docs/refactor: clean check_prime.cpp variable names and guidelines

[yasmeenMohammed]

Refactored check_prime.cpp to fully align with the repository's modern contribution guidelines.

Key Enhancements:

• Variable Renaming: Eliminated short/single-letter variables (num, i) and replaced them with descriptive alternatives (number, factor) for clear code quality.
• Documentation Fix: Corrected an accuracy error in the file comments regarding prime number distribution (corrected even primes distribution description to odd primes).
• Complexity Tracking: Injected explicit Doxygen annotations detailing the Time Complexity of $O(\sqrt{N})$ and Space Complexity of $O(1)$.
• Assertion Scaling: Enhanced the local testing framework by introducing missing boundary conditions like checking for 0.

Closes part of #2456