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Results tagged with prime-numbers
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user 2481
Questions where prime numbers play a key-role, such as: questions on the distribution of prime numbers (twin primes, gaps between primes, Hardy–Littlewood conjectures, etc); questions on prime numbers with special properties (Wieferich prime, Wolstenholme prime, etc.). This tag is often used as a specialized tag in combination with the top-level tag nt.number-theory and (if applicable) analytic-number-theory.
16
votes
Accepted
A stronger form of the Dirichlet Theorem on prime numbers in arithmetic sequences
This is a hybrid of Dirichlet's theorem with Artin's conjecture on primitive roots. Artin's primitive root conjecture says that if $a \in \mathbf{Z}$ is not a perfect square or $-1$, then there are in …
- 37k
12
votes
1
answer
528
views
Roots of unity near 1 in Z / p Z
Let $r \ge 3$ be a fixed integer. I'm interested in primes p such that no integer in the interval $(-\sqrt{p}, \sqrt{p})$, except $1$ (and $-1$ if $r$ is even), is an r-th root of unity modulo p.
The …
- 37k
6
votes
Class number of imaginary quadratic fields
The condition shouldn't be "$n$ is prime" but "$n$ is either 1, 2, or a prime congruent to 3 mod 4". For instance $\mathbb{Q}(-5)$ has class number 2.
The more general statement that the 2-torsion sub …
- 37k