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 ?
3501	2^346078+7695	104180	Lelio R Paula	12/2016
3502	2^346055-19537	104173	Enzo Doria	05/2013
3503	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
3504	2^346037-20125	104168	Enzo Doria	06/2013
3505	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
3506	6^133854-17993	104159	Enzo Doria	03/2013
3507	2^345990+1874239	104154	Enzo Doria	06/2016
3508	2^345988-20373	104153	Enzo Doria	06/2013
3509	(26*10^104132-503)/9	104133	Robert Price	07/2018
3510	3*5^148968+8	104125	Lelio R Paula	11/2014
3511	(7*10^104113+53)/3	104114	Robert Price	05/2018
3512	p(21253)#/2+8	104113	Robert Price	01/2017
3513	322^41507+41507^322	104094	Norbert Schneider	12/2014
3514	6^133768-17423	104092	Enzo Doria	03/2013
3515	2^345786-19557	104092	Enzo Doria	05/2013
3516	171^46606-2	104072	Lelio R Paula	10/2017
3517	2^345704-149	104068	Lelio R Paula	09/2011
3518	6^133704-17273	104042	Enzo Doria	02/2013
3519	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
3520	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
3521	2^345547+11	104021	Lelio R Paula	09/2011
3522	(19*10^104014-49)/3	104015	Robert Price	05/2019
3523	2^345504+723	104008	Lelio R Paula	09/2011
3524	2^345498-20037	104006	Enzo Doria	06/2013
3525	18^82854-37	104005	Lelio R Paula	01/2017
3526	2^345486-109065	104002	Enzo Doria	04/2014
3527	2^345487-1851507	104002	Enzo Doria	08/2015
3528	2^345476+777	103999	Lelio R Paula	09/2011
3529	4*10^103981-83	103982	Robert Price	10/2018
3530	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
3531	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
3532	(19*10^103907+77)/3	103908	Robert Price	05/2019
3533	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
3534	2^345106-112181	103888	Enzo Doria	06/2014
3535	2^345079+99	103880	Lelio R Paula	09/2011
3536	11^99736-1500	103865	Enzo Doria	12/2012
3537	23263^23784-23784^23263	103857	Norbert Schneider	01/2020
3538	2^344842-20157	103808	Enzo Doria	06/2013
3539	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
3540	2^344802-20765	103796	Enzo Doria	06/2013
3541	2^344794-3821	103794	Yves Minet	05/2011
3542	2^344782-109103	103790	Enzo Doria	04/2014
3543	3^217521-112292	103784	Enzo Doria	06/2014
3544	2^344759-3505	103783	Lelio R Paula	11/2016
3545	2^344735-147	103776	Lelio R Paula	09/2011
3546	L(496533)-p(496533)	103770	Robert Price	02/2018
3547	2*10^103749-69	103750	Robert Price	03/2018
3548	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
3549	2^344607-108891	103738	Enzo Doria	03/2014
3550	(148*10^103718-1)/3	103720	Robert Price	03/2020
3551	2^344541-19561	103718	Enzo Doria	05/2013
3552	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
3553	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
3554	2^344444-455	103688	Yves Minet	03/2012
3555	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
3556	2^344317-109933	103650	Enzo Doria	04/2014
3557	2^344309-1852033	103648	Enzo Doria	08/2015
3558	2^344213-21253	103619	Enzo Doria	06/2013
3559	2^344196-465	103614	Lelio R Paula	11/2016
3560	2^344187-20001	103611	Enzo Doria	06/2013
3561	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
3562	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
