496 (four hundred ndninety-six) is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called '' cardinal ...

following

495 __NOTOC__ Year 495 (Roman numerals, CDXCV) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Viator without colleague (or, less frequen ...

and preceding

497 __NOTOC__ Year 497 ( CDXCVII) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Anastasius without colleague (or, less frequently, y ...

In mathematics

496 is most notable for being a

perfect number In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is 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 In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17 ...

31, 2⁵ − 1, with 2⁴ (2⁵ − 1) yielding 496. Also related to its being a perfect number, 496 is a

harmonic divisor number In mathematics, a harmonic divisor number, or Ore number (named after Øystein Ore who defined it in 1948), is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are: : 1, 6, 28, ...

, since the number of proper divisors of 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 In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for situations when the average rate is desired. The harmonic mean can be expressed as the recipro ...

), yields an integer, 5 in this case. A

triangular number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots i ...

and a hexagonal number, 496 is also a

centered nonagonal number A centered nonagonal number (or centered enneagonal 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. The centered nonagonal ...

. Being the 31st triangular number, 496 is the smallest counterexample to the hypothesis that one more than an even triangular prime-indexed number is a

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

. It is the largest happy number less than 500. There is no solution to the equation φ(''x'') = 496, making 496 a nontotient. ''E''₈ has real dimension 496.

In physics

The number 496 is a very important number in superstring theory. In 1984, Michael Green and John H. Schwarz realized that one of the necessary conditions for a superstring theory to make sense is that the

dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...

of the gauge group of

type I string theory In theoretical physics, type I string theory is one of five consistent supersymmetric string theories in ten dimensions. It is the only one whose strings are unoriented (both orientations of a string are equivalent) and the only one which contain ...

must be 496. The group is therefore SO(32). Their discovery started the

first superstring revolution The history of string theory spans several decades of intense research including two superstring revolutions. Through the combined efforts of many researchers, string theory has developed into a broad and varied subject with connections to quantu ...

. It was realized in 1985 that the

heterotic string In string theory, a heterotic string is a closed string (or loop) which is a hybrid ('heterotic') of a superstring and a bosonic string. There are two kinds of heterotic string, the heterotic SO(32) and the heterotic E8 × E8, abbrevi ...

can admit another possible gauge group, namely E₈ x E₈.

Telephone numbers

The UK's

Ofcom The Office of Communications, commonly known as Ofcom, is the government-approved regulatory and competition authority for the broadcasting, telecommunications and postal industries of the United Kingdom. Ofcom has wide-ranging powers acros ...

reserves telephone numbers in many dialing areas in the 496 local block for fictional purposes, such as 0114 496-1234.

References

{{Integers, 4 Integers

In mathematics

In physics

Telephone numbers

See also

References