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

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1. Sep 28, 2014

rajeshmarndi

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. Sep 28, 2014

3. Nov 5, 2014

RamaWolf

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)"