5
$\begingroup$

Find the values of $x \in \mathbb{Z}$ such that there is no prime number between $x$ and $x^2$. Is there any such number?

  • 0
    @Shashi: Did you mean to write "the square root of $x$ is $y$ such that $y^2=x$"?2011-02-08
  • 0
    @Matt: Sorry for typo mistake..2011-02-08
  • 12
    Bertrand's postulate guarantees the existence of a prime between $n$ and $2n$ for all integers $n > 1$. Therefore there are no non-trivial examples of the phenomenon you describe.2011-02-08
  • 2
    "Chebyshev said it before, and I say it again, there is always a prime beteween $n$ and $2n$." -Erdos. http://en.wikipedia.org/wiki/Bertrand's_postulate2011-02-08
  • 0
    The "logic" tag seems unappropiate.2011-02-08
  • 0
    I removed the "logic" tag.2011-02-08
  • 0
    I was going to say this is a dupe, but then I saw the date of posting...2011-06-09
  • 0
    @JDH, the verse is *about*, but not *by*, Erdos. The author was Nathan Fine.2011-12-04

2 Answers 2