Date: Dec 7, 2012 9:16 AM
Author: Robert Hansen
Subject: Re: A Good Activity
I haven't seen this rule before but if you do just the first two iterations of the sieve of Eratosthenes you can see how this pattern arises.
On Dec 6, 2012, at 2:16 PM, Paul Tanner <firstname.lastname@example.org> wrote:
> On Thu, Dec 6, 2012 at 11:06 AM, Robert Hansen <email@example.com> wrote:
>> The other night, my son and I worked out all the primes less than 100.
> One of the "little theorems" or "tricks" on the primes that could come
> in handy is that all primes greater than 3 are either 1 less or 1
> greater than some multiple of 6 - the set of all primes greater than 3
> is a subset of of the set of all positive integers 6c-1 or 6c+1 for
> all positive integers c. (It makes it easier to recall all the primes
> up to whatever number - just count up multiples of six and at each
> count try to recall which of the two numbers in question are composite
> and which of the two are prime.
> I wrote two messages using this fact with respect to primes at
> sci.math about a decade ago, to share some things I found with respect
> to the Twin Prime Conjecture:
> "Twin prime conjecture restated without reference to primes"
> "Re: Twin prime conjecture restated without reference to primes"