3563	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
3564	2^344085-20365	103580	Enzo Doria	06/2013
3565	5^148169+54	103566	Lelio R Paula	11/2016
3566	2^344017-108795	103560	Enzo Doria	03/2014
3567	2^343971-5077	103546	Lelio R Paula	09/2011
3568	(7*10^103531+71)/3	103532	Robert Price	05/2018
3569	2^343899+141	103524	Lelio R Paula	08/2011
3570	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
3571	6^133029-67	103517	Lelio R Paula	11/2016
3572	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
3573	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
3574	5^148014-24	103458	Lelio R Paula	11/2016
3575	(22*10^103450+53)/3	103451	Robert Price	07/2019
3576	2^343604+9931	103436	Yves Minet	01/2011
3577	2^343601-21189	103435	Enzo Doria	06/2013
3578	2^343508-115229	103407	Enzo Doria	06/2015
3579	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
3580	3^216685-113056	103386	Enzo Doria	07/2014
3581	91355!4+1024	103381	Robert Price	09/2019
3582	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
3583	11^99262-20	103371	Lelio R Paula	12/2016
3584	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
3586	2^343356-2791889	103361	Enzo Doria	03/2016
3585	(25*10^103360-241)/9	103361	Robert Price	05/2018
3587	Phi(104989,10)/2939693	103350	Maksym Voznyy	09/2015
3588	2^343182-171	103309	Lelio R Paula	08/2011
3589	(23619^23619+23620^23620)/7187	103294	David Broadhurst	09/2009
3590	2^343079-1835611	103278	Enzo Doria	05/2015
3591	2^343063-1147	103273	Yves Minet	06/2013
3592	9*6^132689+7	103254	Lelio R Paula	11/2014
3593	2^342979-18085	103247	Enzo Doria	05/2013
3594	(16*10^103244-31)/3	103245	Robert Price	03/2019
3595	2^342966-16995	103244	Lelio R Paula	11/2016
3596	(16*10^103214-31)/3	103215	Robert Price	03/2019
3597	(37*10^103211+611)/9	103212	Robert Price	11/2018
3598	5^147650+16	103203	Lelio R Paula	11/2016
3599	gcd(Phi(852060,10),(10^42603+1)^3(10^42603+1-10^21302)+(10^85206+10^42603)(10^21302+1)+10^127809)	103201	Serge Batalov	04/2015
3600	2^342817+2707067	103199	Enzo Doria	03/2016
3601	43^63177-42	103198	Theodore Burton	02/2007
3602	2^342805-21025	103195	Enzo Doria	06/2013
3603	2^342714+12285	103168	Lelio R Paula	11/2016
3604	18^82178-4481	103156	Enzo Doria	03/2013
3605	2^342665-17349	103153	Enzo Doria	05/2013
3606	2^342612+175	103137	Lelio R Paula	08/2011
3607	5*2^342585-3	103130	Lelio R Paula	09/2014
3608	(16*10^103127+77)/3	103128	Robert Price	03/2019
3609	2^342503-19209	103104	Enzo Doria	05/2013
3610	2^342476+51	103096	Lelio R Paula	08/2011
3611	2^342460-18885	103091	Enzo Doria	05/2013
3612	7^121968+82	103075	Lelio R Paula	10/2016
3613	2^342392-108863	103071	Enzo Doria	03/2014
3614	3^216014+28	103065	Lelio R Paula	11/2016
3615	2^342353-108879	103059	Enzo Doria	03/2014
3616	10^103055+276081	103056	Patrick De Geest	12/2016
3617	10^103055-53	103055	Lelio R Paula	11/2016
3618	(58*10^103046+419)/9	103047	Robert Price	05/2019
3619	7^121933+4	103046	Lelio R Paula	11/2014
3620	19^80560-68	103017	Lelio R Paula	10/2016
3621	2^342209+76607	103016	Enzo Doria	05/2016
3623	328^40945+40945^328	103013	Norbert Schneider	12/2014
3622	12^95454-91	103013	Lelio R Paula	10/2016
3624	25833^9716+9716^25833	103009	Hans Havermann	01/2019
3625	65^56809-64^56809	102990	Robert Price	08/2013
