Difference between revisions of "Legendre Conjecture"
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Latest revision as of 19:55, 1 January 2025
The Legendre Conjecture is a conjecture in number theory. It had been presented more than a century ago yet still unsolved. It is one of the famous Landau's Problems.
Statement
The conjecture states that there is a prime between every two pairs of consecutive squares of integers. I.e., for each integer 
there exist a prime number 
such that
![\[n^2 < p < (n+1)^2\]](http://latex.artofproblemsolving.com/9/d/5/9d5ef2039fb8ba223585b1d8a25d5f1e0f9f0f06.png)
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