A Question about Prime

Revision en2, by yspm, 2022-03-05 11:52:09

I met a problem recently which need to prove the below conclusion.

$$$\exists B,\forall n\ge B,\exists p>\sqrt n, \text{p is prime,(2p+1) is prime}$$$

There is a example that $$$n=13,p=5,2p+1=11$$$ meet this constraint

I wrote something and check it's correct when $$$40\le n\le 10^5$$$ but is there any complete proof for such B exists?

I've learnt Bertrand-Chebyshev Theorem that there exists a prime $$$p\in[n,2n]$$$ and it may help.

Thank you.

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en2 English yspm 2022-03-05 11:52:09 5 Tiny change: 'nThere is some example t' -> 'nThere is a example t'
en1 English yspm 2022-03-05 11:48:40 474 Initial revision (published)