Wilson's Theorem

Here's an interesting characterization of primes:

Wilson's Theorem. A number P is prime if and only if

Let's check:
(2-1)!+1 = 2, which is divisible by 2.
(5-1)!+1 = 25, which is divisible by 5.
(9-1)!+1 = 40321, which is not divisible by 9 (cast out nines to see this).

Pretty cool!

The Math Behind the Fact:
However it is not really practical to use this to test if a number is prime, especially if P is large: just try P=101, and you'll see what I mean! There are better primality tests available; you can learn about some of them in a number theory class. See also Fermat's Little Theorem.

How to Cite this Page:
Su, Francis E., et al. "Wilson's Theorem." Math Fun Facts. <http://www.math.hmc.edu/funfacts>.

Keywords:    number theory, primality test Subjects:    number theory Level:    Easy Fun Fact suggested by:   Jorge Aarao Suggestions? Use this form. 3.89 current rating Click to rate this Fun Fact...     *   Awesome! I totally dig it!     *   Fun enough to tell a friend!     *   Mildly interesting     *   Not really noteworthy and see the most popular Facts! Get the Math Fun Facts iPhone App!

Want another Math Fun Fact?

For more fun, tour the Mathematics Department at Harvey Mudd College!