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	(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757	101373	Tony Prest / Never Odd Or Even	04/2016
3502	(2^336871+272895)/19/661/977572033/95853078653/520779768241	101373	Tony Prest / Never Odd Or Even	04/2016
3503	(2^336871+1023429)/2311/415873/991889/3630648341/207732189179	101373	Tony Prest / Never Odd Or Even	04/2016
3504	10^101369+203811	101370	Patrick De Geest	11/2016
3505	10^101369-99	101369	Lelio R Paula	09/2016
3506	(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917	101363	Tony Prest / Never Odd Or Even	04/2016
3507	2^336701-113563	101358	Enzo Doria	08/2014
3508	2^336644-109023	101340	Enzo Doria	04/2014
3509	2^336601-21081	101327	Enzo Doria	06/2013
3510	20^77869+63	101310	Lelio R Paula	09/2016
3511	(13*2^336523-1)/19	101304	Lelio R Paula	03/2014
3513	6^130179-137	101299	Lelio R Paula	10/2016
3512	(2^336506+lucasV(1,2,336506)+1)/2	101299	Mike Oakes	11/2016
3514	(24737*2^336485+1)/7285	101293	Lelio R Paula	07/2014
3515	(2^336448+9)/497405	101276	Lelio R Paula	12/2013
3516	2^336369-19753	101258	Enzo Doria	05/2013
3517	23842^17653+17653^23842	101253	Hans Havermann	11/2018
3518	2^336350-344291	101252	Enzo Doria	07/2015
3519	(56*10^101222-47)/9	101223	Robert Price	02/2019
3520	2^336243-108777	101220	Enzo Doria	03/2014
3521	(31*2^336189-1)/19	101204	Lelio R Paula	03/2014
3522	23535^19954+19954^23535	101202	Hans Havermann	11/2018
3523	(78557*2^336178+1)/1268757	101199	Lelio R Paula	07/2014
3524	2^336150-20393	101192	Enzo Doria	06/2013
3525	23996^16473+16473^23996	101186	Hans Havermann	11/2018
3526	2^336112-1865249	101180	Enzo Doria	03/2016
3527	2^336103-109015	101178	Enzo Doria	04/2014
3528	13^90809-96	101157	Lelio R Paula	10/2016
3529	26199^7258+7258^26199	101150	Hans Havermann	11/2018
3530	19^79098-30	101147	Lelio R Paula	10/2016
3531	19^79095+88	101144	Lelio R Paula	10/2016
3532	15^85976+32	101116	Lelio R Paula	10/2016
3533	2^335872-2776215	101108	Tony Prest / Never Odd Or Even	01/2019
3534	(3^211950+7)/28854513015920697088	101107	Lelio R Paula	11/2013
3535	(4^167933+17)/3	101106	Robert Price	02/2017
3537	2^335858+153	101104	Lelio R Paula	10/2009
3536	(2^335872-2776871)/5/5/479	101104	Tony Prest / Never Odd Or Even	01/2019
3538	(2^335872-2758787)/23/31/20809	101101	Tony Prest / Never Odd Or Even	01/2019
3539	(2^335872-2795083)/3/3/113/283/148367	101097	Tony Prest / Never Odd Or Even	01/2019
3540	6^129918-35	101096	Lelio R Paula	10/2016
3541	3^211885-70	101095	Lelio R Paula	09/2016
3543	(29*2^335835-1)/550599	101093	Lelio R Paula	03/2014
3542	(2^335872-2794771)/3/5/5/61/232312440293	101093	Tony Prest / Never Odd Or Even	01/2019
3544	2^335818-20033	101092	Enzo Doria	06/2013
3545	2^335813-110083	101090	Enzo Doria	04/2014
3546	2^335804+2155	101088	Lelio R Paula	09/2016
3547	(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021	101087	Tony Prest / Never Odd Or Even	01/2019
3548	2^335784-16145	101082	Enzo Doria	04/2013
3549	11^97051+62	101069	Lelio R Paula	10/2016
3550	3*10^101065+11	101066	Robert Price	07/2018
3551	27820^4293+4293^27820	101064	Hans Havermann	10/2018
3552	(2^335691-3)/26515	101049	Lelio R Paula	12/2013
3553	2^335658-94395	101044	Lelio R Paula	09/2016
3554	24514^13215+13215^24514	101024	Hans Havermann	11/2018
3555	2^335586+169	101022	Lelio R Paula	10/2009
3556	(56^57787-1)/55	101021	Paul Bourdelais	08/2017
