OFFSET
1,1
COMMENTS
It is a conjecture that this sequence is finite. A search around 2^n was done up to 2^1500.
PROG
(Magma)
//Program finds primes separated by an even number (called gap) which
//have a power of two between them. The program starts with the smallest
//power of two above gap. Primes less than this starting point can be
//checked inspection. In this example 3 and 5 also work.
gap:=8;
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;
(Magma) [n: n in PrimesUpTo(10^6) | IsPrime(n+8) and exists{t: t in [n+1..n+7 by 2] | IsOne(t/2^Valuation(t, 2))}]; // Bruno Berselli, May 16 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Brad Clardy, Mar 02 2013
STATUS
approved