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Does there always exist primes in between square of two consecutive prime.

  1. Sep 28, 2014 #1
    Does there always exist primes in between square of two consecutive prime i.e Pn-1 and Pn

    where Pn-1 and Pn are consecutive prime.

    That is, in other words, does all the odd places between Pn-1 and Pn, are not divided, by primes less than Pn or by all primes upto Pn-1.


    I can only check randomly upto prime upto 982,451,653 which is available
    http://primes.utm.edu/lists/small/millions/

    and found there exist lot of primes in between any two consecutive prime square.
     
  2. jcsd
  3. Sep 28, 2014 #2
  4. Nov 5, 2014 #3
    Look at: http://en.wikipedia.org/wiki/Bertrand's_postulate

    We have a famous theorem, stating "there is always a prime between n and two n",

    (see http://en.wikipedia.org/wiki/Bertrand's_postulate)

    and that means: we have: "always a prime between n**2 and (n+2)**2 (for n > 4)"

    and that is a answer to your question
     
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