# Tagged Questions

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### Sum of digits of repeating end of reciprocal of prime over period is $\frac{9}{2}$

Take a prime other than 2,3 or 5 and look at the part of it that repeats in base 10. Is it true that the sum of the digits in the end divided by the period(number of repeated digits id always ...
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### ${p^km \choose p^k} \equiv m \pmod p$ [migrated]

Let $p$ be a prime number and $m, k$ two positive integers. Then ${p^km \choose p^k} \equiv m \pmod p$. I've been trying to demonstrate this lemme all the day. Have you got any suggestion? Thank you ...
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### Heronian triangle with two sides that are prime

Can any prime number form a Heronian triangle with a second prime as another side? I cannot find a second prime to form a Heronian triangle with either 23 or 167. I have checked up to the 10^7th prime ...
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### Would Elliott-Halberstam conjecture follow from GRH?

The Wikipedia article about Elliott-Halberstam (EH for short) conjecture says that the so-called Bombieri-Vinogradov theorem, which is a weaker form of EH conjecture, is in some sense an averaged form ...
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### $a_{0}$ such that $0<\lim\sup_{n\to\infty}\frac{p_{n+k}-p_{n}}{H_{k}\log^{a_{0}}(\frac{p_{n+k}+p_{n}}{2})}<\infty$

This question is somehow a follow-up from Would the following conjectures imply Cramer's conjecture? Let $g_{n,k}$ denote the quantity $p_{n+k}-p_{n}$, $s_{n,k}$ denote the quantity ...
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### Prime numbers and limit ordinals

As a set, i.e. as a von Neumann ordinal, the $\omega$-th limit ordinal $\omega^2$ is fairly complex and not so easy to visualize (for the novice). But as an explicit well-ordering of $\mathbb{N}$, ...
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### The number of distinct prime factors of $n\in\mathbb N$
Let $\omega(n)$ be the number of distinct prime factors of a natural number $n$. Note that $\omega(n)=0\iff n=1$, and that $\omega(24)=\omega(2^3\cdot 3^1)=2\ (\not = 4)$. (For more details, you ...
### Primes $p$ for which $pk+1$ is prime for small $k$ (or approximating Sophie Germain)
The twin prime conjecture says there are infinitely many pairs $p,p+2$ that are both prime, and although we still don't know whether it's true there's been a lot of progress recently showing that ...