One day, I was thinking about primes that add up to 30 and all I thought about was:
\((7,23) , (11,19) , (13,17)\)
And I found out that the interesting thing when I got the difference of each pair they were actually powers of 2!
And the prime factorization of 30 was \(2^1\) times \(3^1\) times \(5^1\) which were consecutive primes. So I suspect there is a relationship that does this