A Prime-Representing Constant

• Published in 2020
• Added on 2020-11-06

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.

Links

• http://arxiv.org/abs/2010.15882v1
• http://arxiv.org/pdf/2010.15882v1

Other information

BibTeX entry

@article{APrimeRepresentingConstant,
	key = {APrimeRepresentingConstant},
	type = {article},
	title = {A Prime-Representing Constant},
	author = {Dylan Fridman and Juli Garbulsky and Bruno Glecer and James Grime and Massi Tron Florentin},
	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.},
	comment = {},
	date_added = {2020-11-06},
	date_published = {2020-12-07},
	urls = {http://arxiv.org/abs/2010.15882v1,http://arxiv.org/pdf/2010.15882v1},
	collections = {easily-explained,fun-maths-facts,integerology},
	url = {http://arxiv.org/abs/2010.15882v1 http://arxiv.org/pdf/2010.15882v1},
	year = 2020,
	urldate = {2020-11-06},
	archivePrefix = {arXiv},
	eprint = {2010.15882},
	primaryClass = {math.NT}
}