# Fast Factorial Algorithms

> Source: <http://www.luschny.de/math/factorial/FastFactorialFunctions.htm>
> Published: 2026-05-20 03:55:58+00:00

There are five algorithms which everyone who wants to compute the factorial n! = 1.2.3...n should know.
BigInt recfact(long start, long n) { long i; if (n <= 16) { BigInt r = new BigInt(start); for (i = start + 1; i < start + n; i++) r *= i; return r; } i = n / 2; return recfact(start, i) * recfact(start + i, n - i); } BigInt factorial(long n) { return recfact(1, n); }
An example of a PrimeSwing computation:
As this example shows an efficient computation of the factorial function reduces to an efficient computation of the swinging factorial n≀. Some information about these numbers can be found here and here. The prime factorization of the swing numbers is crucial for the implementation of the PrimeSwing algorithm.
A concise description of this algorithm is given in this write-up (pdf) and in the SageMath link below (Algo 5).
Fast-Factorial-Functions: The Homepage of Factorial Algorithms. (C) Peter Luschny, 2000-2017. All information and all source code in this directory is free under the Creative Commons Attribution-ShareAlike 3.0 Unported License. This page is listed on the famous "Dictionary of Algorithms and Data Structures" at the National Institute of Standards and Technology's web site (NIST). Apr. 2003 / Apr. 2017 : 800,000 visitors! Thank you!