Kang_Byul_2025_Sparse_Prime_Bases.pdf

This paper details the discovery of a unique property of prime number digit sums that appears to hold only for a sparse, specific set of prime bases. I define a base b as possessing this property if, for every prime number p, the sum of its base-b digits is 1, a prime, or a semiprime. For the purpose of discussion, I term the set of such bases the "Kang Byul Bases." An extensive computational search (bases up to 5000, primes up to 10^9) suggests this set is {7, 13, 31, 61, 211, 421, ...}. This conclusion was reached after deeper verification revealed counterexamples for other promising candidates (e.g., base 19). Notably, base 7, the origin of this study, has been verified for all primes up to ten billion (10^10). This paper presents the evidence for this set and poses the central question of what defines these numbers.