Md. Shariful Islam

collaborators

2 papers

math.NT2026

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 $p < 1 0^{n}$ with base- $10$ expansion $p = \sum_{k = 0}^{n (p) - 1} d_{k} (p) 1 0^{k}$ , the positional digit probabilities $P_{n} (d ∣ k)$ satisfy \[…

math.NT2026

The Prime Digit Distribution Conjecture: A Formal Proof of Average Digit Equidistribution in the Prime Numbers

Mahadee Al Mobin, Md. Shariful Islam

Let $S_{n} = {p \in P : p < 1 0^{n}}$ , $N_{n}$ denote the total number of decimal digits occurring in the primes of $S_{n}$ , $C_{n} (d)$ be the number of occurrences of a digit $d\in\{0,\ld…