I apologise beforehand for the informality and lack of precision in this question but it is that way because it comes from only an intuition, nothing more than a heuristic argument.
Say one has two large, relatively coprime numbers relatively close to each other ( relative to their own size) so that both numbers have a large amount of prime factors( large relative to the usual amount for numbers of that size) in their factorisations. Then, their difference is relatively small and cannot be divisible by any prime within the factorisations of the two large numbers. Hence, it seems reasonable that this small number must have a small amount of prime factors(relative to the usual amount for numbers of that size), since there are several primes it cannot be divisible by.
Computing several such examples, I find that this is indeed mostly the case. Often, the difference of the two numbers is prime. What I am wondering is whether there are some rigorous ways to express this fact. I'm thinking maybe it would involve something about the distributions of the values of some function like the divisor function, the sum of divisors function, or the amount of prime factors function or something of the sort.
Any further loose thoughts and ideas that add to this are welcome. Thanks.