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	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
3502	89^52511-88^52511	102365	Robert Price	06/2015
3503	3^214539-112756	102362	Enzo Doria	07/2014
3504	2^340000-19877	102351	Enzo Doria	06/2013
3505	2^339990-114845	102348	Enzo Doria	05/2015
3506	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
3507	20^78661-99	102341	Lelio R Paula	09/2016
3508	2^339951-19585	102336	Enzo Doria	05/2013
3509	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
3510	2^339889+29327	102317	Yves Minet	06/2010
3511	26348^7641+7641^26348	102314	Hans Havermann	03/2019
3512	2^339834-109493	102301	Enzo Doria	04/2014
3513	(16*10^102299-19)/3	102300	Robert Price	02/2019
3514	(11^98221-5^98221)/6	102286	Robert Price	01/2013
3515	3^214365+1820	102279	Lelio R Paula	10/2016
3516	31978^1579+1579^31978	102278	Hans Havermann	03/2019
3517	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
3518	2^339694-16995	102259	Lelio R Paula	09/2016
3519	(56*10^102255+691)/9	102256	Robert Price	05/2019
3520	122^49008+121	102249	Norbert Schneider	10/2018
3522	7^120985-38	102245	Lelio R Paula	10/2016
3521	10^102244+122961	102245	Patrick De Geest	12/2016
3523	10^102244-27	102244	Lelio R Paula	09/2016
3524	7^120982-62	102242	Lelio R Paula	10/2016
3525	4*6^131382-5	102236	Lelio R Paula	11/2014
3526	2^339586-1091	102226	Yves Minet	11/2012
3527	11^98161-3072000	102225	Enzo Doria	12/2012
3528	9*7^120961-4	102225	Lelio R Paula	11/2014
3529	5*3^214250+2	102224	Serge Batalov	10/2010
3530	12^94713-59	102213	Lelio R Paula	10/2016
3531	12^94705+89	102204	Lelio R Paula	10/2016
3532	2^339407-177	102172	Lelio R Paula	08/2011
3533	4*10^102163-57	102164	Robert Price	10/2018
3534	2^339355+65	102157	Lelio R Paula	07/2011
3535	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
3537	2^339168+21	102100	Lelio R Paula	07/2011
3536	2^339167-108807	102100	Enzo Doria	03/2014
3538	2^339156+163	102097	Lelio R Paula	08/2011
3539	(25*10^102076-67)/3	102077	Robert Price	06/2019
3540	2^339081-4543	102074	Yves Minet	03/2019
3541	24327^15668+15668^24327	102053	Hans Havermann	02/2019
3542	25080^11711+11711^25080	102041	Hans Havermann	02/2019
3543	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
3544	2^338891-18885	102017	Enzo Doria	05/2013
3545	8*10^102000+51	102001	Robert Price	08/2019
3546	2^338829-113239	101998	Enzo Doria	07/2014
3547	2^338828-113297	101998	Enzo Doria	07/2014
3548	2^338796+93	101988	Donovan Johnson	06/2008
3549	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
3550	25295^10744+10744^25295	101969	Hans Havermann	01/2019
3551	25712^9243+9243^25712	101969	Hans Havermann	01/2019
3552	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
3553	2^338682-19865	101954	Enzo Doria	06/2013
3554	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
3555	28594^3673+3673^28594	101939	Hans Havermann	02/2019
3556	2^338568+37	101920	Lelio R Paula	07/2011
3557	2^338559-1858777	101917	Enzo Doria	04/2016
3558	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
3559	24502^14419+14419^24502	101903	Hans Havermann	01/2019
3560	2^338497-17041	101898	Enzo Doria	05/2013
3561	2^338475+54615	101892	Lelio R Paula	10/2016
3562	2^338426-19797	101877	Enzo Doria	06/2013
3563	2^338368-20369	101859	Enzo Doria	06/2013
3564	2^338366+74179	101859	Enzo Doria	04/2016
3565	27088^5755+5755^27088	101853	Hans Havermann	01/2019
3566	2^338280-19745	101833	Enzo Doria	06/2013
3567	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
3568	6^130841+103	101815	Lelio R Paula	10/2016
3569	2^338122-20117	101785	Enzo Doria	06/2013
3570	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
3571	35^65917-7092	101781	Enzo Doria	03/2013
3572	2^338010-19833	101752	Enzo Doria	06/2013
3573	3^213215-76	101730	Lelio R Paula	09/2016
3574	23907^17998+17998^23907	101730	Hans Havermann	01/2019
3575	2^337930+63	101728	Lelio R Paula	07/2011
3576	2^337920+1869661	101725	Enzo Doria	05/2016
3577	24116^16509+16509^24116	101715	Hans Havermann	01/2019
3578	2^337859-19645	101706	Enzo Doria	05/2013
3579	2^337754+1869169	101675	Enzo Doria	05/2016
3580	3*10^101657-37	101658	Robert Price	07/2018
3581	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
3582	11^97605-24	101646	Lelio R Paula	10/2016
3583	8^112539-112539	101633	Robert Price	01/2014
3584	25694^9003+9003^25694	101605	Hans Havermann	12/2018
3585	2^337515-19869	101603	Enzo Doria	06/2013
3586	2^337473+719	101590	Lelio R Paula	08/2011
3587	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
