대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제58권6호
  • /
  • Pages.1377-1385
  • /
  • 2021
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

PRIMALITY BETWEEN CONSECUTIVE PRIMORIALS

  • Jung, Kiyuob (Department of Mathematics Kyungpook National University) ;
  • Ko, Eunkyung (Major in Mathematics College of Natural Sciences Keimyung University)
  • 투고 : 2020.09.18
  • 심사 : 2021.09.02
  • 발행 : 2021.11.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

과제정보

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

참고문헌

  1. M. Agrawal, N. Kayal, and N. Saxena, PRIMES is in P, Ann. of Math. (2) 160 (2004), no. 2, 781-793. https://doi.org/10.4007/annals.2004.160.781
  2. A. O. L. Atkin and F. Morain, Elliptic curves and primality proving, Math. Comp. 61 (1993), no. 203, 29-68. https://doi.org/10.2307/2152935
  3. R. Crandall and C. Pomerance, Prime Numbers, second edition, Springer, New York, 2005.
  4. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, sixth edition, Oxford University Press, Oxford, 2008.
  5. J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill Book Company, Inc., New York, 1939.