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	3*10^101657-37	101658	Robert Price	07/2018
3502	(31*2^337677-1)/593	101650	Lelio R Paula	03/2014
3503	11^97605-24	101646	Lelio R Paula	10/2016
3504	8^112539-112539	101633	Robert Price	01/2014
3505	25694^9003+9003^25694	101605	Hans Havermann	12/2018
3506	2^337515-19869	101603	Enzo Doria	06/2013
3507	2^337473+719	101590	Lelio R Paula	08/2011
3508	(2^337485-509203)/656647157	101585	Lelio R Paula	12/2013
3509	2^337452-108815	101584	Enzo Doria	03/2014
3510	2^337453+1185	101584	Lelio R Paula	09/2016
3511	2^337410-113561	101571	Enzo Doria	08/2014
3512	2^337387+855	101564	Lelio R Paula	09/2016
3513	2^337367-17295	101558	Lelio R Paula	09/2016
3514	2^337342-109035	101551	Enzo Doria	04/2014
3515	23703^19238+19238^23703	101548	Hans Havermann	12/2018
3516	2^337267-19	101528	Lelio R Paula	07/2011
3517	2^337183-19989	101503	Enzo Doria	06/2013
3518	2^337149+72425	101492	Enzo Doria	04/2016
3519	24041^16642+16642^24041	101483	Hans Havermann	12/2018
3520	33982^969+969^33982	101482	Hans Havermann	12/2018
3521	2^337101-20241	101478	Enzo Doria	06/2013
3522	2^337035-20001	101458	Enzo Doria	06/2013
3523	2^337017-16995	101453	Lelio R Paula	09/2016
3524	2^336979-115315	101441	Enzo Doria	06/2015
3525	2^336970-20885	101439	Enzo Doria	06/2013
3526	2^336958+79	101435	Lelio R Paula	10/2009
3527	2^336942+169	101430	Lelio R Paula	10/2009
3528	(15185*2^336894-1)/7939	101416	Lelio R Paula	05/2015
3529	4*10^101415-89	101416	Robert Price	11/2018
3530	2^336871+257463	101409	Tony Prest / Never Odd Or Even	04/2016
3531	2^336871+318105	101409	Tony Prest / Never Odd Or Even	04/2016
3532	2^336871+1010813	101409	Tony Prest / Never Odd Or Even	04/2016
3533	2^336871+2302245	101409	Tony Prest / Never Odd Or Even	04/2016
3534	2^336871+389273	101409	Tony Prest / Never Odd Or Even	04/2016
3535	2^336871+1685475	101409	Tony Prest / Never Odd Or Even	04/2016
3536	2^336871+1068119	101409	Tony Prest / Never Odd Or Even	04/2016
3537	2^336871+586905	101409	Tony Prest / Never Odd Or Even	04/2016
3538	2^336871+674571	101409	Tony Prest / Never Odd Or Even	04/2016
3539	2^336871+707009	101409	Tony Prest / Never Odd Or Even	04/2016
3540	2^336871+1210299	101409	Tony Prest / Never Odd Or Even	04/2016
3541	2^336871+1921185	101409	Tony Prest / Never Odd Or Even	04/2016
3542	2^336871+2003973	101409	Tony Prest / Never Odd Or Even	04/2016
3543	2^336871+2656475	101409	Tony Prest / Never Odd Or Even	04/2016
3544	2^336871+2703023	101409	Tony Prest / Never Odd Or Even	04/2016
3545	2^336871+2704545	101409	Tony Prest / Never Odd Or Even	04/2016
3546	2^336871+2766801	101409	Tony Prest / Never Odd Or Even	04/2016
3547	2^336871+2127735	101409	Tony Prest / Never Odd Or Even	04/2016
3548	(2^336871+821089)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3549	(2^336871+119567)/5	101408	Tony Prest / Never Odd Or Even	05/2016
3550	(2^336871+398161)/3	101408	Tony Prest / Never Odd Or Even	05/2016
3551	(2^336871+625889)/7	101408	Tony Prest / Never Odd Or Even	05/2016
3552	24097^16150+16150^24097	101405	Hans Havermann	12/2018
3553	2^336842+94065	101400	Lelio R Paula	09/2016
3554	(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103	101378	Tony Prest / Never Odd Or Even	04/2016
3555	(2^336871+631971)/13/251/1601/294277/614362921/30324278867	101377	Tony Prest / Never Odd Or Even	04/2016
3556	(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879	101374	Tony Prest / Never Odd Or Even	04/2016
