With the help of the Prime Number Theorem, please seek an affirmative answer. The question is stronger than the very related Legendre's Conjecture (https://en.m.wikipedia.org/wiki/Legendre%27s_conjecture).
The answer is affirmative!
Relevant Reference Link:
https://www.quora.com/Can-we-disprove-that-for-any-positive-integer-n-there-are-at-least-two-prime-numbers-between-n-2-and-n-1-2/answer/David-Cole-146
@ Paolo Leonetti
Your argument is very flawed since the great Prime Number Theorem is more than adequate to prove the conjecture in question.
A Key Result of Proof:
π((n+1)^2) - π (n^2) → π(n) = n /log(n) as n →∞.
Example:
π(75,001^2) - π(75,000^2) - π(75,000)
= (262,872,577 - 262,865,922) - 7493
= 6755 - 7493 = -738 (almost 11% error);
6755 - 75,000/log(75,000)
= 6755 - 6681
= 74 (almost 1% error).
Those excellent results agree very well with theory of proof.
@ Paolo Leonetti
Again, your argument is very flawed! Ask an expert in number theory to help you with your flawed math since I cannot convince you here. My work has been confirmed as valid.
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