Primality between consecutive primorials
Bull. Korean Math. Soc. 2021 Vol. 58, No. 6, 1377-1385
https://doi.org/10.4134/BKMS.b200798
Published online November 4, 2021
Printed November 30, 2021
Kiyuob Jung, Eunkyung Ko
Kyungpook National University; Keimyung University
Abstract : 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).
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