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Number of prime pairs below 10^n having a difference of 54.
2

%I #16 Aug 18 2018 06:56:50

%S 0,0,0,0,4,140,2403,33593,410754,4627165,49484726,511589763,

%T 5167085638,51359117940,504751212449,4920758221226,47694473239363,

%U 460356869024451

%N Number of prime pairs below 10^n having a difference of 54.

%C The primes must be consecutive, i.e., there must be no other primes between p and (p+54). - _Harvey P. Dale_, Aug 08 2011

%H Siegfried "Zig" Herzog, <a href="http://zigherzog.net/primes/index.html#compare">Frequency of Occurrence of Prime Gaps</a>

%H T. Oliveira e Silva, S. Herzog, and S. Pardi, <a href="http://dx.doi.org/10.1090/S0025-5718-2013-02787-1">Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4.10^18</a>, Math. Comp., 83 (2014), 2033-2060.

%e a(6) = 140 because there are 140 prime gaps of 54 below 10^6.

%t Table[Count[Partition[Prime[Range[PrimePi[10^i]]],2,1],_?(Last[#] - First[#] == 54&)],{i,9}] (* _Harvey P. Dale_, Aug 08 2011 *)

%Y Cf. A007508, A093980, A093982.

%K nonn,more

%O 1,5

%A _Enoch Haga_, Apr 24 2004

%E a(10)-a(13) from _Washington Bomfim_, Jun 22 2012

%E a(14)-a(18) from S. Herzog's website added by _Giovanni Resta_, Aug 14 2018