Is there any approach proof for Legendre conjecture or it is completed solved?

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Legendre conjecture stated that:for every x there exists a prime number between $x^2$ and $x^2+2x+1$ .then Is there any approach proof for legender conjecture or it is completed solved ?

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From the introductory paragraph of your link

as of 2017, the conjecture has neither been proved nor disproved.