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 ?
3502	328^40945+40945^328	103013	Norbert Schneider	12/2014
3501	12^95454-91	103013	Lelio R Paula	10/2016
3503	25833^9716+9716^25833	103009	Hans Havermann	01/2019
3504	65^56809-64^56809	102990	Robert Price	08/2013
3505	5^147338-6	102985	Lelio R Paula	11/2014
3506	2^342084-112739	102978	Enzo Doria	06/2014
3507	9*6^132330+7	102974	Lelio R Paula	11/2014
3508	2^342034-16737	102963	Enzo Doria	05/2013
3509	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
3510	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
3511	2^341991-17421	102950	Enzo Doria	05/2013
3512	2^341969-112225	102943	Enzo Doria	06/2014
3513	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
3514	2^341859+1869413	102910	Enzo Doria	05/2016
3515	10^102909+61	102910	Lelio R Paula	11/2016
3516	10^102909-67049	102909	Patrick De Geest	12/2016
3517	23814^20935+20935^23814	102898	Hans Havermann	02/2019
3518	28345^4264+4264^28345	102888	Hans Havermann	02/2019
3519	25665^10204+10204^25665	102886	Hans Havermann	02/2019
3520	26288^8181+8181^26288	102860	Hans Havermann	02/2019
3521	2^341659+1836773	102850	Enzo Doria	03/2016
3522	2^341608-110639	102835	Enzo Doria	05/2014
3523	10^102824+49	102825	Lelio R Paula	11/2016
3524	10^102824-168011	102824	Patrick De Geest	12/2016
3525	11^98708-8	102794	Lelio R Paula	10/2016
3526	2^341466+4429	102792	Lelio R Paula	09/2011
3527	2^341460-107	102790	Lelio R Paula	08/2011
3528	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
3529	2^341355+21	102759	Lelio R Paula	08/2011
3530	2^341246+40755	102726	Lelio R Paula	11/2016
3531	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
3532	7^121547+78	102720	Lelio R Paula	10/2016
3533	2^341223-461197	102719	Enzo Doria	06/2015
3534	27838^4893+4893^27838	102711	Hans Havermann	03/2019
3536	2^341190-20577	102709	Enzo Doria	06/2013
3535	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
3537	6^131976-65	102698	Lelio R Paula	10/2016
3538	2^341134+2533	102692	Henri Lifchitz	09/2005
3539	13^92184-54	102688	Lelio R Paula	10/2016
3540	2^341116-20873	102687	Enzo Doria	06/2013
3541	2^341094-19953	102680	Enzo Doria	06/2013
3542	23761^20950+20950^23761	102676	Hans Havermann	03/2019
3543	2^341053+129	102668	Lelio R Paula	08/2011
3544	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
3545	7^121471+94	102655	Lelio R Paula	10/2016
3547	2^341004-173	102653	Lelio R Paula	08/2011
3546	20^78901+3	102653	Lelio R Paula	10/2016
3548	5^146853-52	102646	Lelio R Paula	10/2016
3549	2^340969-216931	102642	Enzo Doria	05/2014
3550	122^49196+121	102641	Norbert Schneider	10/2018
3551	2^340952+1870021	102637	Enzo Doria	05/2016
3552	5*2^340940-3	102634	Lelio R Paula	08/2014
3553	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
3554	25876^9239+9239^25876	102615	Hans Havermann	02/2019
3555	(4*10^102612+83)/3	102613	Robert Price	02/2018
3556	75^54717+74	102598	Norbert Schneider	01/2015
3557	(17*10^102597+13)/3	102598	Robert Price	01/2019
3558	2^340806-20393	102593	Enzo Doria	06/2013
3559	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
3560	6^131821+77	102577	Lelio R Paula	10/2016
3561	2^340688-29	102558	Henri Lifchitz	05/2005
3562	2^340685-109101	102557	Enzo Doria	04/2014
3563	65^56567-64	102552	Norbert Schneider	11/2014
3564	26230^8121+8121^26230	102550	Hans Havermann	03/2019
3565	2^340547-108897	102515	Enzo Doria	03/2014
3566	25592^10119+10119^25592	102500	Hans Havermann	02/2019
3567	7^121268+82	102484	Lelio R Paula	10/2016
3568	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
3569	2^340434-5955	102481	Lelio R Paula	11/2016
3570	(2^340381+47)/7	102465	Lelio R Paula	12/2013
3571	111^50095+110	102461	Norbert Schneider	04/2017
3572	2^340291-20301	102438	Enzo Doria	06/2013
3573	12^94915+89	102431	Lelio R Paula	10/2016
3574	24466^15349+15349^24466	102417	Hans Havermann	03/2019
3575	2^340208-20373	102413	Enzo Doria	06/2013
3576	6^131598-17273	102404	Enzo Doria	02/2013
3577	2^340115-21181	102385	Enzo Doria	06/2013
3578	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
3579	89^52511-88^52511	102365	Robert Price	06/2015
3580	3^214539-112756	102362	Enzo Doria	07/2014
3581	2^340000-19877	102351	Enzo Doria	06/2013
3582	2^339990-114845	102348	Enzo Doria	05/2015
3583	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
3584	20^78661-99	102341	Lelio R Paula	09/2016
3585	2^339951-19585	102336	Enzo Doria	05/2013
