price	03/2011
3724	10^98288-117017	98288	Patrick De Geest	11/2011
3725	(44*10^98284-719)/9	98285	Robert Price	12/2017
3726	2^326421-2797573	98263	Enzo Doria	04/2016
3727	2^326401+16095	98257	Lelio R Paula	07/2016
3728	7^116240-116240^7	98235	Norbert Schneider	05/2017
3729	17^79826-78	98222	Lelio R Paula	08/2016
3730	2^326268-809	98217	Yves Minet	04/2011
3731	(418*10^98199+23)/9	98201	Robert Price	08/2017
3732	12*10^98198-7	98200	Robert Price	11/2017
3733	15^83496-76	98199	Lelio R Paula	08/2016
3734	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
3735	9*5^140471-4	98186	Lelio R Paula	11/2014
3736	2^326069-2383	98157	Yves Minet	10/2013
3737	2^325973+1185	98128	Lelio R Paula	07/2016
3738	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
3739	2^325945-1847269	98120	Enzo Doria	07/2015
3740	8*10^98111-67	98112	Robert Price	10/2017
3741	2^325866+15	98096	Lelio R Paula	12/2012
3742	2^325765+1974305	98066	Enzo Doria	06/2016
3743	2^325733-58695	98056	Lelio R Paula	07/2016
3744	2^325717-3645	98051	Lelio R Paula	07/2016
3745	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
3746	(7*10^98007-13)/3	98008	Robert Price	06/2016
3747	2^325512-459959	97989	Enzo Doria	05/2015
3748	(3^205354-8)/17	97978	Lelio R Paula	09/2013
3749	2^325433+76817	97966	Enzo Doria	05/2016
3750	5*10^97963+81	97964	Robert Price	08/2017

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PRP Records

Probable Primes Top 10000

(247113 PRPs in the top)