🚀 go-pugleaf

In article <1557@anagld.analytics.com> sammy@anagld.analytics.com (Sam Blackburn) writes:

>In my humble excursions into this arena, I've noticed that primes are roughly
>11% of the numbers of x digits in length.  Is it feasible to compile a table
>of primes? Sure.  But it's gonna be one heck of a list.  The number of primes
>is not infinite (I'm probably going to get flamed on that remark).

Flamed? FLAMED? Why, what was the last time anyone on the net was
flamed for being ignorant? :-)

OK, so that this is not just a flame, he're your quick proof (is this
by Euclid?)

Proof that for any number N, there exists a prime larger than N:

Consider N!+1. Now, N!+1 does not have any divisors less than or equal
to N. Therefore, either N!+1 is itself prime, or it has a (prime)
divisor that's larger than N. In either case, there does exist a prime
larger than N, for all N, and therefore the number of primes is infinite. QED.

/ji

PS: Someone else give the proof on the density of primes... my number
theory is rusty at best, and it's too early in the morning anyway.

In-Real-Life: John "Heldenprogrammer" Ioannidis
E-Mail-To: ji@cs.columbia.edu
V-Mail-To: +1 212 854 8120
P-Mail-To: 450 Computer Science \n Columbia University \n New York, NY 10027