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Lemoine’s Conjecture: A Limited Solution Using Computers
  • Naren Dawar
Naren Dawar
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Abstract

This paper provides a limited solution for Lemoine’s conjecture that includes more numbers than previously found on record: 10^9. Lemoine’s conjecture, named after mathematician Émile Lemoine, states that all odd integers greater than 5 can be represented as the sum of an odd prime number and an even semiprime1. Using Python & C++, both popular programming languages often used for automating tasks and general programming, this conjecture can be proved for all values that fall under the criteria up to 10^10. The process of checking each number in Python utilizes math, a standard Python library, along with assisting functions, such as a prime number verification function.