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

[rajeshmarndi]

Does there always exist primes in between square of two consecutive prime i.e P_n-1 and P_n

where P_n-1 and P_n are consecutive prime.

That is, in other words, does all the odd places between P_n-1 and P_n, 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.

 

[johnqwertyful]

http://en.wikipedia.org/wiki/Legendre's_conjecture

Related.

 

[RamaWolf]

Does there always exist primes in between square of two consecutive prime i.e P_n-1 and P_n

where P_n-1 and P_n are consecutive prime.

That is, in other words, does all the odd places between P_n-1 and P_n, 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.

Look at: http://en.wikipedia.org/wiki/Bertrand's_postulate

Does there always exist primes in between square of two consecutive prime i.e P_n-1 and P_n

where P_n-1 and P_n are consecutive prime.

That is, in other words, does all the odd places between P_n-1 and P_n, 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.

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