Michael Farthing wrote:OK John let us reword the standard proof slightly to deal with your sensibilities:

Consider the list of all known primes and take their product plus one. This is not divisible by any known prime and therefore is either prime itself, or divisible by some other prime which is as yet undiscovered. Hence a prime number always exists that has not yet been discovered.

No contradiction there! We have not claimed to be working with a complete set of primes.

Of course, I am of the view that deductive proof is invalid and that the only correct method of proof is by establishing a contradiction: not a widely held view but, IMHO, as reasonable as Nick's and your position (which in your case I suspect is probably purely mischievous - using that word with its gentler, tolerant and, dare I say it, affectionate* meaning).

*This does not imply any let up in our battles: a bit like Peppino and Don Camillo.

Michael, now I am doubly confused -

First, your proof that there must be an infinite number of primes seems to me to be a rehash of the one, without a contradiction, which I provided a link to, above.

Second, are you playing the part of Don Camillo or am?