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Results tagged with prime-numbers
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user 4213
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.
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( …
- 20.8k
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 …
- 20.8k
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 …
- 20.8k