496 (number)
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|---|---|---|---|---|
| Cardinal | four hundred ninety-six | |||
| Ordinal | 496th (four hundred ninety-sixth) | |||
| Factorization | 24 × 31 | |||
| Divisors | 1, 2, 4, 8, 16, 31, 62, 124, 248, 496 | |||
| Greek numeral | ΥϞϚ´ | |||
| Roman numeral | CDXCVI, cdxcvi | |||
| Binary | 1111100002 | |||
| Ternary | 2001013 | |||
| Senary | 21446 | |||
| Octal | 7608 | |||
| Duodecimal | 35412 | |||
| Hexadecimal | 1F016 | |||
496 (four hundred [and] ninety-six) is the natural number following 495 and preceding 497.
In mathematics
[edit]496 is most notable for being the third perfect number,[1][2] and one of the earliest numbers to be recognized as such; its factors (1, 2, 4, 8, 16, 31, 62, 124, 248) sum to 496.[3]
It is also a triangular and a hexagonal number. and a centered nonagonal number.[3][4] Being the 31st triangular number,[3] 496 is the smallest counterexample to the hypothesis that one more than an even triangular prime-indexed number is a prime number. It is the largest happy number less than 500.[5]
496 is also a harmonic divisor number.[6]
The group E8 has real dimension 496.
In physics
[edit]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 of the gauge group of type I string theory must be 496. The group is therefore SO(32).[7] 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.[citation needed]
Telephone numbers
[edit]The UK's Ofcom reserves telephone numbers in many dialing areas in the 496 local block for fictional purposes, such as 0114 496-1234.[8]
See also
[edit]References
[edit]- ↑ "What's Special About This Number?". erich-friedman.github.io. Retrieved 2026-08-03.
- ↑ "A000396 - OEIS". oeis.org. Retrieved 2026-08-03.
- 1 2 3 Vanovschi, Vitalii. "Properties of the number 496". www.numberempire.com. Retrieved 2026-07-22.
- ↑ "Centered 9-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-16.
- ↑ Sloane, N. J. A. (ed.). "Sequence A007770 (Happy numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ↑ Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers: numbers k such that the harmonic mean of the divisors of k is an integer.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2026-08-02.
- ↑ "Mosaic". Mosaic. 17 (4): 30. 1986. Retrieved 2026-08-03.
- ↑ "Fake Number Ranges: Here are the numbers reserved exclusively for TV & Radio shows". NUM3ER Supermarket. 6 September 2018. Retrieved 2022-08-16.
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