--On Monday, November 03, 2003 10:32 PM -0500 Jud McCranie <

j.mccranie@...> wrote:

>

>>> At 12:51 PM 11/2/2003 -0800, Roger Bagula wrote:

>>> > It is reasonable to assume that an infinite prime might exist ,

>>>> but could never be computed.

>

> It is not reasonable to assume that. Are you assuming that because there

> are an infinite number of prime numbers that one of them is infinite? That

> is false. There are an infinite number of primes, but each of them is finite.

Equally, there are infinitely many integers, or even numbers, but there is no one infinite integer - it is simply the case that for any integer n, you can find a successor n+1 which is also an integer.

Every prime also has a successor - there is no largest prime (whereas there IS a largest member of any finite set, for example there is a tallest person in the world, or a smallest planet in the solar system). However, since primes are defined as being a subset of the positive integers, there is no infinite prime.

Does that make sense, Roger?

Regards,

Nathan