An arithmetic series of primes

1. Jan 13, 2009

Loren Booda

List all of the possible sums of prime number pairs with each element taken once.

For instance: 2+3=5, 2+5=7, 3+5=8, 2+7=9, 3+7=10, 5+7=12, 5+11=16, 5+13=18 . . .

Can you find significance in this progression? Have you seen this sequence before?

2. Jan 14, 2009

Gokul43201

Staff Emeritus
That "sequence" will likely consist of every even number that is not of the form 2p as well as every odd number of the form p+2 (p is a prime number). Are you familiar with the Goldbach and Levy conjectures?

If you have a more specific question than the somewhat open-ended question in the OP, please get straight to the specific question.

3. Jan 14, 2009

Loren Booda

I'm sorry, I thought I had found a more fundamental pattern.