Primality Testing
Primality testing is a computational method used to determine whether a given integer is a prime number (divisible only by 1 and itself) or a composite number. It involves algorithms that check for primality, ranging from simple trial division for small numbers to sophisticated probabilistic and deterministic tests for large integers. This concept is fundamental in number theory, cryptography, and computer science for applications like generating secure keys in encryption systems.
Developers should learn primality testing when working in cryptography, security, or algorithm design, as it is essential for implementing encryption schemes like RSA that rely on large prime numbers. It is also crucial in competitive programming, mathematical computing, and any domain requiring efficient number factorization or prime generation, such as in hash functions or random number generation. Understanding these tests helps optimize performance and ensure correctness in systems handling sensitive data.