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	(10^99239-13)/3	99239	Robert Price	02/2017
3502	3^207987+62	99236	Lelio R Paula	08/2016
3503	2^329638+49	99231	Lelio R Paula	12/2012
3504	7^117413-18	99226	Lelio R Paula	08/2016
3505	2^329586-458903	99216	Enzo Doria	04/2015
3506	2^329553+101	99206	Lelio R Paula	12/2012
3507	2^329551-112897	99205	Enzo Doria	06/2014
3508	(3^207925+7)/50	99204	Lelio R Paula	09/2013
3509	6^127458-17993	99182	Enzo Doria	03/2013
3510	27197^4428+4428^27197	99166	Hans Havermann	10/2017
3511	(46*10^99143-1)/9	99144	Robert Price	12/2014
3512	7*10^99133+69	99134	Robert Price	10/2017
3513	18^78968-3065	99127	Enzo Doria	03/2013
3514	25927^6654+6654^25927	99122	Hans Havermann	10/2017
3515	2^329259+189	99117	Lelio R Paula	12/2012
3516	8*10^99113+39	99114	Robert Price	01/2017
3517	6^127364+77	99109	Lelio R Paula	08/2016
3518	6^127285+13	99047	Lelio R Paula	08/2016
3519	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
3520	2^329007+73283	99041	Enzo Doria	04/2016
3521	5*3^207543-8	99024	Lelio R Paula	08/2014
3522	2^328885+149	99005	Lelio R Paula	12/2012
3523	23392^17075+17075^23392	99004	Hans Havermann	09/2017
3524	(2^328879-9)/119	99001	Lelio R Paula	10/2013
3525	5^141618+54	98987	Lelio R Paula	08/2016
3526	8*10^98982+51	98983	Robert Price	05/2017
3527	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
3528	2^328794-2797601	98977	Enzo Doria	04/2016
3529	6^127176+5	98963	Lelio R Paula	11/2014
3530	24262^11989+11989^24262	98960	Hans Havermann	09/2017
3531	2^328700-109709	98949	Enzo Doria	04/2014
3532	46711!2-2^46711	98916	Robert Price	09/2015
3533	9*7^117037+4	98909	Lelio R Paula	11/2014
3534	(10^98890+149)/3	98890	Serge Batalov	12/2014
3535	22775^21978+21978^22775	98889	Hans Havermann	08/2017
3536	2^328497-216933	98888	Enzo Doria	05/2014
3537	2^328487+32769	98885	Lelio R Paula	08/2016
3538	3^207250-112358	98884	Enzo Doria	06/2014
3539	13^88754-90	98867	Lelio R Paula	08/2016
3540	2^328406+709	98861	Lelio R Paula	02/2013
3541	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
3542	7^116976+76	98857	Lelio R Paula	08/2016
3543	2^328335+1155	98839	Lelio R Paula	08/2016
3544	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
3545	287^40210+40210^287	98832	Norbert Schneider	11/2014
3546	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
3547	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
3548	65^54491+48	98788	Lelio R Paula	04/2016
3549	3^207042+98	98785	Lelio R Paula	08/2016
3550	3^206977-112756	98754	Enzo Doria	07/2014
3551	7^116846-50	98747	Lelio R Paula	08/2016
3552	2^327967-28635	98728	Lelio R Paula	08/2016
3553	707^34642+34642^707	98710	Norbert Schneider	12/2017
3554	6^126850-47	98709	Lelio R Paula	08/2016
3555	8*6^126830-7	98694	Lelio R Paula	11/2014
3556	11^94770-270	98693	Enzo Doria	08/2012
3557	2^327832+43	98688	Lelio R Paula	12/2012
3558	2^327795+761	98677	Lelio R Paula	02/2013
3559	10^98669+147411	98670	Patrick De Geest	11/2016
3561	10^98669-9^(98669-1)	98669	Robert Price	05/2016
3560	10^98669-105249	98669	Patrick De Geest	11/2016
3562	2^327671-109801	98639	Enzo Doria	04/2014
3563	5^141090-14	98618	Lelio R Paula	08/2016
3564	20^75799+47	98617	Lelio R Paula	08/2016
3565	2^327515-1017	98592	Lelio R Paula	08/2016
3566	6^126692+97681	98586	Mike Oakes	04/2011
3567	2^327467-741	98578	Lelio R Paula	08/2016
3568	(2^327329+9)/19	98535	Lelio R Paula	10/2013
3569	7^116577-66	98519	Lelio R Paula	08/2016
3570	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
3571	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
3572	2^327162-66945	98486	Lelio R Paula	08/2016
3573	4*10^98472-3	98473	Erik Branger	11/2013
3574	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
3575	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
3576	13^88363+94	98432	Lelio R Paula	08/2016
3577	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
3578	6^126481+41	98422	Lelio R Paula	08/2016
3579	78*10^98413-7	98415	Robert Price	05/2017
3580	7^116416+46	98383	Lelio R Paula	08/2016
3581	7^116407-24	98376	Lelio R Paula	07/2016
3583	2^326782-1860671	98372	Enzo Doria	03/2016
3582	17^79948+58	98372	Lelio R Paula	08/2016
