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 <email@example.com> wrote:
> On Thu, Dec 6, 2012 at 11:06 AM, Robert Hansen <firstname.lastname@example.org> 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