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Re. I think this point can be used as a basis for the judgment of twin prime numbers, if there is no prime number in the interval [p~$p+\sqrt{2p}+\sqrt{2}$], , it is proved that the twin prime number is false.
@LSpice Thank. My main goal is to prove that there must be a prime number in the interval [p~p+$\sqrt{2p}+\sqrt{2}$ ], which is strong than there must be a prime number in the interval [p~2p].
