I recently noticed that many even numbers formed as 2p (p prime number) have at least two pairs of prime numbers that they dercribe that even number via Goldbach's Conjecture.

Examples: 10=25=5+5=7+3 34=217=17+17=23+11=29+5=31+3

I wanted to know if there's any research on how many pairs exist that they describe an even number. I think that, equilevantly, my question is : Is there at least one k >=1 for every p so that p-2k and p+2k are prime at the same time?