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	(9787*2^332070-1)/936402369	99959	Lelio R Paula	05/2015
3502	2^332023+191	99949	Lelio R Paula	02/2011
3503	2^331938+71149	99924	Enzo Doria	04/2016
3504	2^331932-78795	99922	Lelio R Paula	09/2016
3505	2^331921+771	99919	Lelio R Paula	01/2013
3506	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
3507	2^331860-114989	99900	Enzo Doria	05/2015
3508	2^331746-11655	99866	Lelio R Paula	09/2016
3509	11^95891-28	99861	Lelio R Paula	08/2016
3510	(2^331694-5)/11	99849	Lelio R Paula	10/2013
3511	(3^209246+7)/64	99834	Lelio R Paula	09/2013
3512	25062^9617+9617^25062	99823	Hans Havermann	04/2018
3513	15^84866-52	99811	Lelio R Paula	08/2016
3514	13^89600+30	99810	Lelio R Paula	08/2016
3515	22950^22309+22309^22950	99798	Hans Havermann	03/2018
3516	5^142772-38	99794	Lelio R Paula	08/2016
3517	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
3518	2^331416-331416+1	99767	Robert Price	10/2014
3519	2^331256-57	99718	Lelio R Paula	12/2012
3520	28192^3443+3443^28192	99714	Hans Havermann	03/2018
3521	2^331185+737	99697	Lelio R Paula	01/2013
3522	(4*10^99693+149)/9	99693	Robert Price	03/2017
3523	2^331154+1880527	99688	Enzo Doria	10/2016
3524	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
3525	24354^12385+12385^24354	99679	Hans Havermann	03/2018
3526	2^331110+1870459	99675	Enzo Doria	05/2016
3527	5*2^331075+7	99665	Lelio R Paula	08/2014
3528	25776^7351+7351^25776	99659	Hans Havermann	02/2018
3529	(16*10^99656-31)/3	99657	Robert Price	03/2016
3530	2^330968+345	99632	Lelio R Paula	09/2016
3532	2*5^142528-7	99624	Lelio R Paula	11/2014
3531	2^330942+77329	99624	Enzo Doria	05/2016
3533	14^86914-99	99615	Lelio R Paula	08/2016
3534	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
3535	22971^21692+21692^22971	99610	Hans Havermann	03/2018
3536	2^330845+71687	99595	Enzo Doria	04/2016
3537	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
3538	24494^11613+11613^24494	99567	Hans Havermann	03/2018
3539	2^330735+8415	99562	Lelio R Paula	09/2016
3540	2^330720+74071	99557	Enzo Doria	04/2016
3541	31^66738-2	99531	Lelio R Paula	09/2013
3542	7*3^208567+4	99513	Lelio R Paula	08/2014
3543	(13*10^99508+47)/3	99509	Robert Price	01/2017
3544	2^330553+779	99507	Lelio R Paula	01/2013
3545	15^84606-94	99505	Lelio R Paula	08/2016
3546	6^127858+47	99493	Lelio R Paula	08/2016
3547	5^142337+48	99490	Lelio R Paula	08/2016
3548	7^117724-20	99489	Lelio R Paula	08/2016
3549	(29*10^99474-17)/3	99475	Erik Branger	09/2014
3550	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
3551	(68*10^99441+7)/3	99443	Robert Price	03/2016
3552	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
3553	23839^14802+14802^23839	99417	Hans Havermann	02/2018
3554	(2*10^99408+529)/9	99408	Robert Price	01/2017
3555	53^57646-2	99398	Lelio R Paula	09/2013
3556	2^330165+1870025	99390	Enzo Doria	05/2016
3557	2^330142-155	99383	Lelio R Paula	12/2012
3558	2^330088-115259	99367	Enzo Doria	06/2015
3559	24216^12671+12671^24216	99354	Hans Havermann	01/2018
3560	(746*10^99303+1)/9	99305	Robert Price	02/2017
3561	3^208107+40	99293	Lelio R Paula	08/2016
