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I want to prove that the set of natural numbers n having a prime divisor greater than $\sqrt{n}$ is positive. I have a heuristic argument that this density should be $\log 2$, which is approximately ...

This is a question about whether or not some number $\lambda^*$ is normal in base 2. More specifically, I am wondering if $\lambda^*$ is not normal. Proving it is normal would be next to impossible, ...

(Edit. What I called "pseudoprimes" are known as "Cramér random primes" in the literature, of which I was unaware.) Say that a set $S$ of natural numbers is a set of pseudoprimes if they are (a) ...

Let $x \in \mathbb{R}_+$ and $k \in \mathbb{N}^{*}$. Let : $$\mathcal{A}(x)=\#\{(a_1, a_2, \ldots, a_k) \in \mathbb{P}^k \mid (a_1, a_2, \ldots, a_k \text{ verifying some properties}) \, , a_k \...

It is well known that there is a little bias in the distribution of prime residues modulo 4. But the bias eventually vanishes. I looked at the first million primes, and the counts are as follows: ...