User blog comment:KthulhuHimself/The pointless and arbitrary function dustbin./@comment-1605058-20151102085040

A quick note: \(SPi(n)-n\) on average tends to infinity. This is because average size of a gap between primes below \(N\) is asymptotic to \(\ln N\), and a short calculation shows that average of \(SPi(n)-n\) from \(1\) to \(N\) is asymptotic to \(\frac{\ln N}{2}\) which is unbounded.