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From: sttscitrans on 30 Jun 2010 16:11
On 30 June, 20:52, Archimedes Plutonium
<plutonium.archime...(a)gmail.com> wrote:

> And Euclid's IP, Direct or constructive in short-form goes like this:
>  1) Definition of prime
>  2) Given any finite set of primes
>  3) Multiply the lot and add 1 (Euclid's number) which I call W+1
>  4) Either W+1 is prime or we conduct a prime factor search

How do you know w+1 is prime ? If w+1 has no prime fcators
then a prime factor search will find no primes.

>  5) this new prime increases the set cardinality by one more prime

What new prime ?


> 1) Definition of prime
>  2) Hypothetical assumption, suppose set of primes 2,3,5,7,.. is
>  finite with P_k the last and final prime
>  3) Multiply the lot and add 1 (Euclid's number) which I call W+1
>  4) W+1 is necessarily prime

W+1 is not divisible by any prime 2, 3, 6,..pk so must be a unit.
So W+1 is not necessarily prime.

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