224 (number)

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

In mathematics

← 223 224 225 →
Cardinaltwo hundred twenty-four
Ordinal224th
(two hundred twenty-fourth)
Factorization25 × 7
PrimeNo
Greek numeralΣΚΔ´
Roman numeralCCXXIV
Binary111000002
Ternary220223
Senary10126
Octal3408
Duodecimal16812
HexadecimalE016

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

References

  1. ^ Sloane, N. J. A. (ed.). "Sequence A005153 (Practical numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A003325 (Numbers that are the sum of 2 positive cubes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A003998 (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.). "Sequence A141162 (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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