Re: G.H.Hardy gave an invalid proof of Infinitude of Primes in "AMathematician's Apology"

sttscitrans_at_tesco.net
Date: 03/29/05 

Date: 29 Mar 2005 15:32:02 -0800

Archimedes Plutonium wrote:
> Tue, 29 Mar 2005 10:44:35 -0500 Arthur Fischer wrote:

> In the *indirect method* yes of course 510511 is necessarily prime
because
> your total universe space of primes is your assumption that
2,3,5,7,11,13,17
> were all the primes that existed. In that restricted space 510511 is
> necessarily prime and larger than 17 and hence the proof.

If 2,3,5,7,11,13,17 are all the primes that exist
and GCD(51051, p) =1, p in PRIME ={2,3,5,7,11,13,17)
then you have a contradiction. 51051 is an integer >
1 that is not divisible by any prime, but it is a theorem
that every integer >1 is divisible by at least one prime.
You are not following through on your own logic.
If there is no point looking for a prime greater
than the last prime on your list, then it does
not matter whether this prime is W+1 or a divisor of W+1

GCD(x, p) =1, for every prime p => x =1
Are you saying this statement is false ?

Under the assumption that 2,3,5,7,11,13,17 are all the primes that
exist, then 51051 can be anything a unit,
a composite, a prime, a non-integer. It is false to claim that
it is necessarily prime.