3588	2^337452-108815	101584	Enzo Doria	03/2014
3589	2^337453+1185	101584	Lelio R Paula	09/2016
3590	2^337410-113561	101571	Enzo Doria	08/2014
3591	2^337387+855	101564	Lelio R Paula	09/2016
3592	2^337367-17295	101558	Lelio R Paula	09/2016
3593	2^337342-109035	101551	Enzo Doria	04/2014
3594	23703^19238+19238^23703	101548	Hans Havermann	12/2018
3595	2^337267-19	101528	Lelio R Paula	07/2011
3596	2^337183-19989	101503	Enzo Doria	06/2013
3597	2^337149+72425	101492	Enzo Doria	04/2016
3598	24041^16642+16642^24041	101483	Hans Havermann	12/2018
3599	33982^969+969^33982	101482	Hans Havermann	12/2018
3600	2^337101-20241	101478	Enzo Doria	06/2013
3601	2^337035-20001	101458	Enzo Doria	06/2013
3602	2^337017-16995	101453	Lelio R Paula	09/2016
3603	2^336979-115315	101441	Enzo Doria	06/2015
3604	2^336970-20885	101439	Enzo Doria	06/2013
3605	2^336958+79	101435	Lelio R Paula	10/2009
3606	2^336942+169	101430	Lelio R Paula	10/2009
3607	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
3608	4*10^101415-89	101416	Robert Price	11/2018
3609	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
3610	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
3611	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
3612	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
3613	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
3614	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
3615	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
3616	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
3617	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
3618	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
3619	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
3620	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
3621	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
3622	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
3623	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
3624	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
3625	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
3626	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
3627	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3628	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
3629	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3630	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
3631	24097^16150+16150^24097	101405	Hans Havermann	12/2018
3632	2^336842+94065	101400	Lelio R Paula	09/2016
3633	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
3634	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
3635	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
3636	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
3637	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
3638	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
3639	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
3640	10^101369+203811	101370	Patrick De Geest	11/2016
3641	10^101369-99	101369	Lelio R Paula	09/2016
3642	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
3643	2^336701-113563	101358	Enzo Doria	08/2014
3644	2^336644-109023	101340	Enzo Doria	04/2014
3645	2^336601-21081	101327	Enzo Doria	06/2013
3646	20^77869+63	101310	Lelio R Paula	09/2016
3647	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
3649	6^130179-137	101299	Lelio R Paula	10/2016
3648	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
3650	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
3651	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
3652	2^336369-19753	101258	Enzo Doria	05/2013
3653	23842^17653+17653^23842	101253	Hans Havermann	11/2018
3654	2^336350-344291	101252	Enzo Doria	07/2015
3655	(56*10^101222-47)/9	101223	Robert Price	02/2019
3656	2^336243-108777	101220	Enzo Doria	03/2014
3657	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
3658	23535^19954+19954^23535	101202	Hans Havermann	11/2018
3659	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
3660	2^336150-20393	101192	Enzo Doria	06/2013
3661	23996^16473+16473^23996	101186	Hans Havermann	11/2018
3662	2^336112-1865249	101180	Enzo Doria	03/2016
3663	2^336103-109015	101178	Enzo Doria	04/2014
3664	13^90809-96	101157	Lelio R Paula	10/2016
3665	26199^7258+7258^26199	101150	Hans Havermann	11/2018
3666	19^79098-30	101147	Lelio R Paula	10/2016
3667	19^79095+88	101144	Lelio R Paula	10/2016
3668	15^85976+32	101116	Lelio R Paula	10/2016
3669	2^335872-2776215	101108	Tony Prest / Never Odd Or Even	01/2019
