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Source. Conjecture 2, PDF p. 2 of arXiv:2601.10296v2.

Statement

Let $a,b\geq2$ be integers. Choose $k$ and $\ell$ maximal such that

$$a=A^k,\qquad b=B^{\ell}$$

for integers $A,B$. 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 all positive $m,n$ satisfying

$$\gcd(m,\ell)=\gcd(n,k)=1.$$

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