There is much to know about the Fermat numbers. Now I propose the numbers of the form $f = 2^{2^n} +2^j +1 $. Of course if $j$ is even, then $ 3  f$. Also, If $ n = 1, j = 1 $, then $ f = $ 7. If $ n = 2, j = 1 $, then $ f = 19 $. If $ n = 4, j = 1 $, then $ f = $ 65539, i.e. they are twin Fermat primes. The question is, we can say that $ f = 2^{2^n} +2^j +1 $ with $ n> 4 $ and $ 1 \leq j <2^n$ is composite? I have found it is true up to n = 15. Some one know anything else?
