The Position-wise Prime Digit Distribution Theorem: A Formal Proof of Position-wise Digit Equidistribution in the Prime Numbers

Mahadee Al Mobin, Md. Shariful Islam

We state and prove the Theorem: for primes $p<10^n$ with base-$10$ expansion $p={\sum }_{k=0}^{n(p)-1}{d}_k(p)10^k$, the positional digit probabilities $P_n(d\mid k)$ satisfy \[…