3562	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
3563	8*3^208093+5	99287	Lelio R Paula	08/2014
3564	5^142043+56	99284	Lelio R Paula	08/2016
3565	22*10^99275+7	99277	Robert Price	04/2016
3566	2^329778+1876189	99274	Enzo Doria	07/2016
3567	(10^99239-13)/3	99239	Robert Price	02/2017
3568	3^207987+62	99236	Lelio R Paula	08/2016
3569	2^329638+49	99231	Lelio R Paula	12/2012
3570	7^117413-18	99226	Lelio R Paula	08/2016
3571	2^329586-458903	99216	Enzo Doria	04/2015
3572	2^329553+101	99206	Lelio R Paula	12/2012
3573	2^329551-112897	99205	Enzo Doria	06/2014
3574	(3^207925+7)/50	99204	Lelio R Paula	09/2013
3575	6^127458-17993	99182	Enzo Doria	03/2013
3576	27197^4428+4428^27197	99166	Hans Havermann	10/2017
3577	(46*10^99143-1)/9	99144	Robert Price	12/2014
3578	7*10^99133+69	99134	Robert Price	10/2017
3579	18^78968-3065	99127	Enzo Doria	03/2013
3580	25927^6654+6654^25927	99122	Hans Havermann	10/2017
3581	2^329259+189	99117	Lelio R Paula	12/2012
3582	8*10^99113+39	99114	Robert Price	01/2017
3583	6^127364+77	99109	Lelio R Paula	08/2016
3584	6^127285+13	99047	Lelio R Paula	08/2016
3585	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
3586	2^329007+73283	99041	Enzo Doria	04/2016
3587	5*3^207543-8	99024	Lelio R Paula	08/2014
3588	2^328885+149	99005	Lelio R Paula	12/2012
3589	23392^17075+17075^23392	99004	Hans Havermann	09/2017
3590	(2^328879-9)/119	99001	Lelio R Paula	10/2013
3591	5^141618+54	98987	Lelio R Paula	08/2016
3592	8*10^98982+51	98983	Robert Price	05/2017
3593	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
3594	2^328794-2797601	98977	Enzo Doria	04/2016
3595	6^127176+5	98963	Lelio R Paula	11/2014
3596	24262^11989+11989^24262	98960	Hans Havermann	09/2017
3597	2^328700-109709	98949	Enzo Doria	04/2014
3598	46711!2-2^46711	98916	Robert Price	09/2015
3599	9*7^117037+4	98909	Lelio R Paula	11/2014
3600	(10^98890+149)/3	98890	Serge Batalov	12/2014
3601	22775^21978+21978^22775	98889	Hans Havermann	08/2017
3602	2^328497-216933	98888	Enzo Doria	05/2014
3603	2^328487+32769	98885	Lelio R Paula	08/2016
3604	3^207250-112358	98884	Enzo Doria	06/2014
3605	13^88754-90	98867	Lelio R Paula	08/2016
3606	2^328406+709	98861	Lelio R Paula	02/2013
3607	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
3608	7^116976+76	98857	Lelio R Paula	08/2016
3609	2^328335+1155	98839	Lelio R Paula	08/2016
3611	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
3610	287^40210+40210^287	98832	Norbert Schneider	11/2014
3612	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
3613	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
3614	65^54491+48	98788	Lelio R Paula	04/2016
3615	3^207042+98	98785	Lelio R Paula	08/2016
3616	3^206977-112756	98754	Enzo Doria	07/2014
3617	7^116846-50	98747	Lelio R Paula	08/2016
3618	2^327967-28635	98728	Lelio R Paula	08/2016
3619	707^34642+34642^707	98710	Norbert Schneider	12/2017
3620	6^126850-47	98709	Lelio R Paula	08/2016
3621	8*6^126830-7	98694	Lelio R Paula	11/2014
3622	11^94770-270	98693	Enzo Doria	08/2012
3623	2^327832+43	98688	Lelio R Paula	12/2012
3624	2^327795+761	98677	Lelio R Paula	02/2013
3625	10^98669+147411	98670	Patrick De Geest	11/2016
