All Odd Numbers Are Prime — A Corollary
[Rescued from my old blog.]
Once again, Rudbeckia Hirta brings us some funny-but-sad mathematics. The test question was:
Without factoring it, explain how the number
N = (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11) + 1
can be used to argue that there is a prime number larger than 11.
Take a few minutes to think about how you would answer that. Okay, if you haven’t seen a similar proof before, you are allowed to take as many minutes as you need! Euclid’s famous proof of a closely-related theorem (The Infinitude of Primes) is featured in one of my favorite math-for-the-layman books, Journey through Genius: The Great Theorems of Mathematics.
And for those of you who haven’t heard the joke before, here is an extended list of reasons why all odd numbers are prime.