Problem 1055

Erdős Problem #1055: declared status 'open'. Formalized: yes. A prime $p$ is in class $1$ if the only prime divisors of $p+1$ are $2$ or $3$. In general, a prime $p$ is in class $r$ if every prime factor of $p+1$ is in some class $\leq r-1$, with equality for at least one prime factor. Are there infinitely many primes in each class? If $p_r$ is the least prime in class $r$, then how does $p_r^{1/r}$ behave? Prize: no. OEIS: A005113. Tags: number theory, primes.