A recursion equation for prime numbers

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dc.creatorKeller, Joseph B.
dc.date2007-11-26
dc.date2008-10-05
dc.date.accessioned2026-07-07T10:07:15Z
dc.date.available2026-07-07T10:07:15Z
dc.descriptionIt is shown that the first $n$ prime numbers $p_1,...,p_n$ determine the next one by the recursion equation $$ p_{n+1} =\lim\limits_{s\to +\infty} [\prod\limits^n_{k=1} (1-\frac{1}{p^s_k}) \sum\limits^\infty_{j=1} \frac{1}{j^s} -1]^{-1/s}. $$ The upper limit on the sum can be replaced by $2p_n -1$, and the result still holds.
dc.description2 pages; replacement 10/05/2008 corrects typographical error page 2, reference #1, author last name
dc.identifierhttps://arxiv.org/abs/0711.3940
dc.identifierhttp://arxiv.org/abs/0711.3940
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170567
dc.subjectNumber Theory
dc.subject11A41
dc.titleA recursion equation for prime numbers
dc.typetext

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