The Tuti Primality Theorem: A Relationship Between Decimal Digit Sums and the Distribution of Prime Numbers

This paper presents the Tuti Primality Theorem, a mathematical result concerning the relationship between decimal digit sums and prime numbers. The theorem establishes that, for every prime number with n decimal digits, there exists another prime number at a distance of at most n − 1 from its decimal digit sum. The proof uses elementary divisibility properties, finite verifications, and Nagura's theorem. Furthermore, a stronger generalization is established, extending the result to every positive integer with at least four decimal digits, including composite numbers.