The question is as stated in the title. I was given this interesting problem by a friend of mine, but I don't know how to proceed with a solution. The immediate thought I had was that the most common difference is 2 since all primes are odd (except 2), but that seems trivial and silly. Any thoughts/hints/suggestions on how to find the most common difference? I suspect it has something to do with modular arithmetic but I'm not too sure.
Any and all help is appreciated :)
Thanks for reading,
Edit: To specify the term "most common," I mean to ask what is the most abundant or frequently occurring difference between two consecutive primes.