3670	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
3671	(4^167933+17)/3	101106	Robert Price	02/2017
3673	2^335858+153	101104	Lelio R Paula	10/2009
3672	(2^335872-2776871)/5/5/479	101104	Tony Prest / Never Odd Or Even	01/2019
3674	(2^335872-2758787)/23/31/20809	101101	Tony Prest / Never Odd Or Even	01/2019
3675	(2^335872-2795083)/3/3/113/283/148367	101097	Tony Prest / Never Odd Or Even	01/2019
3676	6^129918-35	101096	Lelio R Paula	10/2016
3677	3^211885-70	101095	Lelio R Paula	09/2016
3679	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
3678	(2^335872-2794771)/3/5/5/61/232312440293	101093	Tony Prest / Never Odd Or Even	01/2019
3680	2^335818-20033	101092	Enzo Doria	06/2013
3681	2^335813-110083	101090	Enzo Doria	04/2014
3682	2^335804+2155	101088	Lelio R Paula	09/2016
3683	(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021	101087	Tony Prest / Never Odd Or Even	01/2019
3684	2^335784-16145	101082	Enzo Doria	04/2013
3685	11^97051+62	101069	Lelio R Paula	10/2016
3686	3*10^101065+11	101066	Robert Price	07/2018
3687	27820^4293+4293^27820	101064	Hans Havermann	10/2018
3688	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
3689	2^335658-94395	101044	Lelio R Paula	09/2016
3690	24514^13215+13215^24514	101024	Hans Havermann	11/2018
3691	2^335586+169	101022	Lelio R Paula	10/2009
3692	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
3693	(19*10^100997+737)/9	100998	Robert Price	07/2018
3694	47599!2+1024	100991	Robert Price	02/2015
3695	2^335468-18629	100986	Enzo Doria	05/2013
3696	2^335454-20961	100982	Enzo Doria	06/2013
3697	10^100978+61	100979	Lelio R Paula	09/2016
3698	10^100978-156437	100978	Patrick De Geest	11/2016
3699	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
3700	2^335403-1859167	100967	Enzo Doria	03/2016
3701	23599^18976+18976^23599	100962	Hans Havermann	10/2018
3702	9*2^335364-5	100956	Lelio R Paula	08/2014
3703	2^335349+72287	100951	Enzo Doria	04/2016
3704	2^335329+16095	100945	Lelio R Paula	09/2016
3705	232823#+233663	100937	Makoto Morimoto	10/2017
3706	(232823#+10141)/(10141*1674461)	100927	Makoto Morimoto	06/2019
3707	2^335237-20893	100917	Enzo Doria	06/2013
3708	2^335222-19337	100912	Enzo Doria	05/2013
3709	2^335222-109985	100912	Enzo Doria	04/2014
3710	2^335182-17237	100900	Enzo Doria	05/2013
3711	2^335043-16737	100858	Enzo Doria	05/2013
3712	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
3713	2^335038-20633	100857	Enzo Doria	06/2013
3714	2^335031+1873373	100855	Enzo Doria	06/2016
3715	23489^19650+19650^23489	100847	Hans Havermann	10/2018
3716	3^211354-8816	100842	Enzo Doria	05/2014
3717	2^334984-112757	100841	Enzo Doria	06/2014
3718	29451^2648+2648^29451	100809	Hans Havermann	09/2018
3719	25583^8716+8716^25583	100806	Hans Havermann	08/2018
3721	2^334857+48527	100803	Lelio R Paula	08/2011
3720	12^93406+29	100803	Lelio R Paula	10/2016
3722	28780^3179+3179^28780	100796	Hans Havermann	09/2018
3723	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
3724	2^334809-13	100788	Lelio R Paula	04/2011
3725	(82*10^100780-1)/9	100781	Robert Price	12/2014
3726	31395^1622+1622^31395	100780	Hans Havermann	09/2018
3727	(2^334779+47)/5	100778	Lelio R Paula	12/2013
3728	2^334751+2049	100771	Lelio R Paula	09/2016
3729	13^90443-98	100749	Lelio R Paula	10/2016
3730	(7*10^100737+71)/3	100738	Robert Price	05/2018
3731	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
3732	15^85639-28	100720	Lelio R Paula	10/2016
3733	27068^5259+5259^27068	100718	Hans Havermann	08/2018
3734	2^334562+577294575	100711	Lelio R Paula	09/2016
3735	4*3^211077-5	100710	Lelio R Paula	08/2014
3736	2^334524+145	100702	Lelio R Paula	07/2009
3737	27648^4375+4375^27648	100666	Hans Havermann	09/2018
3738	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
3739	2^334294-113111	100633	Enzo Doria	07/2014
3740	25581^8582+8582^25581	100626	Hans Havermann	08/2018
3741	6^129308-17723	100622	Enzo Doria	03/2013
3742	6^129305+95	100619	Lelio R Paula	10/2016
3743	2^334244-1167	100618	Lelio R Paula	09/2016
3744	(26*10^100566+49)/3	100567	Robert Price	08/2019
3745	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
3746	24885^10984+10984^24885	100555	Hans Havermann	07/2018
3747	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
3748	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
3749	23578^18367+18367^23578	100538	Hans Havermann	07/2018
3750	13^90251+24	100535	Lelio R Paula	10/2016

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Probable Primes Top 10000

(253476 PRPs in the top)