3557	(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489	101373	Tony Prest / Never Odd Or Even	04/2016
3558	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
3559	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
3560	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
3561	10^101369+203811	101370	Patrick De Geest	11/2016
3562	10^101369-99	101369	Lelio R Paula	09/2016
3563	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
3564	2^336701-113563	101358	Enzo Doria	08/2014
3565	2^336644-109023	101340	Enzo Doria	04/2014
3566	2^336601-21081	101327	Enzo Doria	06/2013
3567	20^77869+63	101310	Lelio R Paula	09/2016
3568	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
3570	6^130179-137	101299	Lelio R Paula	10/2016
3569	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
3571	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
3572	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
3573	2^336369-19753	101258	Enzo Doria	05/2013
3574	23842^17653+17653^23842	101253	Hans Havermann	11/2018
3575	2^336350-344291	101252	Enzo Doria	07/2015
3576	(56*10^101222-47)/9	101223	Robert Price	02/2019
3577	2^336243-108777	101220	Enzo Doria	03/2014
3578	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
3579	23535^19954+19954^23535	101202	Hans Havermann	11/2018
3580	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
3581	2^336150-20393	101192	Enzo Doria	06/2013
3582	23996^16473+16473^23996	101186	Hans Havermann	11/2018
3583	2^336112-1865249	101180	Enzo Doria	03/2016
3584	2^336103-109015	101178	Enzo Doria	04/2014
3585	13^90809-96	101157	Lelio R Paula	10/2016
3586	26199^7258+7258^26199	101150	Hans Havermann	11/2018
3587	19^79098-30	101147	Lelio R Paula	10/2016
3588	19^79095+88	101144	Lelio R Paula	10/2016
3589	15^85976+32	101116	Lelio R Paula	10/2016
3590	2^335872-2776215	101108	Tony Prest / Never Odd Or Even	01/2019
3591	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
3592	(4^167933+17)/3	101106	Robert Price	02/2017
3593	2^335858+153	101104	Lelio R Paula	10/2009
3594	(2^335872-2776871)/5/5/479	101104	Tony Prest / Never Odd Or Even	01/2019
3595	(2^335872-2758787)/23/31/20809	101101	Tony Prest / Never Odd Or Even	01/2019
3596	(2^335872-2795083)/3/3/113/283/148367	101097	Tony Prest / Never Odd Or Even	01/2019
3597	6^129918-35	101096	Lelio R Paula	10/2016
3598	3^211885-70	101095	Lelio R Paula	09/2016
3599	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
3600	(2^335872-2794771)/3/5/5/61/232312440293	101093	Tony Prest / Never Odd Or Even	01/2019
3601	2^335818-20033	101092	Enzo Doria	06/2013
3602	2^335813-110083	101090	Enzo Doria	04/2014
3603	2^335804+2155	101088	Lelio R Paula	09/2016
3604	(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021	101087	Tony Prest / Never Odd Or Even	01/2019
3605	2^335784-16145	101082	Enzo Doria	04/2013
3606	11^97051+62	101069	Lelio R Paula	10/2016
3607	3*10^101065+11	101066	Robert Price	07/2018
3608	27820^4293+4293^27820	101064	Hans Havermann	10/2018
3609	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
3610	2^335658-94395	101044	Lelio R Paula	09/2016
3611	24514^13215+13215^24514	101024	Hans Havermann	11/2018
3612	2^335586+169	101022	Lelio R Paula	10/2009
3613	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
3614	(19*10^100997+737)/9	100998	Robert Price	07/2018
3615	47599!2+1024	100991	Robert Price	02/2015
3616	2^335468-18629	100986	Enzo Doria	05/2013
3617	2^335454-20961	100982	Enzo Doria	06/2013
