224 (number)

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224 (two hundred [and] twenty-four) is the natural number following 223 and preceding 225.

Contents

In mathematics

← 223 224 225 →
Cardinal two hundred twenty-four
Ordinal 224th
(two hundred twenty-fourth)
Factorization 25 × 7
Prime No
Greek numeral ΣΚΔ´
Roman numeral CCXXIV
Binary 111000002
Ternary 220223
Senary 10126
Octal 3408
Duodecimal 16812
Hexadecimal E016

224 is a practical number, [1] and a sum of two positive cubes 23 + 63. [2] It is also 23 + 33 + 43 + 53, making it one of the smallest numbers to be the sum of distinct positive cubes in more than one way. [3]

224 is the smallest k with λ(k) = 24, where λ(k) is the Carmichael function. [4]

The mathematician and philosopher Alex Bellos suggested in 2014 that a candidate for the lowest uninteresting number would be 224 because it was, at the time, "the lowest number not to have its own page on [the English-language version of] Wikipedia". [5] That distinction now belongs to 315.

In other areas

In the SHA-2 family of six cryptographic hash functions, the weakest is SHA-224, named because it produces 224-bit hash values. [6] It was defined in this way so that the number of bits of security it provides (half of its output length, 112 bits) would match the key length of two-key Triple DES. [7]

The ancient Phoenician shekel was a standardized measure of silver, equal to 224 grains, although other forms of the shekel employed in other ancient cultures (including the Babylonians and Hebrews) had different measures. [8] Likely not coincidentally, as far as ancient Burma and Thailand, silver was measured in a unit called a tikal, equal to 224 grains. [9]

See also

Related Research Articles

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References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA005153(Practical numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. ↑ Sloane, N. J. A. (ed.). "SequenceA003325(Numbers that are the sum of 2 positive cubes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  3. ↑ Sloane, N. J. A. (ed.). "SequenceA003998(Numbers that are a sum of distinct positive cubes in more than one way)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. ↑ Sloane, N. J. A. (ed.). "SequenceA141162(Smallest k such that lambda(k) = n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. ↑ Bellos, Alex (June 2014). The Grapes of Math: How Life Reflects Numbers and Numbers Reflect Life. illus. The Surreal McCoy (1st Simon & Schuster hardcover ed.). N.Y.: Simon & Schuster. pp. 238 & 319 (quoting p. 319). ISBN   978-1-4516-4009-0.
  6. ↑ "FIPS Publication 180-2 (with Change Notice 1): Announcing the Secure Hash Standard (+ Change Notice to Include SHA-224)" (PDF). NIST. February 25, 2004. Retrieved 2023-03-09.
  7. ↑ Housley, R. (September 2004). "RFC 3874: A 224-bit One-way Hash Function: SHA-224". Network Working Group. Retrieved 2023-03-09.
  8. ↑ Bratcher, Robert G. (October 1959). "Weights, Money, Measures and Time". The Bible Translator. 10 (4). {SAGE} Publications: 165–174. doi:10.1177/000608445901000404. S2CID   125756547.
  9. ↑ Cunningham, Alexander (1891). Coins of Ancient India: From the Earliest Times Down to the Seventh Century A.D. London: B. Quaritch. p. 4.
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