Is anything more known about Legendre's conjecture that there is a prime between n^2 and (n+1)^2 for positive integers n than what appears on MathWorld?(adsbygoogle = window.adsbygoogle || []).push({});

MW says that a prime or semiprime always satisfies this, and that there is always a prime between n and n^{23/42} (21/42 would be equivilent to Legendre's conjecture).

How far has this been checked? It seems 'obvious' that it should hold, and yet there's no clear method of attacking the problem.

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# Legendre's conjecture?

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