> Surely sexy primes are more common than twin primes, so at least for primes that are near each other there should be a higher probability for certain sequence

> Surely sexy primes are more common than twin primes, so at least for primes that are near each other there should be a higher probability for certain sequences of final digits. I think that's conjectural, but prime constellations are also conjectured to be a negligible fraction of primes as a whole, much as primes are a negligible fraction of integers (asymptotically). I think twin primes are conjectured to be distributed as n / (log n) ^2, while primes are n / (log n). Besides, even if (p, p + 6) is significantly more common than (p, p + 2), if the final digit of p is uniformly distributed among 1, 3, 7, and 9, I don't think the statistics as a whole are affected.