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The Prime Counting Function

  • Journal of The Korea Society of Computer and Information
  • Abbr : JKSCI
  • 2011, 16(10), pp.101-110
  • Publisher : The Korean Society Of Computer And Information
  • Research Area : Engineering > Computer Science

Sang-Un, Lee 1 MyeongBok Choi 1

1강릉원주대학교

Accredited

ABSTRACT

The Riemann's zeta function has been known as answer for a number of primes less than given number . In prime number theorem, there are another approximation function , and . The error about is . The logarithmic integral function is . This paper shows that the can be represent with finite , and presents generalized prime counting function . Firstly, the can be represent to and such that . Then, is adjusted by with and error compensation value . As a results, this paper get the for . Then, this paper suggests a generalized function . The function superior than Riemann's zeta function in representation of prime counting.

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