🚀 go-pugleaf

I just accidentally posted this without any subject filled in.
Hopefully some machine somewhere will have filtered it out.
If not, sorry about cluttering up the news with unlabeled articles.
Anyway, here is the article:


If anyone out there is interested in prime twins, I have
a method (similar to Eratosthene's sieve)
of generating them (which I can prove as well),

	Start with the prime number 5.
	Take j=the closest int to 5/6,and then eliminate multiples
	of 5 plus and minus j, i.e. 4,6,9,11,14,16,etc.

	Now continue with the next prime (7), so
	we eliminate mults of 7 plus and minus 1, i.e.
	6,8,13,15,20,22,etc.

	Now repeat with the next prime (11), so
	we eliminate mults of 11 plus and minus 2 (11/6 is closest to 2),
	i.e. 9,13,20,24,etc.

	and keep going forever ...

The numbers remaining 

	i.e. 1,2,3,5,7,10,12,...

correspond to exactly the set of all prime twins in the following manner:

	Take n*6-1 and n*6+1 and they form a prime twin,

so 1 gives 5,7
   2 gives 11,13,
  12 gives 71,73,
  etc.

Note:  The only prime twin this sieve does not leave is 3 and 5.

I have thought about using this to prove the prime twin conjecture
but I never seem to have the time to sit down and really think about it,
since I am not really a mathematician.
A first step might be to say instead of going through eliminating mults of
primes plus and minus j, to use 6n plus minus one instead of the primes.
This would eliminate a superset of the numbers eliminated above, and
if it could be shown that there were infinitely many integers left
after eliminating this superset, the prime twin conjecture would
be solved.

If anyone can use this info. (or if the prime twin conjecture has
already been solved and no one has told me), please let me know.

			
				Anthony Brockwell.