Skip to main content

All Questions

Filter by
Sorted by
Tagged with
14 votes
6 answers
2k views

Density of numbers having large prime divisors (formalizing heuristic probability argument)

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 ...
Vipul Naik's user avatar
  • 7,320
14 votes
1 answer
1k views

Normal numbers, Liouville function, and the Riemann Hypothesis

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, ...
Vincent Granville's user avatar
9 votes
2 answers
1k views

Random pseudoprimes vs. primes

(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) ...
Joseph O'Rourke's user avatar
5 votes
0 answers
614 views

is there a link with the probabilistic model for prime numbers?

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 \...
Lagrida Yassine's user avatar
0 votes
0 answers
257 views

Unexpected autocorrelations in sequence of primes modulo 4

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: ...
Vincent Granville's user avatar