# A Prime-Representing Constant

- Published in 2020
- Added on

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We present a constant and a recursive relation to define a sequence $f_n$ such that the floor of $f_n$ is the $n$th prime. Therefore, this constant generates the complete sequence of primes. We also show this constant is irrational and consider other sequences that can be generated using the same method.

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### BibTeX entry

@article{APrimeRepresentingConstant, title = {A Prime-Representing Constant}, abstract = {We present a constant and a recursive relation to define a sequence {\$}f{\_}n{\$} such that the floor of {\$}f{\_}n{\$} is the {\$}n{\$}th prime. Therefore, this constant generates the complete sequence of primes. We also show this constant is irrational and consider other sequences that can be generated using the same method.}, url = {http://arxiv.org/abs/2010.15882v1 http://arxiv.org/pdf/2010.15882v1}, year = 2020, author = {Dylan Fridman and Juli Garbulsky and Bruno Glecer and James Grime and Massi Tron Florentin}, comment = {}, urldate = {2020-11-06}, archivePrefix = {arXiv}, eprint = {2010.15882}, primaryClass = {math.NT}, collections = {easily-explained,fun-maths-facts,integerology} }