3618	10^100978+61	100979	Lelio R Paula	09/2016
3619	10^100978-156437	100978	Patrick De Geest	11/2016
3620	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
3621	2^335403-1859167	100967	Enzo Doria	03/2016
3622	23599^18976+18976^23599	100962	Hans Havermann	10/2018
3623	9*2^335364-5	100956	Lelio R Paula	08/2014
3624	2^335349+72287	100951	Enzo Doria	04/2016
3625	2^335329+16095	100945	Lelio R Paula	09/2016
3626	232823#+233663	100937	Makoto Morimoto	10/2017
3627	(232823#+10141)/(10141*1674461)	100927	Makoto Morimoto	06/2019
3628	2^335237-20893	100917	Enzo Doria	06/2013
3629	2^335222-19337	100912	Enzo Doria	05/2013
3630	2^335222-109985	100912	Enzo Doria	04/2014
3631	2^335182-17237	100900	Enzo Doria	05/2013
3632	2^335043-16737	100858	Enzo Doria	05/2013
3633	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
3634	2^335038-20633	100857	Enzo Doria	06/2013
3635	2^335031+1873373	100855	Enzo Doria	06/2016
3636	23489^19650+19650^23489	100847	Hans Havermann	10/2018
3637	3^211354-8816	100842	Enzo Doria	05/2014
3638	2^334984-112757	100841	Enzo Doria	06/2014
3639	29451^2648+2648^29451	100809	Hans Havermann	09/2018
3640	25583^8716+8716^25583	100806	Hans Havermann	08/2018
3642	2^334857+48527	100803	Lelio R Paula	08/2011
3641	12^93406+29	100803	Lelio R Paula	10/2016
3643	28780^3179+3179^28780	100796	Hans Havermann	09/2018
3644	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
3645	2^334809-13	100788	Lelio R Paula	04/2011
3646	(82*10^100780-1)/9	100781	Robert Price	12/2014
3647	31395^1622+1622^31395	100780	Hans Havermann	09/2018
3648	(2^334779+47)/5	100778	Lelio R Paula	12/2013
3649	2^334751+2049	100771	Lelio R Paula	09/2016
3650	13^90443-98	100749	Lelio R Paula	10/2016
3651	(7*10^100737+71)/3	100738	Robert Price	05/2018
3652	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
3653	15^85639-28	100720	Lelio R Paula	10/2016
3654	27068^5259+5259^27068	100718	Hans Havermann	08/2018
3655	2^334562+577294575	100711	Lelio R Paula	09/2016
3656	4*3^211077-5	100710	Lelio R Paula	08/2014
3657	2^334524+145	100702	Lelio R Paula	07/2009
3658	27648^4375+4375^27648	100666	Hans Havermann	09/2018
3659	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
3660	2^334294-113111	100633	Enzo Doria	07/2014
3661	25581^8582+8582^25581	100626	Hans Havermann	08/2018
3662	6^129308-17723	100622	Enzo Doria	03/2013
3663	6^129305+95	100619	Lelio R Paula	10/2016
3664	2^334244-1167	100618	Lelio R Paula	09/2016
3665	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
3666	24885^10984+10984^24885	100555	Hans Havermann	07/2018
3667	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
3668	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
3669	23578^18367+18367^23578	100538	Hans Havermann	07/2018
3670	13^90251+24	100535	Lelio R Paula	10/2016
3671	2^333963+789	100533	Lelio R Paula	08/2011
3672	2^333919-1840087	100520	Enzo Doria	06/2015
3673	2^333911+72623	100518	Enzo Doria	04/2016
3674	24605^12168+12168^24605	100517	Hans Havermann	08/2018
3675	18^80064-67	100503	Lelio R Paula	10/2016
3676	5^143742-48	100472	Lelio R Paula	10/2016
3677	24095^14784+14784^24095	100472	Hans Havermann	08/2018
3678	2^333757-112123	100471	Enzo Doria	06/2014
3679	27358^4693+4693^27358	100444	Hans Havermann	07/2018
3680	2^333603-108861	100425	Enzo Doria	03/2014
3681	9*7^118818-2	100414	Lelio R Paula	11/2014
3682	2^333546-17097	100408	Enzo Doria	05/2013
3683	17^81597+72	100401	Lelio R Paula	10/2016
3684	p(20559)#/2+8	100384	Robert Price	01/2017
