# neat prime observation

#### phillip1882

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?

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#### billymac00

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.

#### phillip1882

no, what i'm proposing is the twin prime conjecture on steroids.