Number Theory

    

Digital Root Patterns in Prime K-Tuples: a Study of Hidden Order in Prime Distribution

Authors: Halaoui Ayyoub

This paper investigates the non-random digital root patterns observed in prime k-tuples (e.g., twin primes, prime triplets). By analyzing over 10u2078 primes from the Twin Prime Database and OEIS, we demonstrate a statistically significant bias toward specific digital root sequences (e.g., (8,1) for twins, (5,7,2) for triplets) with frequencies up to 3.5× higher than random expectation. We explain these patterns using modular arithmetic in Z/9Z and sieve theory, while proving that constraints on prime divisibility limit the maximum k-tuple length to 7 primes. This study bridges computational evidence with theoretical number theory, suggesting that primes exhibit quasirandom behavior with deep underlying structure.

Comments: 3 Pages.

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Submission history

[v1] 2025-05-09 21:20:56

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