[seqfan] Problem

[Tomasz Ordowski]

Dear readers!

Are there infinitely many primes p = k2^n+1 with k odd such that q = k+2^n
is prime?

It has to be proved that there are infinitely many primes p = (q-2^n)2^n+1
for n > 0, where q runs over all odd primes.
By the dual Sierpinski conjecture, for every odd prime q, there exists n >
0 such that it is a prime p, which ends the conditional proof.
Can you prove it unconditionally?

Best regards,

Thomas
__________
Most primes seem to have this property, but it is the illusory "law of
small numbers", I think.