Is this language defined using twin primes regular?
If the twin prime conjecture is true, then $L = a^{*}$, which is regular. If the twin prime conjecture is not true, then there are finitely many twin primes; indeed, there is a largest pair of twin primes $\{p, p + 2\}$. In this case, $L = \{a^{n} | n &lt; p + 1\}$, a finite language. In either case, you get a regular language, so I think it's safe to conclude that $L$ is a regular language... we just won't know which one it is until the twin prime conjecture is resolved.