Article
The Tail Distribution of the Sum of Digits of Prime Numbers
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Abstract
Let sq(n) denote the base q sum of digits function, which for n ≤ x, is centered around q −2 1 log q x. In this paper we provide bounds on the tails of the distribution of sq(n), and prove that given α in the range 1 2 ≤ α 0, there exists a constant c depending on ǫ such thatp ≤ x, p prime : sq(p) ≥ α(q − 1) log q (x)≥ 2 2 5 x2(1 − α)e− c√log q(log x)1/2+ǫ for sufficiently large x. In particular, this shows that there are infinitely many primes with more than twice as many ones than zeros in their binary expansion.
Keywords
Mersenne primes, Sum of Digits, Digits of primes, Prime numbers.
Citation
Naslund, E. (2015). The tail distribution of the sum of digits of prime numbers. Uniform Distribution Theory, 10(1), 63–68.
E. Naslund, “The tail distribution of the sum of digits of prime numbers,” Uniform Distribution Theory, vol. 10, no. 1, pp. 63–68, 2015.
Naslund E. The tail distribution of the sum of digits of prime numbers. Uniform Distribution Theory. 2015;10(1):63–68.
Naslund, E. (2015), ‘The tail distribution of the sum of digits of prime numbers’, Uniform Distribution Theory, 10(1), pp. 63–68.
Naslund, Eric. “The Tail Distribution of the Sum of Digits of Prime Numbers.” Uniform Distribution Theory, vol. 10, no. 1, 2015, pp. 63–68.
Naslund, Eric. “The Tail Distribution of the Sum of Digits of Prime Numbers.” Uniform Distribution Theory 10, no. 1 (2015): 63–68.
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Published by: Engineering Journals