3685	11^96390-24	100380	Lelio R Paula	10/2016
3687	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
3686	23565^18136+18136^23565	100353	Hans Havermann	07/2018
3688	2^333354+763	100350	Lelio R Paula	08/2011
3689	2^333289-109483	100330	Enzo Doria	04/2014
3690	2^333240-2790209	100316	Enzo Doria	03/2016
3691	23601^17798+17798^23601	100314	Hans Havermann	05/2018
3693	(2^333227-2^166614+1)/5	100311		11/2006
3692	2^333225+719	100311	Lelio R Paula	08/2011
3694	2^333221-2785333	100310	Enzo Doria	10/2015
3695	76^53332-75	100308	Norbert Schneider	02/2015
3696	6^128892-17573	100298	Enzo Doria	03/2013
3697	(47*10^100283-119)/9	100284	Robert Price	05/2019
3698	2^333105-113215	100275	Enzo Doria	07/2014
3699	(31*2^333102+1)/2375	100272	Lelio R Paula	11/2013
3700	4*10^100257-83	100258	Robert Price	10/2018
3701	17^81476-74	100253	Lelio R Paula	10/2016
3702	23392^19207+19207^23392	100199	Hans Havermann	06/2018
3703	17^81417-16	100180	Theodore Burton	11/2005
3704	2^332739-113215	100165	Enzo Doria	07/2014
3705	2^332730-1865621	100162	Enzo Doria	03/2016
3706	91^51127-2	100160	Lelio R Paula	09/2013
3707	15^85159-32	100155	Lelio R Paula	10/2016
3708	6^128661+97	100118	Lelio R Paula	10/2016
3709	19^78285+40	100108	Lelio R Paula	07/2016
3710	6^128640+5	100102	Lelio R Paula	11/2014
3711	(14*10^100075+61)/3	100076	Robert Price	12/2018
3712	28562^3189+3189^28562	100072	Hans Havermann	05/2018
3713	6^128565-127	100044	Lelio R Paula	08/2016
3714	2^332309-133	100035	Lelio R Paula	02/2011
3715	2^332307+731	100035	Lelio R Paula	07/2011
3716	2^332301+12927	100033	Lelio R Paula	04/2013
3717	23406^18781+18781^23406	100031	Hans Havermann	04/2018
3718	2^332277-4573	100026	Yves Minet	03/2019
3719	12^92684-13	100023	Lelio R Paula	07/2016
3720	78557*2^332193+55669	100005	Jorge Menendez	04/2019
3721	78557*2^332192+72689	100005	Jorge Menendez	04/2019
3722	10^100003+45799	100004	Stefano Morozzi	04/2019
3723	10^100003+155461	100004	Stefano Morozzi	04/2019
3724	10^100003+211389	100004	Stefano Morozzi	04/2019
3725	10^100003+381027	100004	Stefano Morozzi	04/2019
3726	10^100003+540703	100004	Stefano Morozzi	04/2019
3727	10^100003+823977	100004	Stefano Morozzi	04/2019
3738	10^100002+236023	100003	Stefano Morozzi	05/2018
3739	10^100002+433741	100003	Stefano Morozzi	05/2018
3728	2^332202+104659	100003	Stefano Morozzi	04/2019
3729	2^332202+857539	100003	Stefano Morozzi	04/2019
3730	2^332202+181773	100003	Stefano Morozzi	04/2019
3731	2^332202+687543	100003	Stefano Morozzi	04/2019
3732	2^332202+941595	100003	Stefano Morozzi	04/2019
3733	2^332202+445813	100003	Stefano Morozzi	04/2019
3734	2^332202+1599727	100003	Stefano Morozzi	04/2019
3735	2^332202+1389567	100003	Stefano Morozzi	04/2019
3736	2^332202+1206315	100003	Stefano Morozzi	04/2019
3737	2^332202+1958647	100003	Stefano Morozzi	04/2019
3740	(10^100002-1)/9-10^33441	100002	Akihiko Yoshida	03/2018
3741	(10^100002-1)/9-10^44692	100002	Akihiko Yoshida	03/2018
3742	10^100002-249519	100002	Patrick De Geest	07/2018
3743	10^100001+314199	100002	Patrick De Geest	07/2018
3744	10^100000+11187931	100001	Robert Price	03/2018
3745	10^100000+11264721	100001	Robert Price	04/2018
3746	10^100000+11477661	100001	Robert Price	05/2018
3747	10^100000+11644653	100001	Robert Price	07/2018
3748	10^100001-431439	100001	Patrick De Geest	07/2018
3749	10^100000+11769399	100001	Robert Price	08/2018
3750	10^100000+11848159	100001	Robert Price	08/2018

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