Khnichin’s theorem is a surprising and still relatively little known result. It can be used as a specific criterion for determining whether or not any given number is irrational. In this paper we apply this theorem as well as the Gauss-Kuzmin theorem to several thousand high precision (up to more than 53 000 significant digits) initial Stieltjes constants γn, n = = 0, 1, 2, . . . , 5000 in order to confirm that, as is commonly believed, they are irrational numbers (and even transcendental). We also study the normality of these important constants.
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