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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.

5 votes

Chebyshev's approach to the distribution of primes

According to the notes in fifth edition of Niven, Zuckerman and Montgomery's An Introduction to the Theory of Numbers for each $\epsilon\in(0,1)$ there is a series of parameters in Chebyshev's method …
Robin Chapman's user avatar
6 votes

Is the probability that n and phi(n) (totient function) are coprime one for random squarefre...

I'm not sure what you mean by a random integer $n$, but would you agree that the probability that a random squarefree integer be divisible by $55$ is nonzero? For if $55\mid n$ then $5\mid\gcd(n,\phi( …
Robin Chapman's user avatar
12 votes

Dirichlet's theorem for number fields

To expand on the excellent comments a bit, one needs both a bit more and a bit less than Chebotarev's density theorem. :-) Let's take a number field $K$, and a nonzero ideal $\mathfrak{N}$ of the rin …
Robin Chapman's user avatar