Four hundred and ninety-six

The four hundred and ninety-six (496) is the natural number that follows the four hundred and ninety-five and precedes the four hundred and ninety-seven.

Mathematical properties

• It is a composite number, which has the following factors: 1, 2, 4, 8, 16, 31, 62, 124 and 248. As the sum of its factors is 496, it is a perfect number, after 28 and before 8128. It was one of the first perfect numbers discovered. As a perfect number, it is linked to the prime number of Mersenne 31, 2⁵ - One, two.⁴ (22)⁵ - 1) = 496. Also related to its characteristic as a perfect number, 496 is a harmonic divider, since the number of divisors of 496 divided by the sum of the reciprocals of these divisors, 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496, (harmonic means), is an integer, 5 in this case.

There is no solution to the equation φ(x)=496, which makes 496 non-right.

• It's 31.♪ triangular number, after 465 and before 528. That is why the smaller counter-example to the hypothesis that one more than a triangular pair number is a prime number.
• It is the 16th hexagonal number, after 435 and before 561.
• It's a nonagonal number centered.
• It's an 11-gonal number focused.
• It's the biggest happy number, less than 500.
• The real dimension of E8 is 496.

In physics

The number 496 is very important in superstring theory. In 1984, Michael Green and John H. Schwarz verified that one of the necessary conditions for this theory to make sense was that the dimension of the gauge group of Type I String Theory must be 496. The group is SO(32). This discovery promoted the first superstring revolution. In 1985 it was discovered that heterotic strings can admit other possible Gauge groups, properly [[E₈ x E₈]].