Continued fractions constructed from prime numbers

Details Continued fractions constructed from prime numbers Continued fractions constructed from prime numbers

2010-03-21

arxiv.org/abs/1003.4015v2

Mathematics

Number Theory

Considerably extended version of previous submission. We add the discussion of transcendentality of continued fractions constr

Scientific paper

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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