A220951 Primes p such that p+6 is also prime and there is a power of two in the interval (p,p+6).

5, 7, 11, 13, 31, 61, 251, 4093

Offset: 1

Author

Brad Clardy, Feb 20 2013

Keywords

• nonn
• more

Comments

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.

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

Crossrefs

Cf. A023201, A220746, A221211.

Programs

Magma

//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.
gap:=6;
start:=Ilog2(gap)+1;
for i:= start to 1000 do
   powerof2:=2^i;
   for k:=powerof2-gap+1 to powerof2-1 by 2 do
      if (IsPrime(k) and IsPrime(k+gap)) then
         k;
      end if;
   end for;
end for;

Mathematica

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 *)