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As a matter of fact, P. L. Chebyshev knew already that for any $\epsilon > \frac{1}{5}$, there exists an $n(\epsilon) \in \mathbb{N}$ such that for all $n\geq n(\epsilon),$

$\pi((1+\epsilon)n)-\pi(n)>0.$

In [2], one can find a short report on the problem of determining explicit values for the smallest $n(\epsilon)$ explicitly once that $\epsilon$ has been fixed.

References

[1] P. L. Chebyshev. Mémoire sur les nombres premiers. Mémoires de l'Acad. Imp. Sci. de St. Pétersbourg, VII, 1850.

[2] H. Harborth & A. Kemnitz. Calculations for Bertrand's Postulate. Mathematics Magazine, 54 (1), pp. 33-34.

3 added 20 characters in body; deleted 12 characters in body

As a matter of fact, P. L. Chebyshev knew already that for any $\epsilon > \frac{1}{5}$, there exists an $n(\epsilon) \in \mathbb{N}$ such that for all $n\geq n(\epsilon),$

$\pi((1+\epsilon)n)-\pi(n)>0.$

In [2], one can find a short account of report on the problem of determining explicit values for the smallest $n(\epsilon)$ for fixed values of once that $\epsilon$.\epsilon$has been fixed. References [1] P. L. Chebyshev. Mémoire sur les nombres premiers. Mémoires de l'Acad. Imp. Sci. de St. Pétersbourg, VII, 1850. [2] H. Harborth & A. Kemnitz. Calculations for Bertrand's Postulate. Mathematics Magazine, 54 (1), pp. 33-34. 2 added 92 characters in body As a matter of fact, P. L. Chebyshev knew already that for any$\epsilon > \frac{1}{5}$, there exists an$n(\epsilon) \in \mathbb{N}$such that for all$n\geq n(\epsilon),\pi((1+\epsilon)n)-\pi(n)>0.$In [2], one can find a short account of the problem of determining explicit values for the smallest$n(\epsilon)$.n(\epsilon)$ for fixed values of $\epsilon$.

References

[1] P. L. Chebyshev. Mémoire sur les nombres premiers. Mémoires de l'Acad. Imp. Sci. de St. Pétersbourg, VII, 1850.

[2] H. Harborth & A. Kemnitz. Calculations for Bertrand's Postulate. Mathematics Magazine, 54 (1), pp. 33-34.

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