3627	10^98669-9^(98669-1)	98669	Robert Price	05/2016
3626	10^98669-105249	98669	Patrick De Geest	11/2016
3628	2^327671-109801	98639	Enzo Doria	04/2014
3629	5^141090-14	98618	Lelio R Paula	08/2016
3630	20^75799+47	98617	Lelio R Paula	08/2016
3631	2^327515-1017	98592	Lelio R Paula	08/2016
3632	6^126692+97681	98586	Mike Oakes	04/2011
3633	2^327467-741	98578	Lelio R Paula	08/2016
3634	(2^327329+9)/19	98535	Lelio R Paula	10/2013
3635	7^116577-66	98519	Lelio R Paula	08/2016
3636	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
3637	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
3638	2^327162-66945	98486	Lelio R Paula	08/2016
3639	4*10^98472-3	98473	Erik Branger	11/2013
3640	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
3641	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
3642	13^88363+94	98432	Lelio R Paula	08/2016
3643	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
3644	6^126481+41	98422	Lelio R Paula	08/2016
3645	78*10^98413-7	98415	Robert Price	05/2017
3646	7^116416+46	98383	Lelio R Paula	08/2016
3647	7^116407-24	98376	Lelio R Paula	07/2016
3648	439^37228+37228^439	98374	Norbert Schneider	08/2018
3649	2^326782-1860671	98372	Enzo Doria	03/2016
3650	17^79948+58	98372	Lelio R Paula	08/2016
3651	3^206143-98	98356	Lelio R Paula	08/2016
3652	8*5^140705+7	98350	Lelio R Paula	11/2014
3653	2^326585+11	98312	Lelio R Paula	12/2012
3654	2^326582-459161	98311	Enzo Doria	05/2015
3655	(2^326548+9)/5	98301	Lelio R Paula	10/2013
3656	2^326538+71659	98298	Enzo Doria	04/2016
3657	15^83575-58	98292	Lelio R Paula	08/2016
3658	10^98288+3	98289	Robert Price	03/2011
3659	10^98288-117017	98288	Patrick De Geest	11/2011
3660	(44*10^98284-719)/9	98285	Robert Price	12/2017
3661	2^326421-2797573	98263	Enzo Doria	04/2016
3662	2^326401+16095	98257	Lelio R Paula	07/2016
3663	7^116240-116240^7	98235	Norbert Schneider	05/2017
3664	17^79826-78	98222	Lelio R Paula	08/2016
3665	2^326268-809	98217	Yves Minet	04/2011
3666	(418*10^98199+23)/9	98201	Robert Price	08/2017
3667	12*10^98198-7	98200	Robert Price	11/2017
3668	15^83496-76	98199	Lelio R Paula	08/2016
3669	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
3670	9*5^140471-4	98186	Lelio R Paula	11/2014
3671	2^326069-2383	98157	Yves Minet	10/2013
3672	2^325973+1185	98128	Lelio R Paula	07/2016
3673	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
3674	2^325945-1847269	98120	Enzo Doria	07/2015
3675	8*10^98111-67	98112	Robert Price	10/2017
3676	2^325866+15	98096	Lelio R Paula	12/2012
3677	2^325765+1974305	98066	Enzo Doria	06/2016
3678	2^325733-58695	98056	Lelio R Paula	07/2016
3679	2^325717-3645	98051	Lelio R Paula	07/2016
3680	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
3681	(7*10^98007-13)/3	98008	Robert Price	06/2016
3682	2^325512-459959	97989	Enzo Doria	05/2015
3683	(3^205354-8)/17	97978	Lelio R Paula	09/2013
3684	2^325433+76817	97966	Enzo Doria	05/2016
3685	5*10^97963+81	97964	Robert Price	08/2017
3686	2^325390-109061	97953	Enzo Doria	04/2014
3687	13^87921+24	97940	Lelio R Paula	08/2016
3688	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
3689	2^325215+12909	97900	Lelio R Paula	07/2016
