This short proof that $\sum 1/p \rightarrow \infty$ from this source, pdf the author takes logs of divergent series.
I have seen many comments saying that such proofs are invalid because you can't arbitrarily split and reorder divergent series.
Question: I would like advice on why what the author has done is valid, if indeed it is?
For easy reference, the following is a snapshot of the proof from the paper:
