On Sat, Sep 29, 2012 at 6:54 PM, Stephen P. King <stephe...@charter.net>wrote:

>  On 9/29/2012 10:11 AM, Bruno Marchal wrote:
> Indeed. I think 17 is intrinsically a prime number in all possible
> realities.
>     It is not a reality in a world that only has 16 objects in it. I can
> come up with several other counter-examples in terms of finite field, but
> that is overly belaboring a point.
This can clearly be shown to be false.  For me to be responding to this
post (using a a secure connection to my mail server) requires the use of
prime numbers of 153 decimal digits in length.

There are on the order of 10^90 particles in the observable universe.  This
is far smaller than the prime numbers which are larger than 10^152.  So
would you say these numbers are not prime, merely because we don't have
10^153 things we can point to?

If a number P can be prime in a universe with fewer than P objects in it,
might P be prime in a universe with 0 objects?


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