Remark on the irrationality of the Brun's constant

Details Remark on the irrationality of the Brun's constant Remark on the irrationality of the Brun's constant

2010-02-22

arxiv.org/abs/1002.4174v1

Mathematics

Number Theory

Scientific paper

We have calculated numerically geometrical means of the denominators of the continued fraction approximations to the Brun constant B2. We get values close to the Khinchin constant. Next we calculated the n-th square roots of the denominators of the n-th convergents of these continued fractions obtaining values close to the Khinchin-Levy constant. These two results suggests that B2 is irrational, supporting the common believe that there is an infinity of twins.

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