Four hundred and ninety-six is the natural number following four hundred and ninety-five and preceding four hundred and ninety-seven. Natural number can mean either a positive integer (1, 2, 3, 4, ...) or a non-negative integer (0, 1, 2, 3, 4, ...). Natural numbers have two main purposes: they can be used for counting (there are 3 apples on the table), or they can be used for ordering (this is...

496
Cardinal	496
Ordinal	496th
Factorization
Roman numeral	CDXCVI
Binary	111110000
Hexadecimal	1F0

496 is most notable for being a perfect number, and one of the earliest numbers to be recognized as such. As a perfect number, it is tied to the Mersenne prime 31, 2⁵ - 1, with 2⁴ ( 2⁵ - 1 ) yielding 496. Also related to its being a perfect number, 496 is a harmonic divisor number, since 496 divided by the sum of the reciprocals of its divisors, 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496, (the harmonic mean), yields an integer, 5 in this case. In linguistics, cardinal numbers is the name given to number words that are used for quantity (one, two, three), as opposed to ordinal numbers, words that are used for order (first, second, third). ... Commonly, ordinal numbers, or ordinals for short, are numbers used to denote the position in an ordered sequence: first, second, third, fourth, etc. ... This article is about the mathematical concept. ... The system of Roman numerals is a numeral system originating in ancient Rome, and was adapted from Etruscan numerals. ... The binary or base-two numeral system is a system for representing numbers in which a radix of two is used; that is, each digit in a binary numeral may have either of two different values. ... In mathematics and computer science, hexadecimal or simply hex is a numeral system with a radix or base of 16 usually written using the symbols 0–9 and A–F or a–f. ... In mathematics, a perfect number is defined as an integer which is the sum of its proper positive divisors, excluding itself. ... In mathematics, a Mersenne prime is a prime number that is one less than a power of two. ... 31 is the natural number following 30 and preceding 32. ... A harmonic divisor number, or Ore number, is a number whose divisors, averaged in a harmonic mean, results in an integer. ... In mathematics, the harmonic mean is one of several methods of calculating an average. ...

A triangular number and a hexagonal number, 496 is also a centered nonagonal number and a centered 11-gonal number. Being the 31st triangular number, 496 is the smallest counterexample to the hypothesis that one more than an even indexed triangular number is a prime. A triangular number is a number that can be arranged in the shape of an equilateral triangle. ... A hexagonal number is a figurate number that represents a hexagon. ... A centered nonagonal number is a centered figurate number that represents a nonagon with a dot in the center and all other dots surrounding the center dot in successive nonagonal layers. ...

There is no solution to the equation φ(x) = 496, making 496 a nontotient. In number theory, the totient φ(n) of a positive integer n is defined to be the number of positive integers less than or equal to n and coprime to n. ... A nontotient is a positive integer n which is not in the range of Eulers totient function φ, that is, for which φ(x) = n has no solution. ...

The number 496 is a very important number in superstring theory. In 1984 (which incidentally equals four times 496), Michael Green and John Schwarz realized that one of the necessary conditions for a superstring theory to make sense is that the dimension of the gauge group of type I string theory must be 496. The group is therefore SO(32). Their discovery started the first superstring revolution. It was realized in 1985 that the heterotic string can admit another possible gauge group, namely E₈ x E₈. Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. ... 1984 is a leap year starting on Sunday of the Gregorian calendar. ... John Schwarz is one of the fathers of string theory. ... This article is being considered for deletion in accordance with Wikipedias deletion policy. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In theoretical physics, type I string theory is one of five consistent supersymmetric string theories in ten dimensions. ... In mathematics, the orthogonal group of degree n over a field F (written as O(n,F)) is the group of n-by-n orthogonal matrices with entries from F, with the group operation that of matrix multiplication. ... In physics, the first superstring revolution is a period of important discoveries in string theory roughly between 1984 and 1986. ... 1985 is a common year starting on Tuesday of the Gregorian calendar. ... In physics, a heterotic string is a peculiar mixture (or hybrid) of the bosonic string and the superstring (the adjective heterotic comes from the Greek word heterosis). ... In mathematics, E8 is the name of a Lie group and also its Lie algebra . ...

See also: four hundred Four hundred is the natural number following three hundred ninety-nine and preceding four hundred one. ...

For the year AD, see 496. Events Battle of Tolbiac; Clovis I defeats the Alamanni accepts Catholic baptism at Reims. ...