Mills' constant is irrational

Kota Saito

doi:10.1112/mtk.70027

Mills' constant is irrational

Kota Saito

研究成果: ジャーナルへの寄稿 › 記事 › 査読

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Let (Formula presented.) denote the integer part of (Formula presented.). In 1947, Mills constructed a real number (Formula presented.) such that (Formula presented.) is always a prime number for every positive integer (Formula presented.). We define Mills' constant as the smallest real number (Formula presented.) satisfying this property. Determining whether this number is irrational has been a long-standing problem. In this paper, we show that Mills' constant is irrational. Furthermore, we obtain partial results on the transcendency of this number.

本文言語	英語
論文番号	e70027
ジャーナル	Mathematika
巻	71
号	3
DOI	https://doi.org/10.1112/mtk.70027
出版ステータス	出版済み - 7月 2025

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Mills' constant is irrational

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