224 (number)
In mathematics
{{Infobox number
| number = 224
| prime = No
}}
224 is a practical number,{{Cite OEIS|A005153|name=Practical numbers}}
and a sum of two positive cubes {{nowrap|23 + 63}}.{{Cite OEIS|A003325|Numbers that are the sum of 2 positive cubes}} It is also {{nowrap|23 + 33 + 43 + 53}}, making it one of the smallest numbers to be the sum of distinct positive cubes in more than one way.{{cite OEIS|A003998|Numbers that are a sum of distinct positive cubes in more than one way}}
224 is the smallest k with λ(k) = 24, where λ(k) is the Carmichael function.{{Cite OEIS|A141162|name=Smallest k such that lambda(k) = n}}
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".{{Cite book|last=Bellos|first=Alex|others=illus. The Surreal McCoy|date=June 2014|title=The Grapes of Math: How Life Reflects Numbers and Numbers Reflect Life|edition=1st Simon & Schuster hardcover|publisher=Simon & Schuster|publication-place=N.Y.|at=pp. 238 & 319 (quoting p. 319)|isbn=978-1-4516-4009-0}} 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.{{cite web|title = FIPS Publication 180-2 (with Change Notice 1): Announcing the Secure Hash Standard (+ Change Notice to Include SHA-224)|date=February 25, 2004|publisher=NIST|url=https://csrc.nist.gov/csrc/media/publications/fips/180/2/archive/2002-08-01/documents/fips180-2withchangenotice.pdf|access-date=2023-03-09}} 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.{{cite web|url=https://datatracker.ietf.org/doc/html/rfc3874|title=RFC 3874: A 224-bit One-way Hash Function: SHA-224|first=R.|last=Housley|publisher=Network Working Group|date=September 2004|access-date=2023-03-09}}
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.{{cite journal | last = Bratcher | first = Robert G. | date = October 1959 | doi = 10.1177/000608445901000404 | issue = 4 | journal = The Bible Translator | pages = 165–174 | publisher = {SAGE} Publications | title = Weights, Money, Measures and Time | volume = 10| s2cid = 125756547 }} Likely not coincidentally, as far as ancient Burma and Thailand, silver was measured in a unit called a tikal, equal to 224 grains.{{cite book|title=Coins of Ancient India: From the Earliest Times Down to the Seventh Century A.D.|first=Alexander|last=Cunningham|url=https://archive.org/details/coinsancientind00cunngoog|publisher=B. Quaritch|location=London|year=1891|page=4}}