Here’s an interesting characterization of primes:<\/p>\n\n\n\n
Wilson’s Theorem. A number P is prime if and only if<\/p>\n\n\n\n
(P-1)! + 1 is divisible by P.<\/p>\n\n\n\n
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).<\/p>\n\n\n\n
Pretty cool!<\/p>\n\n\n\n
The Math Behind the Fact:<\/strong> How to Cite this Page:<\/strong> Fun Fact suggested by: <\/strong> Here’s an interesting characterization of primes: Wilson’s Theorem. A number P is prime if and only if (P-1)! + 1...<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[3,10,103,49],"class_list":["post-287","page","type-page","status-publish","hentry","tag-easy","tag-numtheory","tag-primality-test","tag-prime"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/287","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/comments?post=287"}],"version-history":[{"count":4,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/287\/revisions"}],"predecessor-version":[{"id":1705,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/287\/revisions\/1705"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=287"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=287"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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.<\/p>\n\n\n\n
Su, Francis E., et al. “Wilson’s Theorem.” Math Fun Facts<\/em>. <http:\/\/www.math.hmc.edu\/funfacts>.<\/p>\n\n\n\n
Jorge Aarao <\/p>\n","protected":false},"excerpt":{"rendered":"