3584	3^206143-98	98356	Lelio R Paula	08/2016
3585	8*5^140705+7	98350	Lelio R Paula	11/2014
3586	2^326585+11	98312	Lelio R Paula	12/2012
3587	2^326582-459161	98311	Enzo Doria	05/2015
3588	(2^326548+9)/5	98301	Lelio R Paula	10/2013
3589	2^326538+71659	98298	Enzo Doria	04/2016
3590	15^83575-58	98292	Lelio R Paula	08/2016
3591	10^98288+3	98289	Robert Price	03/2011
3592	10^98288-117017	98288	Patrick De Geest	11/2011
3593	(44*10^98284-719)/9	98285	Robert Price	12/2017
3594	2^326421-2797573	98263	Enzo Doria	04/2016
3595	2^326401+16095	98257	Lelio R Paula	07/2016
3596	7^116240-116240^7	98235	Norbert Schneider	05/2017
3597	17^79826-78	98222	Lelio R Paula	08/2016
3598	2^326268-809	98217	Yves Minet	04/2011
3599	(418*10^98199+23)/9	98201	Robert Price	08/2017
3600	12*10^98198-7	98200	Robert Price	11/2017
3601	15^83496-76	98199	Lelio R Paula	08/2016
3602	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
3603	9*5^140471-4	98186	Lelio R Paula	11/2014
3604	2^326069-2383	98157	Yves Minet	10/2013
3605	2^325973+1185	98128	Lelio R Paula	07/2016
3606	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
3607	2^325945-1847269	98120	Enzo Doria	07/2015
3608	8*10^98111-67	98112	Robert Price	10/2017
3609	2^325866+15	98096	Lelio R Paula	12/2012
3610	2^325765+1974305	98066	Enzo Doria	06/2016
3611	2^325733-58695	98056	Lelio R Paula	07/2016
3612	2^325717-3645	98051	Lelio R Paula	07/2016
3613	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
3614	(7*10^98007-13)/3	98008	Robert Price	06/2016
3615	2^325512-459959	97989	Enzo Doria	05/2015
3616	(3^205354-8)/17	97978	Lelio R Paula	09/2013
3617	2^325433+76817	97966	Enzo Doria	05/2016
3618	5*10^97963+81	97964	Robert Price	08/2017
3619	2^325390-109061	97953	Enzo Doria	04/2014
3620	13^87921+24	97940	Lelio R Paula	08/2016
3621	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
3622	2^325215+12909	97900	Lelio R Paula	07/2016
3623	7*10^97874-69	97875	Robert Price	01/2017
3624	(17^79537+5^79537)/22	97865	Robert Price	06/2013
3625	15^83212+22	97865	Lelio R Paula	08/2016
3626	2^325087-109057	97861	Enzo Doria	04/2014
3627	2^325074+1870657	97858	Enzo Doria	05/2016
3629	2^325066-2111	97855	Yves Minet	08/2013
3628	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
3630	18^77944-89	97841	Lelio R Paula	07/2016
3631	6^125720-17663	97830	Enzo Doria	02/2013
3632	2^324972-2069	97827	Yves Minet	05/2013
3633	2^324944-2788319	97818	Enzo Doria	03/2016
3635	4*10^97799-9	97800	Erik Branger	11/2013
3634	2^324882+577294575	97800	Lelio R Paula	09/2016
3636	2^324863-1867921	97794	Enzo Doria	04/2016
3637	6^125662-18473	97785	Enzo Doria	03/2013
3638	12^90604+11	97779	Lelio R Paula	07/2016
3639	5^139830+24	97737	Lelio R Paula	04/2016
3640	2^324612+1155	97718	Lelio R Paula	07/2016
3641	19^76404-44	97702	Lelio R Paula	07/2016
3642	2^324505-2983	97686	Yves Minet	04/2011
3643	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
3644	6^125488-17843	97649	Enzo Doria	02/2013
3645	7^115515-2	97622	Lelio R Paula	09/2013
3646	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
3647	6^125418-5	97595	Lelio R Paula	11/2014
3648	2^324076+1155	97557	Lelio R Paula	07/2016
3649	(2^324074+9)/13	97555	Lelio R Paula	10/2013
3650	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
3651	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
3652	2^323946+73939	97518	Enzo Doria	04/2016
3653	2^323937+1866947	97515	Enzo Doria	03/2016
3654	6^125290-18533	97495	Enzo Doria	03/2013
3655	2^323845+101	97488	Lelio R Paula	12/2012
3656	18^77662+65	97487	Lelio R Paula	07/2016
3657	2^323772+76771	97466	Enzo Doria	05/2016
3658	2^323765-112213	97463	Enzo Doria	06/2014
3659	2^323720-6555	97450	Lelio R Paula	07/2016
3660	2^323694-1860401	97442	Enzo Doria	03/2016
3661	20^74886+3	97429	Lelio R Paula	06/2016
3663	3*10^97399+73	97400	Robert Price	04/2016
3662	7^115252-50	97400	Lelio R Paula	07/2016
3664	224737#+393581	97389	Nicolas PALAU	12/2016
3665	(26*10^97353+31)/3	97354	Robert Price	07/2016
3666	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
3667	(38*10^97329+187)/9	97330	Robert Price	11/2017
3668	p(19982)#/2-1024	97293	Robert Price	09/2017
3669	6^125021-85	97286	Lelio R Paula	08/2016
