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.

Bob Hansen

On Dec 6, 2012, at 2:16 PM, Paul Tanner <upprho@gmail.com> wrote:

> On Thu, Dec 6, 2012 at 11:06 AM, Robert Hansen <bob@rsccore.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"
> http://mathforum.org/kb/message.jspa?messageID=507327
>
> "Re: Twin prime conjecture restated without reference to primes"
> http://mathforum.org/kb/message.jspa?messageID=507328