3586	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
3587	2^339889+29327	102317	Yves Minet	06/2010
3588	26348^7641+7641^26348	102314	Hans Havermann	03/2019
3589	Phi(239414,10)/6333218543	102303	Makoto Kamada	08/2019
3590	2^339834-109493	102301	Enzo Doria	04/2014
3591	(16*10^102299-19)/3	102300	Robert Price	02/2019
3592	(11^98221-5^98221)/6	102286	Robert Price	01/2013
3593	3^214365+1820	102279	Lelio R Paula	10/2016
3594	31978^1579+1579^31978	102278	Hans Havermann	03/2019
3595	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
3596	2^339694-16995	102259	Lelio R Paula	09/2016
3597	(56*10^102255+691)/9	102256	Robert Price	05/2019
3598	122^49008+121	102249	Norbert Schneider	10/2018
3600	7^120985-38	102245	Lelio R Paula	10/2016
3599	10^102244+122961	102245	Patrick De Geest	12/2016
3601	10^102244-27	102244	Lelio R Paula	09/2016
3602	7^120982-62	102242	Lelio R Paula	10/2016
3603	4*6^131382-5	102236	Lelio R Paula	11/2014
3604	2^339586-1091	102226	Yves Minet	11/2012
3605	11^98161-3072000	102225	Enzo Doria	12/2012
3606	9*7^120961-4	102225	Lelio R Paula	11/2014
3607	5*3^214250+2	102224	Serge Batalov	10/2010
3608	12^94713-59	102213	Lelio R Paula	10/2016
3609	12^94705+89	102204	Lelio R Paula	10/2016
3610	2^339407-177	102172	Lelio R Paula	08/2011
3611	4*10^102163-57	102164	Robert Price	10/2018
3612	2^339355+65	102157	Lelio R Paula	07/2011
3613	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
3614	2^339168+21	102100	Lelio R Paula	07/2011
3615	2^339167-108807	102100	Enzo Doria	03/2014
3616	2^339156+163	102097	Lelio R Paula	08/2011
3617	(25*10^102076-67)/3	102077	Robert Price	06/2019
3618	2^339081-4543	102074	Yves Minet	03/2019
3619	24327^15668+15668^24327	102053	Hans Havermann	02/2019
3620	25080^11711+11711^25080	102041	Hans Havermann	02/2019
3621	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
3622	2^338891-18885	102017	Enzo Doria	05/2013
3623	8*10^102000+51	102001	Robert Price	08/2019
3624	2^338829-113239	101998	Enzo Doria	07/2014
3625	2^338828-113297	101998	Enzo Doria	07/2014
3626	2^338796+93	101988	Donovan Johnson	06/2008
3627	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
3628	25295^10744+10744^25295	101969	Hans Havermann	01/2019
3629	25712^9243+9243^25712	101969	Hans Havermann	01/2019
3630	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
3631	2^338682-19865	101954	Enzo Doria	06/2013
3632	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
3633	28594^3673+3673^28594	101939	Hans Havermann	02/2019
3634	2^338568+37	101920	Lelio R Paula	07/2011
3635	2^338559-1858777	101917	Enzo Doria	04/2016
3636	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
3637	24502^14419+14419^24502	101903	Hans Havermann	01/2019
3638	2^338497-17041	101898	Enzo Doria	05/2013
3639	2^338475+54615	101892	Lelio R Paula	10/2016
3640	2^338426-19797	101877	Enzo Doria	06/2013
3641	2^338368-20369	101859	Enzo Doria	06/2013
3642	2^338366+74179	101859	Enzo Doria	04/2016
3643	27088^5755+5755^27088	101853	Hans Havermann	01/2019
3644	2^338280-19745	101833	Enzo Doria	06/2013
3645	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
3646	6^130841+103	101815	Lelio R Paula	10/2016
3647	2^338122-20117	101785	Enzo Doria	06/2013
3648	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
3649	35^65917-7092	101781	Enzo Doria	03/2013
3650	2^338010-19833	101752	Enzo Doria	06/2013
3651	3^213215-76	101730	Lelio R Paula	09/2016
3652	23907^17998+17998^23907	101730	Hans Havermann	01/2019
3653	2^337930+63	101728	Lelio R Paula	07/2011
3654	2^337920+1869661	101725	Enzo Doria	05/2016
3655	24116^16509+16509^24116	101715	Hans Havermann	01/2019
3656	2^337859-19645	101706	Enzo Doria	05/2013
3657	2^337754+1869169	101675	Enzo Doria	05/2016
3658	3*10^101657-37	101658	Robert Price	07/2018
3659	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
3660	11^97605-24	101646	Lelio R Paula	10/2016
3661	8^112539-112539	101633	Robert Price	01/2014
3662	25694^9003+9003^25694	101605	Hans Havermann	12/2018
3663	2^337515-19869	101603	Enzo Doria	06/2013
3664	2^337473+719	101590	Lelio R Paula	08/2011
3665	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
3666	2^337452-108815	101584	Enzo Doria	03/2014
3667	2^337453+1185	101584	Lelio R Paula	09/2016
3668	2^337410-113561	101571	Enzo Doria	08/2014
3669	2^337387+855	101564	Lelio R Paula	09/2016
3670	2^337367-17295	101558	Lelio R Paula	09/2016
3671	2^337342-109035	101551	Enzo Doria	04/2014
