I believe that the number
$$2^{2^{2t+1}+2t-1}-1$$
is composite for all positive integer $t$. I tested this for many $t$'s, but so far I didn't get a proof. Any idea?
I believe that the number
$$2^{2^{2t+1}+2t-1}-1$$
is composite for all positive integer $t$. I tested this for many $t$'s, but so far I didn't get a proof. Any idea?
If your expression is composite for all large $t$, then either (a) $4\cdot 2^w+w$ is composite for all large $w$ or (b) $2^p-1$ is composite for infinitely many primes $p$. Now (a) is probably false while (b) is probably (surely!) true --- however, no one has succeeded in showing (b) unconditionally!