3690	7*10^97874-69	97875	Robert Price	01/2017
3692	(17^79537+5^79537)/22	97865	Robert Price	06/2013
3691	15^83212+22	97865	Lelio R Paula	08/2016
3693	2^325087-109057	97861	Enzo Doria	04/2014
3694	2^325074+1870657	97858	Enzo Doria	05/2016
3695	2^325066-2111	97855	Yves Minet	08/2013
3696	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
3697	18^77944-89	97841	Lelio R Paula	07/2016
3698	119^47136+118	97833	Norbert Schneider	09/2018
3699	6^125720-17663	97830	Enzo Doria	02/2013
3700	2^324972-2069	97827	Yves Minet	05/2013
3701	2^324944-2788319	97818	Enzo Doria	03/2016
3703	4*10^97799-9	97800	Erik Branger	11/2013
3702	2^324882+577294575	97800	Lelio R Paula	09/2016
3704	2^324863-1867921	97794	Enzo Doria	04/2016
3705	6^125662-18473	97785	Enzo Doria	03/2013
3706	12^90604+11	97779	Lelio R Paula	07/2016
3707	5^139830+24	97737	Lelio R Paula	04/2016
3708	2^324612+1155	97718	Lelio R Paula	07/2016
3709	19^76404-44	97702	Lelio R Paula	07/2016
3710	2^324505-2983	97686	Yves Minet	04/2011
3711	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
3712	6^125488-17843	97649	Enzo Doria	02/2013
3713	7^115515-2	97622	Lelio R Paula	09/2013
3714	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
3715	6^125418-5	97595	Lelio R Paula	11/2014
3716	2^324076+1155	97557	Lelio R Paula	07/2016
3717	(2^324074+9)/13	97555	Lelio R Paula	10/2013
3718	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
3719	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
3720	2^323946+73939	97518	Enzo Doria	04/2016
3721	2^323937+1866947	97515	Enzo Doria	03/2016
3722	6^125290-18533	97495	Enzo Doria	03/2013
3723	2^323845+101	97488	Lelio R Paula	12/2012
3724	18^77662+65	97487	Lelio R Paula	07/2016
3725	2^323772+76771	97466	Enzo Doria	05/2016
3726	2^323765-112213	97463	Enzo Doria	06/2014
3727	2^323720-6555	97450	Lelio R Paula	07/2016
3728	2^323694-1860401	97442	Enzo Doria	03/2016
3729	20^74886+3	97429	Lelio R Paula	06/2016
3731	3*10^97399+73	97400	Robert Price	04/2016
3730	7^115252-50	97400	Lelio R Paula	07/2016
3732	224737#+393581	97389	Nicolas PALAU	12/2016
3733	(26*10^97353+31)/3	97354	Robert Price	07/2016
3734	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
3735	(38*10^97329+187)/9	97330	Robert Price	11/2017
3736	p(19982)#/2-1024	97293	Robert Price	09/2017
3737	6^125021-85	97286	Lelio R Paula	08/2016
3738	2^323164-47355	97283	Lelio R Paula	07/2016
3739	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
3740	2^323054-6555	97249	Lelio R Paula	07/2016
3741	9*10^97247-29	97248	Robert Price	05/2017
3742	(31*10^97242+41)/9	97243	Robert Price	04/2015
3743	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
3744	12^90098-41	97233	Lelio R Paula	07/2016
3745	2^322928-216929	97212	Enzo Doria	05/2014
3746	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
3747	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
3748	2^322725+75761	97150	Enzo Doria	04/2016
3749	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
3750	(41*10^97085+373)/9	97086	Robert Price	04/2017

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PRP Records

Probable Primes Top 10000

(224660 PRPs in the top)