3557	(19*10^100997+737)/9	100998	Robert Price	07/2018
3558	47599!2+1024	100991	Robert Price	02/2015
3559	2^335468-18629	100986	Enzo Doria	05/2013
3560	2^335454-20961	100982	Enzo Doria	06/2013
3561	10^100978+61	100979	Lelio R Paula	09/2016
3562	10^100978-156437	100978	Patrick De Geest	11/2016
3563	(15*2^335417+1)/481	100970	Lelio R Paula	12/2013
3564	2^335403-1859167	100967	Enzo Doria	03/2016
3565	23599^18976+18976^23599	100962	Hans Havermann	10/2018
3566	9*2^335364-5	100956	Lelio R Paula	08/2014
3567	2^335349+72287	100951	Enzo Doria	04/2016
3568	2^335329+16095	100945	Lelio R Paula	09/2016
3569	232823#+233663	100937	Makoto Morimoto	10/2017
3570	2^335237-20893	100917	Enzo Doria	06/2013
3571	2^335222-19337	100912	Enzo Doria	05/2013
3572	2^335222-109985	100912	Enzo Doria	04/2014
3573	2^335182-17237	100900	Enzo Doria	05/2013
3574	2^335043-16737	100858	Enzo Doria	05/2013
3575	(21181*2^335049+1)/1343811	100858	Lelio R Paula	07/2014
3576	2^335038-20633	100857	Enzo Doria	06/2013
3577	2^335031+1873373	100855	Enzo Doria	06/2016
3578	23489^19650+19650^23489	100847	Hans Havermann	10/2018
3579	3^211354-8816	100842	Enzo Doria	05/2014
3580	2^334984-112757	100841	Enzo Doria	06/2014
3581	29451^2648+2648^29451	100809	Hans Havermann	09/2018
3582	25583^8716+8716^25583	100806	Hans Havermann	08/2018
3584	2^334857+48527	100803	Lelio R Paula	08/2011
3583	12^93406+29	100803	Lelio R Paula	10/2016
3585	28780^3179+3179^28780	100796	Hans Havermann	09/2018
3586	(5*2^334825+1)/47	100792	Lelio R Paula	12/2013
3587	2^334809-13	100788	Lelio R Paula	04/2011
3588	(82*10^100780-1)/9	100781	Robert Price	12/2014
3589	31395^1622+1622^31395	100780	Hans Havermann	09/2018
3590	(2^334779+47)/5	100778	Lelio R Paula	12/2013
3591	2^334751+2049	100771	Lelio R Paula	09/2016
3592	13^90443-98	100749	Lelio R Paula	10/2016
3593	(7*10^100737+71)/3	100738	Robert Price	05/2018
3594	(24737*2^334628+1)/3	100737	Lelio R Paula	07/2014
3595	15^85639-28	100720	Lelio R Paula	10/2016
3596	27068^5259+5259^27068	100718	Hans Havermann	08/2018
3597	2^334562+577294575	100711	Lelio R Paula	09/2016
3598	4*3^211077-5	100710	Lelio R Paula	08/2014
3599	2^334524+145	100702	Lelio R Paula	07/2009
3600	27648^4375+4375^27648	100666	Hans Havermann	09/2018
3601	(1017*2^334391-1)/3535	100662	Lelio R Paula	05/2015
3602	2^334294-113111	100633	Enzo Doria	07/2014
3603	25581^8582+8582^25581	100626	Hans Havermann	08/2018
3604	6^129308-17723	100622	Enzo Doria	03/2013
3605	6^129305+95	100619	Lelio R Paula	10/2016
3606	2^334244-1167	100618	Lelio R Paula	09/2016
3607	(21*2^334050+1)/935	100558	Lelio R Paula	12/2013
3608	24885^10984+10984^24885	100555	Hans Havermann	07/2018
3609	(78557*2^334018+1)/4326021	100548	Lelio R Paula	07/2014
3610	(35*10^100542+1)/9	100543	Serge Batalov	11/2010
3611	23578^18367+18367^23578	100538	Hans Havermann	07/2018
3612	13^90251+24	100535	Lelio R Paula	10/2016
3613	2^333963+789	100533	Lelio R Paula	08/2011
3614	2^333919-1840087	100520	Enzo Doria	06/2015
3615	2^333911+72623	100518	Enzo Doria	04/2016
3616	24605^12168+12168^24605	100517	Hans Havermann	08/2018
3617	18^80064-67	100503	Lelio R Paula	10/2016
3618	5^143742-48	100472	Lelio R Paula	10/2016
3619	24095^14784+14784^24095	100472	Hans Havermann	08/2018
3620	2^333757-112123	100471	Enzo Doria	06/2014
3621	27358^4693+4693^27358	100444	Hans Havermann	07/2018
