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Old 2007-08-01, 18:58   #6
davar55's Avatar
May 2004
New York City

5×7×112 Posts

I would think that with the great computational skills evident
on this forum that the following derivation would be considered excessive:

Let Pp be the probability that a random prime p is a number n.

By the lemma, Pp = Pp-1 = ... .

Hence multiplying the Pp gives

(Pp)n --> 1 or 0

depending on whether there exist any primes.

Additional Lemma: There are primes!

Proof: Start counting at 1 and continue until a number is reached
whose only factors are (well, you know). This process terminates at p=2.
Hence there are primes!

Corollary: The desired probability is 1 (if there really are primes).

Last fiddled with by davar55 on 2007-08-01 at 19:05 Reason: details, details
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