Interesting Esoterica

Continued fractions constructed from prime numbers

Article by Wolf, Marek
  • Published in 2010
  • Added on
In the collection
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.

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Other information

arxivId
1003.4015
isbn
9999637051
journal
Arxiv preprint arXiv:1003.4015
keywords
History and Overview,Number Theory
number
1
pages
35
volume
1

BibTeX entry

@article{Wolf2010,
	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.},
	archivePrefix = {arXiv},
	arxivId = {1003.4015},
	author = {Wolf, Marek},
	eprint = {1003.4015},
	isbn = 9999637051,
	journal = {Arxiv preprint arXiv:1003.4015},
	keywords = {History and Overview,Number Theory},
	month = {mar},
	number = 1,
	pages = 35,
	title = {Continued fractions constructed from prime numbers},
	url = {http://arxiv.org/abs/1003.4015 http://arxiv.org/pdf/1003.4015v2},
	volume = 1,
	year = 2010,
	primaryClass = {math.NT},
	urldate = {2012-02-01},
	collections = {Easily explained}
}