neat prime observation

May 2013
100
10
start with an even number E.
between 1 and 2*E there will be a number such that both it and it+E are prime.
after this, there will be a number such that, the low number from the previous pair + the high number from the previous pair, between that range, there will be another number such that it is prime, and it+E is prime.

let E = 8.
3,11 have a difference of 8.
between 3 and 14,
5,13
between 5 and 18
11,19
between 11 and 30
23,31

let E be 14
3,17
5,19
17,31
23,37
thoughts?
 
Last edited by a moderator:
Aug 2008
355
7
Blacksburg VA USA
well, surely you are familiar with Goldbach's conjecture. Taking the example of you E=14, we could continue with sums&differences as :
7+7=14
19-5=14
61-47=14

You could likely say every such E is the result of a sum or difference of 2 prime numbers, essentially infinitely.

If E=8154, E=8191-37

So you observation may be true, but there is no real need for it to produce a subset of all of the other "triples" out there, reflecting the established work surrounding gaps between prime numbers.
 
May 2013
100
10
no, what i'm proposing is the twin prime conjecture on steroids.