Extension of Corollary 12 to primes greater than 23

Let $p$ be a prime. Corollary 12 gives the asymptotic formula for $a_p(n)$ stated earlier in the paper.

Extension conjecture. Corollary 12 also holds for primes $p>23$.

The conjecture is motivated by numerical experiments, since the condition used in Theorem 21 fails when $p>23$.