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arXiv · 1211.2455

Bounds For The Tail Distribution Of The Sum Of Digits Of Prime Numbers

Eric Naslund
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Abstract

Let s_q(n) denote the base q sum of digits function, which for n alpha(q-1)log_q x}| >>x^{2(1-alpha)}e^{-c(log x)^{1/2+epsilon}} for 1/2<alpha<0.7375. To attain this lower bound, we note that the multinomial distribution is sharply peaked, and apply results regarding primes in short intervals. This proves that there are infinitely many primes with more than twice as many ones than zeros in their binary expansion.

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Eric Naslund. 2012-11-11. Bounds For The Tail Distribution Of The Sum Of Digits Of Prime Numbers. https://arxiv.org/abs/1211.2455

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