I suggest to delete this answer. It mainly consists of a reference to another question+answer from the same author, but I fail to see how it answers the specific question here.
Does this proof strategy work?
Function h(s): We have h(s) = (γ(s) / γ'(s)) * ζ(1 - s). This function aims to isolate prime power contributions from the Riemann zeta function (ζ(s)) using its derivative (γ(s) = ζ(s) / ζ(1 - s)).
Assumption: We assume a non-trivial zero (ρ) of ζ(s) exists off the ...