Some properties of the series of composed numbers (Q2782175)
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scientific article; zbMATH DE number 1727719
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some properties of the series of composed numbers |
scientific article; zbMATH DE number 1727719 |
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28 April 2002
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\(n\)th prime number
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\(n\)th composite number
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inequalities
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0.89462125
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0.88990873
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0.88539207
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0.8836447
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0.87803084
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Some properties of the series of composed numbers (English)
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The author proves several inequalities involving the \(n\)th prime number \(p_n\) and the \(n\)th composite number \(c_n\). The proofs are elementary, using known inequalities and results on \(p_n\) and \(c_n\). For example, it is shown that NEWLINE\[NEWLINE p_n > c_n\log c_n\quad(n \geq 30398), \quad \pi(n)p_n > c_n^2 \quad(n \geq 19421) NEWLINE\]NEWLINE where, as usual, \(\pi(x)\) is the number of primes not exceeding \(x\).
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