Can Every Integer n > 1 have at Least One Prime Number Between n+1 and n^2?

[Myslius]

How do you prove/disprove the following: For any integer n higher then 1, there exists at least one prime number in interval [n+1, n^2]?

 

[camilus]

Show that n^2-n-1>n for n>2 and apply Bertrand's postulate that there is a prime in [n,2n] for all n>2.

 

[Myslius]

Thank you