Proof of no prime-representing polynomial in 2 variables

I asked the same question at MathOverflow (linking here) where I noted that, at least as of 1982, the problem was still open because even universal Diophantine equations were not known to be impossible with two variables.

On further searching I found a FOM posting (see link above) which shows that the universal Diophantine equation problem is still open, so it looks like Ribenboim's book is in error (probably a typo, as Alon suggests).

Given all the evidence so far, I'm inclined to declare Ribenboim's parenthetic remark a typo. He probably meant either "it cannot be 1" or "it must be at least 2". It would be confusing and unusual for him to mention this off-hand with no reference as if it's a simple observation. That it certainly isn't.