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CRGreathouse

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## Main Question or Discussion Point

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?

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.

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.