3670	2^323164-47355	97283	Lelio R Paula	07/2016
3671	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
3672	2^323054-6555	97249	Lelio R Paula	07/2016
3673	9*10^97247-29	97248	Robert Price	05/2017
3674	(31*10^97242+41)/9	97243	Robert Price	04/2015
3675	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
3676	12^90098-41	97233	Lelio R Paula	07/2016
3677	2^322928-216929	97212	Enzo Doria	05/2014
3678	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
3679	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
3680	2^322725+75761	97150	Enzo Doria	04/2016
3681	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
3682	(41*10^97085+373)/9	97086	Robert Price	04/2017
3683	2^322413+77	97056	Lelio R Paula	12/2012
3684	2^322406+177	97054	Lelio R Paula	12/2012
3685	(14*10^97044+31)/9	97045	Robert Price	02/2015
3686	2^322302+255255	97023	Lelio R Paula	07/2016
3687	2^322196-113093	96991	Enzo Doria	07/2014
3688	2^322000-1861469	96932	Enzo Doria	03/2016
3689	2^321971-112747	96923	Enzo Doria	06/2014
3690	11^93062-92	96915	Lelio R Paula	06/2016
3691	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
3692	3^203051+34	96880	Lelio R Paula	05/2016
3693	2*10^96867-51	96868	Robert Price	11/2017
3694	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
3695	2^321716-2786939	96847	Enzo Doria	03/2016
3697	2^321701-113053	96842	Enzo Doria	07/2014
3696	2^321700-28635	96842	Lelio R Paula	06/2016
3698	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
3699	6^124433-124433	96828	Robert Price	01/2014
3700	2^321631+69	96821	Lelio R Paula	12/2012
3701	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
3702	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
3703	(59*10^96798+31)/9	96799	Robert Price	09/2015
3704	223319#+231223	96790	Makoto Morimoto	02/2016
3705	2^321519-28635	96787	Lelio R Paula	06/2016
3706	2^321487-1867237	96778	Enzo Doria	03/2016
3707	2^321461-63	96770	Lelio R Paula	12/2012
3708	2^321439+123	96763	Lelio R Paula	12/2012
3709	2^321434+709	96762	Lelio R Paula	02/2013
3710	14^84413+89	96749	Lelio R Paula	07/2016
3711	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
3712	13^86847+96	96743	Lelio R Paula	06/2016
3713	9*2^321336-7	96733	Lelio R Paula	08/2014
3714	(209*10^96722-17)/3	96724	Robert Price	05/2017
3715	2^321187-1159	96687	Yves Minet	11/2012
3716	2^321182-1850081	96686	Enzo Doria	08/2015
3717	2^321116-112829	96666	Enzo Doria	06/2014
3718	2^321108-109499	96664	Enzo Doria	04/2014
3719	2^321098+2793859	96661	Enzo Doria	03/2016
3720	2^321057+4097	96648	Lelio R Paula	06/2016
3721	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
3722	p(19849)#/2-64	96581	Robert Price	04/2017
3723	2^320817+189	96576	Lelio R Paula	12/2012
3724	(361*10^96567-163)/9	96569	Robert Price	10/2017
3725	2^320788-110327	96567	Enzo Doria	05/2014
3726	2^320764+793	96560	Lelio R Paula	02/2013
3727	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
3728	2^320616-78795	96516	Lelio R Paula	03/2016
3729	2^320612-461939	96514	Enzo Doria	07/2015
3730	5*2^320431+7	96461	Lelio R Paula	08/2014
3731	19^75431-90	96458	Lelio R Paula	06/2016
3732	(2^320370+3)/67	96440	Lelio R Paula	10/2013
3733	2^320309+1871477	96423	Enzo Doria	05/2016
3734	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
3735	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
3736	2^320232-173	96400	Lelio R Paula	12/2012
3737	175^42975-2	96395	Lelio R Paula	10/2017
3738	10^96377+199911	96378	Patrick De Geest	12/2016
3739	10^96377-20001	96377	Robert Price	11/2016
3740	2^320124-2790449	96367	Enzo Doria	03/2016
3741	2^320043-108775	96343	Enzo Doria	04/2014
3742	10^96338+424939	96339	Patrick De Geest	03/2016
3743	10^96338-9281	96338	Robert Price	09/2015
3744	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
3745	2^319838+4257	96281	Lelio R Paula	03/2016
3746	2^319830-16995	96279	Lelio R Paula	03/2016
3747	6^123713+143	96268	Lelio R Paula	05/2016
3748	(28*10^96265-97)/3	96266	Robert Price	07/2016
3749	103^47825-102	96264	Norbert Schneider	10/2016
3750	2^319713-81	96244	Lelio R Paula	11/2012

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PRP Records

Probable Primes Top 10000

(218736 PRPs in the top)