Neumann's open problem on number of projective special linear groups whose order has exactly six prime factors counting multiplicities

Statement
This problem asks whether there are infinitely many primes $$p$$ for which the order of the projective special linear group $$PSL(2,p)$$ has exactly six prime factors counting multiplicities (i.e., the sum of the exponents on all the prime factors equals $$6$$). For odd $$p$$, this order is:

$$\frac{p(p+1)(p-1)}{2}$$.

Related facts

 * Prime power order implies nilpotent
 * Order has only two prime factors implies solvable
 * Classification of finite simple groups whose order has at most five prime factors counting muliplicities