Hello, I have questions.

Is the following proposition known?

"There exists a prime number between n^{2}and n(n+1) for any integer n>=2."

Do you know whether this is true or false?

Thank you.

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- November 2nd 2012, 07:30 AMTakumiSatoA proposition about prime numbers
Hello, I have questions.

Is the following proposition known?

"There exists a prime number between n^{2}and n(n+1) for any integer n>=2."

Do you know whether this is true or false?

Thank you. - November 2nd 2012, 11:42 AMamywRe: A proposition about prime numbers
Can you prove that by induction? (base case n=2)

- November 2nd 2012, 06:17 PMagentmulderRe: A proposition about prime numbers
"chebyshev proved it and i'll say it again, theres always a prime between n and 2n"

- November 3rd 2012, 04:14 AMTakumiSatoRe: A proposition about prime numbers
I don't have a mathematically rigorous proof.

I have checked n up to 15000. - November 3rd 2012, 10:10 PMTakumiSatoRe: A proposition about prime numbers
I found this proposition fell under the following conjecture.

Oppermann's conjecture - Wikipedia, the free encyclopedia

Thanks.