All Questions
5 questions
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 ...
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, ...
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) ...
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 \...
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:
...