3626	5^147338-6	102985	Lelio R Paula	11/2014
3627	2^342084-112739	102978	Enzo Doria	06/2014
3628	9*6^132330+7	102974	Lelio R Paula	11/2014
3629	2^342034-16737	102963	Enzo Doria	05/2013
3630	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
3631	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
3632	2^341991-17421	102950	Enzo Doria	05/2013
3633	2^341969-112225	102943	Enzo Doria	06/2014
3634	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
3636	2^341859+1869413	102910	Enzo Doria	05/2016
3635	10^102909+61	102910	Lelio R Paula	11/2016
3637	10^102909-67049	102909	Patrick De Geest	12/2016
3638	23814^20935+20935^23814	102898	Hans Havermann	02/2019
3639	28345^4264+4264^28345	102888	Hans Havermann	02/2019
3640	25665^10204+10204^25665	102886	Hans Havermann	02/2019
3641	26288^8181+8181^26288	102860	Hans Havermann	02/2019
3642	2^341659+1836773	102850	Enzo Doria	03/2016
3643	2^341608-110639	102835	Enzo Doria	05/2014
3644	10^102824+49	102825	Lelio R Paula	11/2016
3645	10^102824-168011	102824	Patrick De Geest	12/2016
3646	11^98708-8	102794	Lelio R Paula	10/2016
3647	2^341466+4429	102792	Lelio R Paula	09/2011
3648	2^341460-107	102790	Lelio R Paula	08/2011
3649	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
3650	2^341355+21	102759	Lelio R Paula	08/2011
3651	2^341246+40755	102726	Lelio R Paula	11/2016
3652	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
3653	7^121547+78	102720	Lelio R Paula	10/2016
3654	2^341223-461197	102719	Enzo Doria	06/2015
3655	27838^4893+4893^27838	102711	Hans Havermann	03/2019
3657	2^341190-20577	102709	Enzo Doria	06/2013
3656	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
3658	6^131976-65	102698	Lelio R Paula	10/2016
3659	2^341134+2533	102692	Henri Lifchitz	09/2005
3660	13^92184-54	102688	Lelio R Paula	10/2016
3661	2^341116-20873	102687	Enzo Doria	06/2013
3662	2^341094-19953	102680	Enzo Doria	06/2013
3663	23761^20950+20950^23761	102676	Hans Havermann	03/2019
3664	2^341053+129	102668	Lelio R Paula	08/2011
3666	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
3665	7^121471+94	102655	Lelio R Paula	10/2016
3668	2^341004-173	102653	Lelio R Paula	08/2011
3667	20^78901+3	102653	Lelio R Paula	10/2016
3669	5^146853-52	102646	Lelio R Paula	10/2016
3670	2^340969-216931	102642	Enzo Doria	05/2014
3671	122^49196+121	102641	Norbert Schneider	10/2018
3672	2^340952+1870021	102637	Enzo Doria	05/2016
3673	5*2^340940-3	102634	Lelio R Paula	08/2014
3674	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
3675	25876^9239+9239^25876	102615	Hans Havermann	02/2019
3676	(4*10^102612+83)/3	102613	Robert Price	02/2018
3677	75^54717+74	102598	Norbert Schneider	01/2015
3678	(17*10^102597+13)/3	102598	Robert Price	01/2019
3679	2^340806-20393	102593	Enzo Doria	06/2013
3680	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
3681	6^131821+77	102577	Lelio R Paula	10/2016
3682	2^340688-29	102558	Henri Lifchitz	05/2005
3683	2^340685-109101	102557	Enzo Doria	04/2014
3684	65^56567-64	102552	Norbert Schneider	11/2014
3685	26230^8121+8121^26230	102550	Hans Havermann	03/2019
3686	(536*10^102533-23)/9	102535	Robert Price	02/2020
3687	2^340547-108897	102515	Enzo Doria	03/2014
3688	25592^10119+10119^25592	102500	Hans Havermann	02/2019
