# 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 product^{} of a Mersenne prime^{} 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 number^{} 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 symmetric^{} 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 representation^{} of the gauge group ${E}_{8}\times {E}_{8}$.” (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.

## References

- 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” http://arxiv.org/abs/hep-th/9802051v1ArXiv 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 |