"how numbers are stored and used in computers"
Prime factorization is the process of expressing a number as a product of prime numbers. For example, the prime factorization of
Prime factorization is a crucial concept in number theory and cryptography, which often involves the decomposition of a composite number into a product of prime numbers. There are several algorithms designed to perform prime factorization, each with its own strengths and weaknesses.
Divide the number by all integers up to its square root. Simple but inefficient for large numbers.
Adapted for factorization by precomputing primes up to a limit to divide the number.
Probabilistic and effective for small factors.
Uses the difference of two squares. Effective for factors near the square root.
Fast for numbers up to 100 digits using sieving and linear algebra.
Most efficient for very large numbers over 100 digits.
Uses elliptic curves for small to medium factors. Similar time complexity to Pollard's Rho, and often more efficient.