The p-1 method is a mathematical algorithm used for integer factorization, particularly effective for finding small factors of large numbers. It is based on the idea of using smooth numbers, which are integers that have only small prime factors. This method is often employed in cryptography and number theory to break down composite numbers into their prime components. Developed by John Pollard in the 1970s, the p-1 algorithm is particularly useful when the factors of a number are relatively close to each other. It works by selecting a base and performing calculations that involve modular arithmetic, making it a valuable tool in various applications, including RSA encryption.