Primes that differ by 6 are no more silly than primes that differ by 2, and the twin prime conjecture is one of the most famous outstanding conjectures in mathematics–a proof would be huge (even a result that makes a tiny bit of progress towards a proof is a major chievement, so Yitan Zhang’s result proving there are an infinite number of prime pairs differing by some number that is less than 70 million was shocking to mathematicians, and actually made front page news in 2013.
Plus there are lots of reasons why working mod 6 is interesting, 6 being the first product of distinct primes itself. All odd primes are either 1 more than a multiple of 6, or one less than a multiple of 6.
So when you say it’s a silly recreational math problem, you just mean it has a silly name. I just thought I’d clear that up!
