African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 261

Article in Press

The set containing positive integers as ratios in geometric progressions, and the primes of alpha filtrate.

Nguthu Ng’elu

  •  Received: 24 October 2022
  •  Accepted: 27 April 2023
We answer the undocumented question of whether there exists a uniform algebraic expression that defines terms in Geometric Progressions (GP) whose ratios are positive integers; if so, whether the said expression defines terms in any GP whose ratios are not integers. As a solution to an easier method of generating large primes, we discover a set whose items are not pseudo-primes to base 2 of Fermat’s primality test. Finally, we discuss the application of the aforementioned method in pseudo-random number generation and in public-key cryptography.

Keywords: Fermat’s primality test, pubic-key cryptography, pseudo-random number generation, PAF algorithm