Let
$\qquad L = \{a^n \mid \exists_{p \geq n}\ p\,,\ p+2 \text{ are prime}\}.$
Is $L$ regular?
This question looked suspicious at the first glance and I've realized that it is connected with the twin prime conjecture. My problem is that the conjecture has not been resolved yet, so I am not sure how can I proceed with deciding that the language is regular.