3689	7^121268+82	102484	Lelio R Paula	10/2016
3690	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
3691	2^340434-5955	102481	Lelio R Paula	11/2016
3692	(2^340381+47)/7	102465	Lelio R Paula	12/2013
3693	111^50095+110	102461	Norbert Schneider	04/2017
3694	2^340291-20301	102438	Enzo Doria	06/2013
3695	12^94915+89	102431	Lelio R Paula	10/2016
3696	24466^15349+15349^24466	102417	Hans Havermann	03/2019
3697	2^340208-20373	102413	Enzo Doria	06/2013
3698	6^131598-17273	102404	Enzo Doria	02/2013
3699	2^340115-21181	102385	Enzo Doria	06/2013
3700	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
3701	89^52511-88^52511	102365	Robert Price	06/2015
3702	3^214539-112756	102362	Enzo Doria	07/2014
3703	23159^23450-23450^23159	102353	Norbert Schneider	12/2019
3704	2^340000-19877	102351	Enzo Doria	06/2013
3705	2^339990-114845	102348	Enzo Doria	05/2015
3706	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
3707	20^78661-99	102341	Lelio R Paula	09/2016
3708	2^339951-19585	102336	Enzo Doria	05/2013
3709	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
3710	2^339889+29327	102317	Yves Minet	06/2010
3711	(167*10^102315-17)/3	102317	Robert Price	03/2020
3712	26348^7641+7641^26348	102314	Hans Havermann	03/2019
3713	Phi(239414,10)/6333218543	102303	Makoto Kamada	08/2019
3714	2^339834-109493	102301	Enzo Doria	04/2014
3715	(16*10^102299-19)/3	102300	Robert Price	02/2019
3716	(11^98221-5^98221)/6	102286	Robert Price	01/2013
3717	3^214365+1820	102279	Lelio R Paula	10/2016
3718	31978^1579+1579^31978	102278	Hans Havermann	03/2019
3719	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
3720	2^339694-16995	102259	Lelio R Paula	09/2016
3721	(56*10^102255+691)/9	102256	Robert Price	05/2019
3722	122^49008+121	102249	Norbert Schneider	10/2018
3724	7^120985-38	102245	Lelio R Paula	10/2016
3723	10^102244+122961	102245	Patrick De Geest	12/2016
3725	10^102244-27	102244	Lelio R Paula	09/2016
3726	7^120982-62	102242	Lelio R Paula	10/2016
3727	4*6^131382-5	102236	Lelio R Paula	11/2014
3728	2^339586-1091	102226	Yves Minet	11/2012
3729	11^98161-3072000	102225	Enzo Doria	12/2012
3730	9*7^120961-4	102225	Lelio R Paula	11/2014
3731	5*3^214250+2	102224	Serge Batalov	10/2010
3732	12^94713-59	102213	Lelio R Paula	10/2016
3733	12^94705+89	102204	Lelio R Paula	10/2016
3734	2^339407-177	102172	Lelio R Paula	08/2011
3735	4*10^102163-57	102164	Robert Price	10/2018
3736	2^339355+65	102157	Lelio R Paula	07/2011
3737	(28*10^102142-31)/3	102143	Robert Price	12/2019
3738	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
3739	2^339168+21	102100	Lelio R Paula	07/2011
3740	2^339167-108807	102100	Enzo Doria	03/2014
3741	2^339156+163	102097	Lelio R Paula	08/2011
3742	(25*10^102076-67)/3	102077	Robert Price	06/2019
3743	2^339081-4543	102074	Yves Minet	03/2019
3744	24327^15668+15668^24327	102053	Hans Havermann	02/2019
3745	25080^11711+11711^25080	102041	Hans Havermann	02/2019
3746	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
3747	2^338891-18885	102017	Enzo Doria	05/2013
3748	8*10^102000+51	102001	Robert Price	08/2019
3749	2^338829-113239	101998	Enzo Doria	07/2014
3750	2^338828-113297	101998	Enzo Doria	07/2014

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