Technically, the parent post literally said "No prime divides the new number ... so you've just produced a new prime". It does not make the direct claim that the new prime is equal to the new number.
It is possible that the OP did not make the mistake that you are attributing to them, although best case is that the exposition was simply unclear.
It is possible that the OP did not make the mistake that you are attributing to them, although best case is that the exposition was simply unclear.