Detecting a Regularity in the Generation and Utilization of Primes in the Multiplicative Number Theory - Natural Science

NS > Vol.11 No.6, June 2019

Detecting a Regularity in the Generation and Utilization of Primes in the Multiplicative Number Theory ()

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Download as PDF (Size: 315KB) PP. 187-196

DOI: 10.4236/ns.2019.116019 656 Downloads 1,536 Views Citations

Author(s)

Silviu Guiasu

Affiliation(s)

Department of Mathematics and Statistics, York University, Toronto, Canada.

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.

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

Share and Cite:

Guiasu, S. (2019) Detecting a Regularity in the Generation and Utilization of Primes in the Multiplicative Number Theory. Natural Science, 11, 187-196. doi: 10.4236/ns.2019.116019.

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