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Source. Conjecture 1, PDF p. 1 of arXiv:2601.10296v2.

Statement

Let $a,b\geq2$ be integers, neither of which is a power of an integer; that is, neither can be written as $A^k$ with integers $A$ and $k\geq2$. Then, as $m,n$ range over the positive integers,

$$|a^m-b^n|$$

takes infinitely many distinct prime values, unless there is a nonzero integer $Q$ such that

$$\gcd(a^m-b^n,Q)>1$$

for every pair of positive integers $m,n$.

This asserts infinitely many prime values of the displayed expression, not merely infinitely many prime divisors among its values.

Proof scope. This is a conjecture, not a proved result in the source. No exact numbered Erdős-problem relationship is assigned here.