Date: Feb 13, 2013 4:51 PM
Author: Clyde Greeno
Subject: Re: Largest Known Prime Number Discovered

The line of primes is of the Peano kind:
# Linearly ordered, and discretely so
# having a minimum point, and
# having no maximum point
Thereby, it is order-isomorphic to the line of finite cardinals.

So, are you asking, in essence, for an upper bound to whatever cardinal
numbers mankind (or Sam) can "discover?" Or is it conceivable that a
particular algorithm through which the mind ... or other machine ...
identifies primes has its own limitations ... perhaps because of limitations
of the respective "machines"?

- --------------------------------------------------
From: "Joe Niederberger" <niederberger@comcast.net>
Sent: Wednesday, February 13, 2013 9:26 AM
To: <math-teach@mathforum.org>
Subject: Re: Largest Known Prime Number Discovered

> I think the remark (which I ascribe, perhaps flippantly
> and wrongly to ultra-finitists) "How many more?" deserves some
> consideration. I hope its uncontroversial that humans will only ever have
> a finite stockpile of "discovered" primes in their arsenal. So the next
> question is can we figure out an estimate of where the boundary (on
> magnitude, which I think also gives an estimate of total number of) might
> be? Or even give a very loose upper bound with a convincing argument?
> Seems like it may be possible. I have no trick up my sleeve here, it was
> just a passing thought.
>
> Anybody?
>
> Cheers,
> Joe N