Continued fractions constructed from prime numbers

• Published in 2010
• Added on 2012-02-01

We give 50 digits values of the simple continued fractions whose denominators are formed from a) prime numbers, b) twin primes, c) generalized $d$-twins, d) primes of the form $m^2+n^4$, e)primes of the form $m^2+1$, f) Mersenne primes and g) primorial primes. All these continued fractions belong to the set of measure zero of exceptions to the theorems of Khinchin and Levy. We claim that all these continued fractions are transcendental numbers. Next we propose the conjecture which indicates the way to deduce the transcendence of some continued fractions from transcendence of another ones.

Links

• http://arxiv.org/abs/1003.4015
• http://arxiv.org/pdf/1003.4015v2

Other information

BibTeX entry

@article{Wolf2010,
	key = {Wolf2010},
	type = {article},
	title = {Continued fractions constructed from prime numbers},
	author = {Wolf, Marek},
	abstract = {We give 50 digits values of the simple continued fractions whose denominators are formed from a) prime numbers, b) twin primes, c) generalized {\$}d{\$}-twins, d) primes of the form {\$}m^2+n^4{\$}, e)primes of the form {\$}m^2+1{\$}, f) Mersenne primes and g) primorial primes. All these continued fractions belong to the set of measure zero of exceptions to the theorems of Khinchin and Levy. We claim that all these continued fractions are transcendental numbers. Next we propose the conjecture which indicates the way to deduce the transcendence of some continued fractions from transcendence of another ones.},
	comment = {},
	date_added = {2012-02-01},
	date_published = {2010-03-01},
	urls = {http://arxiv.org/abs/1003.4015,http://arxiv.org/pdf/1003.4015v2},
	collections = {Easily explained},
	archivePrefix = {arXiv},
	arxivId = {1003.4015},
	eprint = {1003.4015},
	isbn = 9999637051,
	journal = {Arxiv preprint arXiv:1003.4015},
	keywords = {History and Overview,Number Theory},
	month = {mar},
	number = 1,
	pages = 35,
	url = {http://arxiv.org/abs/1003.4015 http://arxiv.org/pdf/1003.4015v2},
	volume = 1,
	year = 2010,
	primaryClass = {math.NT},
	urldate = {2012-02-01}
}