Comments on: Ruby Generators

By: Gavin

Gavin — Mon, 23 Nov 2009 11:35:41 +0000

The above proof is nearly complete. Instead of “Hence this number is prime…” it should say “This number is prime or composite. If it’s prime, that’s a contraction; QED. If it’s composite, it can be factored into primes, none of which we previously knew about; contradiction; QED.”

In short, given any finite list of primes, it’s always possible to find a new one. Therefore the list is infinite. This proof goes back to Euclid’s time.

By: Joshua Cheek

Joshua Cheek — Sat, 03 Oct 2009 14:03:13 +0000

Montana says “there are not a finite number of primes.”

Anthony says “Prove it”

Assume there are a finite number of primes. If you multiply them all together, you will have a number for which every prime is a multiple. Add one to this number, and you will have a new number which no prime divides. Hence this new number is prime. This is a contradiction, since it is not in the finite set of all primes, so the assumption is wrong and there are an infinite number of primes.

Or, in haiku http://xkcd.com/622/

By: Shot

Shot — Sat, 03 Oct 2009 11:39:07 +0000

If you’re after code similarity, you can use Enumerable#any? instead of Enumerable#all?:

if p.any? { |f| n % f == 0 }

if p.any? { |f| (n % f).zero? }

(IMHO using positive checks like the above is also simpler to read and parse by humans).

By: roger rubygems

roger rubygems — Thu, 03 Sep 2009 22:29:11 +0000

Checkout fibers, too, I suppose :)
-r

By: A

Wed, 27 May 2009 13:10:36 +0000

Love this. I was hunting for the exact solution to chain more than one “filter” on a large list. Perfect fit for me.

By: Anthony

Anthony — Sat, 18 Apr 2009 01:28:05 +0000

Prove it :-)

By: Montana

Montana — Fri, 17 Apr 2009 22:57:43 +0000

Just to note, there are not a finite number of primes. :)

By: kemiisto

kemiisto — Fri, 26 Dec 2008 14:08:35 +0000

Thanks. Today it was very useful during the Python vs Ruby “holy war” on one russian programmers forum! ;-)