# nt.number-theory's questions - English 1answer

9.979 nt.number-theory questions.

### -6 About inverse function of π(x) (the prime counting function) [closed]

If for a given π(prime(n)) or f(π(prime(n))), we can find prime(n), is this enough to help on solve RH?

### 10 Recognizing the Galois group from the field discriminant

0 answers, 151 views nt.number-theory galois-theory
Along the lines of the general question "How much does the discriminant of a number field reveal about the field?", I was wondering how often it happens that the discriminant of some number field ...

### 8 Are there infinitely many primes of this form?

The semiprime $87 = 3*29$ has a curious property: it's the fact that both $87^2 + 29^2 + 3^2 = 8419$ and $87^2 - 29^2 - 3^2 = 6719$ are prime numbers. This intrigued me and led me to wonder if ...

### -2 On the generalized taxicab number Taxicab(4,2,3) [closed]

Is there a number that can be represented as a sum of two fourth powers in three different ways?

I hope it is OK to ask the following reference request. If my question is not suitable, please let me know and I will do my best to modify it! Let $N\in\mathbb{N}$, let $q$ be a point in the open ...

### 4 How to compute Dedekind eta function efficiently?

According to wiki: https://en.wikipedia.org/wiki/Dedekind_eta_function, Dedekind eta function is defined in many equivalent forms. But none of them is an explicit description (say in algorithmic ...

### 29 Is there an 11-term arithmetic progression of primes beginning with 11?

i.e. does there exist an integer $C > 0$ such that $11, 11 + C, ..., 11 + 10C$ are all prime?

### 6 Primality test for specific class of Proth numbers

Can you provide a proof or a counterexample for the following claim : Let $P_m(x)=2^{-m}\cdot \left(\left(x-\sqrt{x^2-4}\right)^{m}+\left(x+\sqrt{x^2-4}\right)^{m}\right)$ Let $N=k\cdot 2^n+1$...

### 3 Higher roots modulo prime complexity best algorithm

Given integers $a,\ell$ and prime $p$ we need to find the roots of the algebraic equation $x^\ell\equiv a\bmod p$. We know there are at most $\ell$ such $x$. What is the best method to find all such ...

### 5 Does every prime $p$ appear in a $p$-term arithmetic progression of primes? [duplicate]

This is a follow-up to an earlier question. The answer to that question was found on this page. The discussion on OEIS seems to suggest that, for any prime $p$, there should exist a $p$-length ...

### -2 Can this criterion to indicate the randomness some numbers? [closed]

1 answers, 521 views nt.number-theory random-functions
John Derbyshire in his book PRIME OBSESSION says on page 366: CHAPTER 3 10. "Here is an example of e turning up unexpectedly. Select a random number between 0 and 1. Now select another and add ...

### 92 Why does the Riemann zeta function have non-trivial zeros?

This is a very basic question of course, and exposes my serious ignorance of analytic number theory, but what I am looking for is a good intuitive explanation rather than a formal proof (though a ...

### Infinite difference length of integer subsets

Let $A$ be a set of integers. In our recent researches, we've faced to the following property and definition: We say $A$ has infinite difference length, if (a) For every integer $n$ there exist a ...

### -3 Random numbers between 0 and 1 [closed]

0 answers, 86 views nt.number-theory random-functions
John Derbyshire in his book PRIME OBSESSION says on page 366: CHAPTER 3 10. "Here is an example of e turning up unexpectedly. Select a random number between 0 and 1. Now select another and add ...

### 6 Are all totally ramified $\mathbb{Z}_p$-extensions of local fields come from (relative) Lubin-Tate formal groups?

The setup is as follows: $k/\mathbb{Q}_p$ is a finite extension, $\mathfrak{p}$ is the maximal ideal of $\mathcal{O}_k$, $q=\#(\mathcal{O}_k/\mathfrak{p})$ $k'/k$ is a finite unramified extension of ...