Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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PRIMALITY BETWEEN CONSECUTIVE PRIMORIALS

  • Jung, Kiyuob (Department of Mathematics Kyungpook National University) ;
  • Ko, Eunkyung (Major in Mathematics College of Natural Sciences Keimyung University)
  • Received : 2020.09.18
  • Accepted : 2021.09.02
  • Published : 2021.11.30
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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 pn# when pn# < x < pn+1# and establish a necessary and sufficient condition for x in between consecutive primorials to be determined as a prime number.

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Acknowledgement

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

References

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