3672	23703^19238+19238^23703	101548	Hans Havermann	12/2018
3673	(26*10^101537-167)/3	101538	Robert Price	10/2019
3674	2^337267-19	101528	Lelio R Paula	07/2011
3675	2^337183-19989	101503	Enzo Doria	06/2013
3676	2^337149+72425	101492	Enzo Doria	04/2016
3677	24041^16642+16642^24041	101483	Hans Havermann	12/2018
3678	33982^969+969^33982	101482	Hans Havermann	12/2018
3679	2^337101-20241	101478	Enzo Doria	06/2013
3680	2^337035-20001	101458	Enzo Doria	06/2013
3681	2^337017-16995	101453	Lelio R Paula	09/2016
3682	2^336979-115315	101441	Enzo Doria	06/2015
3683	2^336970-20885	101439	Enzo Doria	06/2013
3684	2^336958+79	101435	Lelio R Paula	10/2009
3685	2^336942+169	101430	Lelio R Paula	10/2009
3686	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
3687	4*10^101415-89	101416	Robert Price	11/2018
3688	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
3689	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
3690	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
3691	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
3692	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
3693	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
3694	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
3695	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
3696	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
3697	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
3698	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
3699	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
3700	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
3701	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
3702	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
3703	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
3704	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
3705	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
3706	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3707	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
3708	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3709	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
3710	24097^16150+16150^24097	101405	Hans Havermann	12/2018
3711	2^336842+94065	101400	Lelio R Paula	09/2016
3712	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
3713	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
3714	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
3715	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
3716	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
3717	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
3718	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
3719	10^101369+203811	101370	Patrick De Geest	11/2016
3720	10^101369-99	101369	Lelio R Paula	09/2016
3721	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
3722	2^336701-113563	101358	Enzo Doria	08/2014
3723	89717!4-512	101351	Robert Price	11/2019
3724	2^336644-109023	101340	Enzo Doria	04/2014
3725	2^336601-21081	101327	Enzo Doria	06/2013
3726	20^77869+63	101310	Lelio R Paula	09/2016
3727	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
3728	6^130179-137	101299	Lelio R Paula	10/2016
3729	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
3730	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
3731	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
3732	2^336369-19753	101258	Enzo Doria	05/2013
3733	23842^17653+17653^23842	101253	Hans Havermann	11/2018
3734	2^336350-344291	101252	Enzo Doria	07/2015
3735	(56*10^101222-47)/9	101223	Robert Price	02/2019
3736	2^336243-108777	101220	Enzo Doria	03/2014
3737	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
3738	23535^19954+19954^23535	101202	Hans Havermann	11/2018
3739	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
3740	2^336150-20393	101192	Enzo Doria	06/2013
3741	23996^16473+16473^23996	101186	Hans Havermann	11/2018
3742	2^336112-1865249	101180	Enzo Doria	03/2016
3743	2^336103-109015	101178	Enzo Doria	04/2014
3744	13^90809-96	101157	Lelio R Paula	10/2016
3745	26199^7258+7258^26199	101150	Hans Havermann	11/2018
3746	19^79098-30	101147	Lelio R Paula	10/2016
3747	19^79095+88	101144	Lelio R Paula	10/2016
3748	15^85976+32	101116	Lelio R Paula	10/2016
3749	2^335872-2776215	101108	Tony Prest / Never Odd Or Even	01/2019
3750	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013

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