Body: I am solving this problem:1474B - Different Divisors

We need to find the smallest integer a such that:

a has at least 4 divisors the difference between any two divisors of a is at least d

My idea is to construct a as:

a = p⋅q

where:

p is the smallest prime such that p≥d+1 q is the smallest prime such that q≥p+d

Then I output a=p⋅q. 373450651

This works for all samples I tested, but I am not fully sure about correctness for all d. Can someone confirm if this construction is always optimal, or provide a counterexample if it fails?