On the primes in the interval \([3n,4n]\) (Q2898688)

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scientific article; zbMATH DE number 6054673
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On the primes in the interval \([3n,4n]\)
scientific article; zbMATH DE number 6054673

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    11 July 2012
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    prime numbers
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    math.NT
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    On the primes in the interval \([3n,4n]\) (English)
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    Modifying the elementary argument used by \textit{P. Erdős} to prove Bertrand's postulate stating that for any positive integer \(n\) there is always a prime number in the interval \([n, 2n]\) (see [Acta Litt. Sci. Szeged 5, 194--198 (1932; Zbl 0004.10103)]), this reviewer extended Bertrand's postulate and proved that for any positive integer \(n\) there is a prime number in the interval \([2n, 3n]\), [Int. J. Contemp. Math. Sci. 1, No. 13--16, 617--621 (2006; Zbl 1154.11303)]. In the paper at hand, the author uses similar arguments to prove that for any positive integer \(n\) there exists a prime in the interval \([3n, 4n]\). Moreover, the author gives a lower bound for the number of primes in \([3n, 4n]\) which implies that the number of primes in this interval tends to infinity as \(n\) approaches infinity.
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