cp's OEIS Frontend

A213677 Numbers n such that n and n + 12 are prime and there is a power of two in the interval (n, n+12).

%I A213677 #8 Sep 08 2022 08:46:02
%S A213677 5,7,11,29,31,59,61,127,251,509,1019,1021,262139,1048571,2147483647
%N A213677 Numbers n such that n and n + 12 are prime and there is a power of two in the interval (n, n+12).
%C A213677 It is a conjecture that this is a finite sequence. A search was conducted out to 2^1500.
%o A213677 (Magma)
%o A213677 //Program finds primes separated by an even number (called gap) which
%o A213677 //have a power of two between them. Program starts with the smallest
%o A213677 //power of two above gap. Primes less than this starting point can be
%o A213677 //checked by inspection.
%o A213677 gap:=12;
%o A213677 start:=Ilog2(gap)+1;
%o A213677 for i:= start to 1000 do
%o A213677     powerof2:=2^i;
%o A213677     for k:=powerof2-gap+1 to powerof2-1 by 2 do
%o A213677         if (IsPrime(k) and IsPrime(k+gap)) then k;
%o A213677         end if;
%o A213677     end for;
%o A213677 end for;
%Y A213677 A046133, A221211.
%K A213677 nonn
%O A213677 1,1
%A A213677 _Brad Clardy_, Mar 04 2013