3622	2^333603-108861	100425	Enzo Doria	03/2014
3623	9*7^118818-2	100414	Lelio R Paula	11/2014
3624	2^333546-17097	100408	Enzo Doria	05/2013
3625	17^81597+72	100401	Lelio R Paula	10/2016
3626	p(20559)#/2+8	100384	Robert Price	01/2017
3627	11^96390-24	100380	Lelio R Paula	10/2016
3628	4832563059*2^333333+30029	100353	Donovan Johnson	01/2008
3629	23565^18136+18136^23565	100353	Hans Havermann	07/2018
3630	2^333354+763	100350	Lelio R Paula	08/2011
3631	2^333289-109483	100330	Enzo Doria	04/2014
3632	2^333240-2790209	100316	Enzo Doria	03/2016
3633	23601^17798+17798^23601	100314	Hans Havermann	05/2018
3635	(2^333227-2^166614+1)/5	100311		11/2006
3634	2^333225+719	100311	Lelio R Paula	08/2011
3636	2^333221-2785333	100310	Enzo Doria	10/2015
3637	76^53332-75	100308	Norbert Schneider	02/2015
3638	6^128892-17573	100298	Enzo Doria	03/2013
3639	2^333105-113215	100275	Enzo Doria	07/2014
3640	(31*2^333102+1)/2375	100272	Lelio R Paula	11/2013
3641	4*10^100257-83	100258	Robert Price	10/2018
3642	17^81476-74	100253	Lelio R Paula	10/2016
3643	23392^19207+19207^23392	100199	Hans Havermann	06/2018
3644	17^81417-16	100180	Theodore Burton	11/2005
3645	2^332739-113215	100165	Enzo Doria	07/2014
3646	2^332730-1865621	100162	Enzo Doria	03/2016
3647	91^51127-2	100160	Lelio R Paula	09/2013
3648	15^85159-32	100155	Lelio R Paula	10/2016
3649	6^128661+97	100118	Lelio R Paula	10/2016
3650	19^78285+40	100108	Lelio R Paula	07/2016
3651	6^128640+5	100102	Lelio R Paula	11/2014
3652	(14*10^100075+61)/3	100076	Robert Price	12/2018
3653	28562^3189+3189^28562	100072	Hans Havermann	05/2018
3654	6^128565-127	100044	Lelio R Paula	08/2016
3655	2^332309-133	100035	Lelio R Paula	02/2011
3656	2^332307+731	100035	Lelio R Paula	07/2011
3657	2^332301+12927	100033	Lelio R Paula	04/2013
3658	23406^18781+18781^23406	100031	Hans Havermann	04/2018
3659	2^332277-4573	100026	Yves Minet	03/2019
3660	12^92684-13	100023	Lelio R Paula	07/2016
3661	78557*2^332193+55669	100005	Jorge Menendez	04/2019
3662	10^100002+236023	100003	Stefano Morozzi	05/2018
3663	10^100002+433741	100003	Stefano Morozzi	05/2018
3664	(10^100002-1)/9-10^33441	100002	Akihiko Yoshida	03/2018
3665	(10^100002-1)/9-10^44692	100002	Akihiko Yoshida	03/2018
3666	10^100002-249519	100002	Patrick De Geest	07/2018
3667	10^100001+314199	100002	Patrick De Geest	07/2018
3720	25206!+p(4114)	100001	Henri Lifchitz	09/2005
3721	25206!-p(5447)	100001	Henri Lifchitz	10/2005
3722	25206!-p(12402)	100001	Henri Lifchitz	04/2006
3723	25206!-p(16290)	100001	Henri Lifchitz	09/2006
3724	25206!-p(19647)	100001	Henri Lifchitz	02/2007
3725	2^332194+11473	100001	Henri Lifchitz	03/2007
3719	10^100000+342909	100001	Milton L. Brown	12/2007
3684	10^100000+346579	100001	Robert Price	04/2012
3685	10^100000+829767	100001	Robert Price	05/2012
3686	10^100000+871899	100001	Robert Price	05/2012
3687	10^100000+1475997	100001	Robert Price	07/2012
3696	10^100000+1751769	100001	Robert Price	08/2012
3697	10^100000+2155489	100001	Robert Price	10/2012
3698	10^100000+2483527	100001	Robert Price	12/2012
3699	10^100000+2503087	100001	Robert Price	12/2012
3700	10^100000+2686179	100001	Robert Price	12/2012
3701	10^100000+2688933	100001	Robert Price	12/2012
3702	10^100000+3667159	100001	Robert Price	08/2013
3688	10^100000+3938473	100001	Robert Price	05/2015
3689	10^100000+3979761	100001	Robert Price	05/2015
