Finding prime pairs with particular gaps (Q2723543)
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scientific article; zbMATH DE number 1614811
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finding prime pairs with particular gaps |
scientific article; zbMATH DE number 1614811 |
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Finding prime pairs with particular gaps (English)
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5 July 2001
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prime gaps
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prime triples
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0.8663956
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The author describes an algorithm to determine consecutive primes \(p\) and \(p+g\) with a prescribed \(g\) and justifies its applicability by a heuristic argument. In particular, the author obtained the first such couple with \(g=1000\) (a result now superseded by the ones of \textit{S. Weintraub}, \textit{A. O. L. Atkin} and also \textit{B. Nyman}). In addition, the author considers the production of triples of primes of the shape \((6m+1,12m-1,12m+1)\) and, as a by-product, proves that all binomial coefficients \({2n\choose n}\) are divisible by the square of a prime \(\geq\sqrt{n/5}\) if \(n\geq 2082\). Such a result was announced and partially proven by \textit{A. Granville} and \textit{O. Ramaré} [Mathematika 43, 73-107 (1996; Zbl 0868.11009)].
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