How to determine in polynomial time if a number is a product of two consecutive primes?
All I can figure out is that if Cramér's conjecture is true, then we can use the AKS primality test to find $p_i < \sqrt n < p_{i+1}$, then check if $p_i * p_{i+1} = n$. Is there some way to determine if a number is of this form in polynomial time that doesn't rely on any unproven assumptions?
Also, given that a number is of this form, what is the quickest way to factor it? How fast will modern general-purpose factoring algorithms such as the quadratic sieve factor a product of consecutive primes?