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 .” (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 |