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Hardy, G.H. and Wright, E.M. (1962) Introduction to the Theory of Numbers. 4th Edition, Clarendon Press, Oxford.

has been cited by the following article:

• TITLE: Detecting a Regularity in the Generation and Utilization of Primes in the Multiplicative Number Theory

  AUTHORS: Silviu Guiasu

  KEYWORDS: Goldbach’s Conjecture, Symmetric Prime Cousins, Systemic Approach in Number Theory, Parallel System Covering Integers with Primes, Euler’s Formula for the Product of Reciprocals of Primes, Formula for the Exact Number of Primes Less than or Equal to an Arbitrary Bound

  JOURNAL NAME: Natural Science, Vol.11 No.6, June 25, 2019

  ABSTRACT: If Goldbach’s conjecture is true, then for each prime number p there is at least one pair of primes symmetric with respect to p and whose sum is 2p. In the multiplicative number theory, covering the positive integers with primes, during the prime factorization, may be viewed as being the outcome of a parallel system which functions properly if and only if Euler’s formula of the product of the reciprocals of the primes is true. An exact formula for the number of primes less than or equal to an arbitrary bound is given. This formula may be implemented using Wolfram’s computer package Mathematica.