<ruby id="d9npn"></ruby>

      <sub id="d9npn"><progress id="d9npn"></progress></sub>

      <nobr id="d9npn"></nobr>

      <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

      <th id="d9npn"><meter id="d9npn"></meter></th>

      Stack Exchange Network

      Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

      Visit Stack Exchange

      Questions tagged [prime-numbers]

      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.

      0
      votes
      0answers
      78 views

      How many solutions to $p_i|a_{i,1} p_1 + \dotsc + a_{i,n} p_n$?

      Consider a system of $n$ divisibility conditions on $n$ prime variables: $$p_i|a_{i,1} p_1 + \dotsc + a_{i,n} p_n,\;\;\;\;\;1\leq i\leq n,$$ where $a_{i,j}$ are bounded integers. How many solutions ...
      8
      votes
      0answers
      186 views

      A006517: Integers with $n\mid 2^n+2$

      The following question was asked at Math StackExchange but, having attracted some attention, didn't get solved. Problem 323 from the Mathematical Excalibur Vol. 14, No. 2, May-Sep. 09, linked here (...
      1
      vote
      0answers
      43 views

      Wieferich primes and arithmetic prgressions

      Let $p$ be an odd prime number. Let $K$ be a number field with Galois group $G$ and $H$ be a subgroup of $G$ stable under conjugation. Then the Cebotarev density theorem gives that $$\mathcal{L}=\{\...
      6
      votes
      0answers
      114 views

      Additive and multiplicative convolution deeply related in modular forms

      From the fact spaces of modular forms are finite dimensional, from the decomposition in Hecke eigenforms, and from the duplication formula for $\Gamma(s)$ there are a lot of identities mixing additive ...
      2
      votes
      1answer
      118 views

      On an oscillation Theorem involving the Chebyshev function and the zeros of the Riemann zeta function

      Define $\theta(x)=\sum_{p\leq x} \log p $, where $p>1$ denotes a prime. Nicolas proved that if the Riemann zeta function $\zeta(s)$ vanishes for some $s$ with $\Re(s)\leq 1/2 + b$, where $b\in(0, 1/...
      -2
      votes
      0answers
      118 views

      Is the sequence $\left(\pi\left(\frac{n(n+1)}2+1\right)\right)_{n\ge1}$ an addition chain?

      A (finite or infinite) strictly increasing sequence with the initial term $1$ is called an addition chain if each term after the initial one can be written as the sum of two earlier (not necessarily ...
      0
      votes
      0answers
      53 views

      Is the fundamental partition associated to $n$ the partition of $r_{0}(n)$ in $k_{0}(n)$ parts that maximizes entropy?

      As usual, under Goldbach's conjecture, let's define for a large enough composite integer $n$ the quantities $r_{0}(n):=\inf\{r\geq 0,(n-r,n+r)\in\mathbb{P}^{2}\}$ and $k_{0}(n):=\pi(n+r_{0}(n))-\pi(n-...
      4
      votes
      1answer
      208 views

      Why does each integer between two consecutive primes have at least one “unique” non-trivial divisor?

      Why does each integer $x$ between two consecutive primes have at least one non-trivial divisor that unique on set of all integers between these two consequtive primes except $x$? We call a divisor $d$...
      1
      vote
      0answers
      277 views

      Iterated Twin Prime conjecture [closed]

      "Conjecture. The sum of a twin prime pair greater than or equal to 24 can be expressed as the sum of two twin prime pairs." Examples: ...
      8
      votes
      0answers
      171 views

      Prime character sums

      Let $p$ be a (large) prime number, and let $\chi : (\mathbf{Z}/p\mathbf{Z})^{\times} \rightarrow \mathbf{C}^{\times}$ be a Dirichlet character of conductor $p$. We have good estimates on the character ...
      19
      votes
      4answers
      976 views

      Can anything deep be said uniformly about conjectures like Goldbach's?

      This is a soft question sparked by my curiosity about the intrinsic depth of Goldbach-like conjectures as perceived by current experts in number theory. The incompleteness theorem implies that, if our ...
      5
      votes
      2answers
      265 views

      Least (and largest) possible number of non-relatively prime pairs among consecutive integers

      Given a set of positive integers consider the graph whose vertices are those integers, two of which are joined by an edge if and only if they have a common divisor greater than 1 (i.e, they are not ...
      4
      votes
      0answers
      129 views

      Consecutive integers each of which has a large prime factor

      There are many results about consecutive integers all having small prime factors. But what about consecutive integers each of which has a large prime factor? More precisely, let $P(n)$ be the ...
      3
      votes
      1answer
      101 views

      Cipolla's Prime numbers function: Computing the coefficients of the polynomial

      In many publications dealing with asymptotic determinations of the n-th prime number, the following paper is cited: [1]: M. Cipolla, La determinazione asintotica dell’n-esimo numero primo. rendiconti ...
      4
      votes
      1answer
      231 views

      Why do polynomials $x^n + 1 \bmod N$ close a shorter cycle when $n$ is even than when $n$ is odd?

      Polynomials $f(x) \bmod N$, where $f(x)$ is of integer coefficients and $N$ is a composite of two distinct primes $p, q$, form a cycle --- usually leaving a tail because the cycle tends to close not ...

      15 30 50 per page
      特码生肖图
      <ruby id="d9npn"></ruby>

          <sub id="d9npn"><progress id="d9npn"></progress></sub>

          <nobr id="d9npn"></nobr>

          <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

          <th id="d9npn"><meter id="d9npn"></meter></th>

          <ruby id="d9npn"></ruby>

              <sub id="d9npn"><progress id="d9npn"></progress></sub>

              <nobr id="d9npn"></nobr>

              <rp id="d9npn"><big id="d9npn"><th id="d9npn"></th></big></rp>

              <th id="d9npn"><meter id="d9npn"></meter></th>