Generalized Harmonic Laws for Prime Digit-Length Transitions in Base Representations: Unique Structure in Base 7
Year: 2025
Type: article
Abstract: In the base 7 representations of prime numbers, the lengths of their digit expansions exhibit a striking dichotomy: they remain constant (interval 0) for most consecutive primes, and increase by exactly one digit only at specific primes crossing powers of 7. These +1 jumps occur with a mean frequency of approximately 1/56, and the normalized gaps between these primes include cyclic fractions of 1/7. This structure, unique to base 7 and absent in other bases, may represent a novel contribution to number theory.
Author: Hassanine, Sam
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6893234388
FWCI:
Cites:
Cited by:
Related to: