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This research is an attempt to highlight the rarity of Cluster primes in the world of number systems. We will also look into the solution of an equation \(p^x+q^y=z^2\) where p and q are primes. This also assumes more significance when only a select few of the Cluster prime numbers are found eligible and satisfy the given equation. The paper is further corroborated by means of programming to delve into a bigger range of values which further substantiates the claim that a few cluster primes will go ahead and satisfy the said equation.

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On the Exponential Diophantine Equation Related to the Powers of Cluster Primes

  • 会议论文

  • 发表日期：

    2025年

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  • Manju Somanath,
  • V. A. Bindu,
  • Radhika Das

摘要

This research is an attempt to highlight the rarity of Cluster primes in the world of number systems. We will also look into the solution of an equation \(p^x+q^y=z^2\) where p and q are primes. This also assumes more significance when only a select few of the Cluster prime numbers are found eligible and satisfy the given equation. The paper is further corroborated by means of programming to delve into a bigger range of values which further substantiates the claim that a few cluster primes will go ahead and satisfy the said equation.