Loading ...
Sorry, an error occurred while loading the content.

on the randomness of primes

Expand Messages
  • Joshua Zucker
    As a layman s version of the Green/Tao proof on arithmetic progressions of primes, I found one of the user comments at
    Message 1 of 1 , Feb 6, 2007
    • 0 Attachment
      As a "layman's version" of the Green/Tao proof on arithmetic
      progressions of primes, I found one of the user comments at
      http://crookedtimber.org/2004/06/11/riemann-hypothesis-proved saying
      this:
      If primes were distributed "randomly" throughout the integers, one
      would certainly expect infinitely many twin primes. Interestingly, the
      Green-Tao theorem alluded to above (caveat: I haven't read the paper
      so only know about the argument by hearsay) gives a precise sense to
      the assertion "the primes are distributed in an approximately random
      way" and shows that ANY sequence of integers which is "approximately
      random" in their sense contains arbitrarily long arithmetic
      progressions. In some sense, their theorem is not really a theorem
      about primes at all.


      Me:
      Can anyone give a slightly less layman-like description of the
      Green/Tao proof and tell me more about what they mean by "random way"
      and so on? Or, alternatively, correct this "layman's version" and
      tell me what the Green/Tao paper really proved?

      Thanks,
      --Joshua Zucker
    Your message has been successfully submitted and would be delivered to recipients shortly.