Questions tagged [distribution-of-primes]

Use this tag for questions related to the branch of number theory studying distribution laws of prime numbers among natural numbers.

73 questions
32 views

Distribution of Digits of Binary Expansion of Primes

In considering the binary expansion of prime numbers, I'm interesting in the skew of digits towards 0 or 1. I searched through other questions and arrived at: Last digits of primes I just want to ...
42 views

Algorithm generating subset of primes, can we classify which of them or estimate how large percent of primes are generated?

Assume I have following algorithm: Two lists of numbers, first starting at 2, second starting empty. We now follow rule: Add a number to first list which makes difference with latest number the ...
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A ratio connected to the distribution of primes

According to the Prime Number Theorem, a number $n$, roughly speaking, has probability of primality $\sigma_n:=1/\ln n$. As every schoolchild learns, one can test the primality of $n$ by looking for ...
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Has a Pattern been explored? The sequence of prime factors for a factorial expression?

I have been studying this sequence and I was wondering if there is any pattern to the sequence? Has this been explored? Is there a way to generate an expression that creates these sequences? Is it/...
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Let $s_n$ denote the sum of the first $n$ primes. Prove that for each $n$ there exists an integer whose square lies between $s_n$ and $s_{n+1}$.

Let $s_n$ denote the sum of the first $n$ primes. Prove that for each $n$ there exists an integer whose square lies between $s_n$ and $s_{n+1}$. I cannot give a proof to this, although I have try on ...