Are there infinitely many primes p such that p + 2 is prime?
Well numbers go on infinately and since primes also theoretically go on infinately, so yes, but the number of primes found by using p+2 will exponetially decrease.
I do not know radio. In theory at least I think there are infinitely many primes BUT
You have taken this a step further - I am not so sure your 'yes' would stand up to close scrutiny.