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Function f(x) is the most closest prime number not less than $x$.\\
          $f(5)=5\qquad  f(9)=11$\\


Conjecture: $ x\leqslant f(x)\leqslant x+x^{\log_{113}13}   \{x|1\leqslant x\leqslant+\infty,x\in \mathrm{positive~integer}\}$?\\

             States that there is a prime number between $x$ and $x+x^{\log_{113}13}$ for every positive integer $x$?\\

             For all positive integer $n$, where $p_n$ is the $n$th prime number.

           $p_{n+1}-1-p_n\leqslant {\left(p_n\right)}^{\log_{113}13}$\qquad ?\\


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