3690	10^100000+4293973	100001	Robert Price	09/2015
3716	10^100000+4858267	100001	Robert Price	12/2015
3717	10^100000+5113299	100001	Robert Price	02/2016
3718	10^100000+5169411	100001	Robert Price	02/2016
3676	10^100000+5354043	100001	Robert Price	05/2016
3677	10^100000+5717979	100001	Robert Price	05/2016
3678	10^100000+6080631	100001	Robert Price	07/2016
3679	10^100000+6308469	100001	Robert Price	07/2016
3680	10^100000+6512023	100001	Robert Price	08/2016
3681	10^100000+6596557	100001	Robert Price	08/2016
3682	10^100000+7115409	100001	Robert Price	10/2016
3683	10^100000+7235803	100001	Robert Price	10/2016
3703	10^100000+7867333	100001	Robert Price	12/2016
3704	10^100000+8743093	100001	Robert Price	02/2017
3705	10^100000+8955391	100001	Robert Price	03/2017
3706	10^100000+9180019	100001	Robert Price	03/2017
3707	10^100000+9225987	100001	Robert Price	04/2017
3708	10^100000+9265587	100001	Robert Price	04/2017
3709	10^100000+9287049	100001	Robert Price	04/2017
3710	10^100000+9425053	100001	Robert Price	05/2017
3711	10^100000+9450769	100001	Robert Price	05/2017
3712	10^100000+9528747	100001	Robert Smith	05/2017
3713	10^100000+9548071	100001	Robert Price	06/2017
3714	10^100000+10064287	100001	Robert Price	08/2017
3715	10^100000+10229569	100001	Robert Price	10/2017
3668	10^100000+11187931	100001	Robert Price	03/2018
3669	10^100000+11264721	100001	Robert Price	04/2018
3670	10^100000+11477661	100001	Robert Price	05/2018
3671	10^100000+11644653	100001	Robert Price	07/2018
3672	10^100001-431439	100001	Patrick De Geest	07/2018
3673	10^100000+11769399	100001	Robert Price	08/2018
3674	10^100000+11848159	100001	Robert Price	08/2018
3675	10^100000+11863467	100001	Robert Price	08/2018
3691	10^100000+11992051	100001	Robert Price	09/2018
3692	2^332196-1-2*29696	100001	Matt Stath	11/2018
3693	10^100000+12363957	100001	Robert Price	11/2018
3694	2^332196+1+2*17152	100001	Matt Stath	12/2018
3695	10^100000+12778033	100001	Robert Price	02/2019
3726	10^99999+309403	100000	Daniel Heuer	01/2004
3727	10^100000-260199	100000	Patrick De Geest	01/2010
3728	10^99999-59511	99999	Patrick De Geest	07/2009
3729	2^332141-113073	99985	Enzo Doria	07/2014
3731	(3^209561+2)/728101255	99978	Lelio R Paula	09/2013
3730	23827^15702+15702^23827	99978	Hans Havermann	04/2018
3732	2^332085+1865897	99968	Enzo Doria	03/2016
3733	(9787*2^332070-1)/936402369	99959	Lelio R Paula	05/2015
3734	2^332023+191	99949	Lelio R Paula	02/2011
3735	2^331938+71149	99924	Enzo Doria	04/2016
3736	2^331932-78795	99922	Lelio R Paula	09/2016
3737	2^331921+771	99919	Lelio R Paula	01/2013
3738	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
3739	2^331860-114989	99900	Enzo Doria	05/2015
3740	2^331746-11655	99866	Lelio R Paula	09/2016
3741	11^95891-28	99861	Lelio R Paula	08/2016
3742	(2^331694-5)/11	99849	Lelio R Paula	10/2013
3743	(3^209246+7)/64	99834	Lelio R Paula	09/2013
3744	25062^9617+9617^25062	99823	Hans Havermann	04/2018
3745	15^84866-52	99811	Lelio R Paula	08/2016
3746	13^89600+30	99810	Lelio R Paula	08/2016
3747	22950^22309+22309^22950	99798	Hans Havermann	03/2018
3748	5^142772-38	99794	Lelio R Paula	08/2016
3749	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
3750	2^331416-331416+1	99767	Robert Price	10/2014

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PRP Records

Probable Primes Top 10000

(252675 PRPs in the top)