224 (two hundred [and] twenty-four) is the natural number following 223 and preceding 225.
In mathematics
edit
| ||||
|---|---|---|---|---|
| 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
editIn 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
editReferences
edit- ^ Sloane, N. J. A. (ed.). "Sequence A005153 (Practical numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A141162 (Smallest k such that lambda(k) = n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ "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.
- ^ Housley, R. (September 2004). "RFC 3874: A 224-bit One-way Hash Function: SHA-224". Network Working Group. Retrieved 2023-03-09.
- ^ 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.
- ^ 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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