Thread: A proposition about prime numbers

Hello, I have questions.
Is the following proposition known?

"There exists a prime number between n² and n(n+1) for any integer n>=2."

Do you know whether this is true or false?


Thank you.

Can you prove that by induction? (base case n=2)

"chebyshev proved it and i'll say it again, theres always a prime between n and 2n"

I don't have a mathematically rigorous proof.
I have checked n up to 15000.

I found this proposition fell under the following conjecture.
Oppermann's conjecture - Wikipedia, the free encyclopedia

Thanks.