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 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.
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 |