Legendre and His Formula: Speeding Up Factorial Calculations

Factorial calculations are a fundamental mathematical operation in computer science, commonly used in algorithms and equations. The factorial of a non-negative integer 'n' is defined as the product of all positive integers from 1 to 'n.' Computing factorials can be computationally expensive, especially for large values of 'n,' and optimizing this process is crucial in various applications.

One of the pioneers in this field was Adrien-Marie Legendre, an 18th-century French mathematician, renowned...