Kota Saito

collaborators

2 papers

math.NT2025

Transcendency of variants of Mills' constant

Kota Saito

Let $⌊ x ⌋$ denote the integer part of $x$ . For every sequence $(C_{k})_{k \geq 1}$ of positive integers, we define $I^¾ (C_{k})$ as the smallest real number $I^¾ > 1$ such that $\…

math.NT2025

Mills' constant is irrational

Kota Saito

Let $⌊ x ⌋$ denote the integer part of $x$ . In 1947, Mills constructed a real number $I^¾ > 1$ such that $⌊ I^¾^{3^{k}} ⌋$ is always a prime number for eve…