# A Prime-Representing Constant

• Published in 2020
In the collections
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.

### 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}
}