The P-1 algorithm is a method used in number theory, particularly for finding large prime factors of composite numbers. It is based on the idea of using smooth numbers, which are integers that have only small prime factors, to help identify potential factors of a given number. The algorithm is efficient for numbers with specific properties, making it a useful tool in computational mathematics. Developed by John Pollard in 1974, the P-1 algorithm is often employed in cryptography and computer science, especially in the context of factoring large integers. Its effectiveness increases when the number being factored has prime factors that are close to each other, allowing for quicker computations and results.