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⚫ '''224''' ('''two hundred twenty-four''') is the natural number following ] and preceding ].
{{See also|Area codes 847 and 224|l1=Area code 224}}
⚫ 224 (Two Hundred Twenty Four) is the natural number following 223 and proceeding 225.


== In mathematics ==
{{Infobox number
| number = 224
| prime = No
}}


224 is a ],<ref>{{Cite OEIS|A005153|name=Practical numbers}}</ref>
and a sum of two positive cubes {{nowrap|2<sup>3</sup> + 6<sup>3</sup>}}.<ref>{{Cite OEIS|A003325|Numbers that are the sum of 2 positive cubes}}</ref> It is also {{nowrap|2<sup>3</sup> + 3<sup>3</sup> + 4<sup>3</sup> + 5<sup>3</sup>}}, making it one of the smallest numbers to be the sum of distinct positive cubes in more than one way.<ref>{{cite OEIS|A003998|Numbers that are a sum of distinct positive cubes in more than one way}}</ref>


224 is the smallest ''k'' with λ(''k'') = 24, where λ(''k'') is the ].<ref>{{Cite OEIS|A141162|name=Smallest k such that lambda(k) = n}}</ref>


The mathematician and philosopher ] suggested in 2014 that a candidate for the lowest ] would be 224 because it was, at the time, "the lowest number not to have its own page on ]".<ref>{{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}}</ref> That distinction now belongs to ].


== In Mathematics == == In other areas ==
In the ] family of six ]s, the weakest is SHA-224, named because it produces 224-bit hash values.<ref>{{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}}</ref> 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 ].<ref>{{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}}</ref>
224 =2<sup>5</sup>·7


The ancient Phoenician ] was a standardized measure of ], equal to 224 grains, although other forms of the shekel employed in other ancient cultures (including the Babylonians and Hebrews) had different measures.<ref>{{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 }}</ref> Likely not coincidentally, as far as ancient ] and ], silver was measured in a unit called a ''tikal'', equal to 224 grains.<ref>{{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}}</ref>
The sum of its prime factors is 17 (9 counting only distinct numbers)


==See also==
224 is non-trivially palindromic in base 3 and 15
*]


==References==
224 is the sum of 2 cubes:
{{Reflist}}


{{Integers|2}}
224 = 23 + 63
224 is the sum of the cubes of 4 consecutive integers:


]
224 = 23 + 33 + 43 + 53


{{Num-stub}}
== In Popular Culture ==
224 is renowned for being the smallest number without a Misplaced Pages page. It is the first number user CPU502 changed on their route to add Misplaced Pages articles for every number <1000.

Latest revision as of 17:25, 27 August 2024

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

In mathematics

Natural number
← 223 224 225 →
← 220 221 222 223 224 225 226 227 228 229 → ← 0 100 200 300 400 500 600 700 800 900 →
Cardinaltwo hundred twenty-four
Ordinal224th
(two hundred twenty-fourth)
Factorization2 × 7
PrimeNo
Greek numeralΣΚΔ´
Roman numeralCCXXIV
Binary111000002
Ternary220223
Senary10126
Octal3408
Duodecimal16812
HexadecimalE016

224 is a practical number, and a sum of two positive cubes 2 + 6. It is also 2 + 3 + 4 + 5, making it one of the smallest numbers to be the 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.

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 Misplaced Pages". 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. 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.

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. Likely not coincidentally, as far as ancient Burma and Thailand, silver was measured in a unit called a tikal, equal to 224 grains.

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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