four hundred ninety-six

The third perfect number, four hundred ninety-six (496) has been known since antiquity. With just one larger perfect number known to him, Euclid was able to prove that all even perfect numbers are the productPlanetmathPlanetmath of a Mersenne primeMathworldPlanetmath and the nearest smaller power of two. In the case of 496, these are 31 and 16.

As a counterexample, 496 disproves Thomas Greenwood’s conjecture that an even triangular numberMathworldPlanetmath with a prime index is one less than a prime, since although 496 is the 31st triangular number, 497 is not a prime.

496 is an important number in physics, and specifically string theory. “The massless bosonic states in this theory consist of a symmetricPlanetmathPlanetmath rank two field, an anti-symmetric rank two field, a scalar field known as the dilaton and a set of 496 gauge fields filling up the adjoint representationMathworldPlanetmath of the gauge group E8×E8.” (Sen, 1998) This discovery of the importance of 496, by Michael Green and John Schwartz is credited with ushering in an era of important revelations in string theory.


  • 1 D. Wells The Dictionary of Curious and Interesting Numbers Suffolk: Penguin Books (1987): 155
  • 2 A. Sen “An Introduction to Non-perturbative String Theory” preprint
Title four hundred ninety-six
Canonical name FourHundredNinetysix
Date of creation 2013-03-22 17:10:51
Last modified on 2013-03-22 17:10:51
Owner CompositeFan (12809)
Last modified by CompositeFan (12809)
Numerical id 4
Author CompositeFan (12809)
Entry type Feature
Classification msc 11A99
Synonym four hundred and ninety-six