The simultaneous-primes conjecture for $9q^2-2$ and $9q^2+2$

Let $q$ be a prime satisfying $q>3$ and $q\equiv 3\pmod 4$. Simultaneous-primes conjecture. There are infinitely many numbers $3q$ such that both $9q^2-2$ and $9q^2+2$ are prime. This is an infinitude assertion of prime values in a quadratic pattern; the source presents it without a proof, and it is used to motivate the existence of infinitely many examples rather than established in the paper.