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%I #24 Sep 08 2022 08:46:04
%S 5,7,11,13,31,61,251,4093
%N Primes p such that p+6 is also prime and there is a power of two in the interval (p,p+6).
%C A search for sexy primes bracketing a power of two was conducted up to 2^1500. It is conjectured that this is a finite sequence.
%C On the basis of existing work about primes of the form 2^n+k and 2^n-k, plus a few additional tests, we have a(9) > 2^750740. - _Giovanni Resta_, Feb 21 2013
%t pptQ[n_]:=AllTrue[{n,n+6},PrimeQ]&&Count[Log[2,#]&/@Range[n,n+6], _?IntegerQ] > 0; Select[Range[4100],pptQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Nov 01 2015 *)
%o (Magma)
%o //Program finds primes separated by an even number (called gap) which have a power of two between them. Program starts with the smallest power of two above gap. Primes less than this starting point can be checked by inspection.
%o gap:=6;
%o start:=Ilog2(gap)+1;
%o for i:= start to 1000 do
%o powerof2:=2^i;
%o for k:=powerof2-gap+1 to powerof2-1 by 2 do
%o if (IsPrime(k) and IsPrime(k+gap)) then
%o k;
%o end if;
%o end for;
%o end for;
%Y Cf. A023201, A220746, A221211.
%K nonn,more
%O 1,1
%A _Brad Clardy_, Feb 20 2013
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