Bulletin of the
Korean Mathematical Society BKMS

In this paper, we consider a general number system with a base $m$ in order to determine if a positive integer $x$ is prime. We show that the base $m$ providing the most efficient test is the primorial $p_n\sharp$ when $p_{n}\sharp < x < p_{n+1}\sharp$ and establish a necessary and sufficient condition for $x$ in between consecutive primorials to be determined as a prime number.

Keywords: Prime number, primorial, primality

MSC numbers: 11A41, 11A51, 11A63

Supported by: E. Ko was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (NRF-2020R1F1A1A01065912).