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224 (number)
224 (two hundred ndtwenty-four) is the natural number following 223 and preceding 225. In mathematics 224 is a practical number, and a sum of two positive cubes . It is also , 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 he English-language version ofWikipedia". 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
223 (number)
223 (two hundred ndtwenty-three) is the natural number following 222 and preceding 224. In mathematics 223 is a prime number. Among the 720 permutations of the numbers from 1 to 6, exactly 223 of them have the property that at least one of the numbers is fixed in place by the permutation and the numbers less than it and greater than it are separately permuted among themselves. In connection with Waring's problem, 223 requires the maximum number of terms (37 terms) when expressed as a sum of positive fifth powers, and is the only number that requires that many terms. In other fields * .223 (other), the caliber of several firearm cartridges * The years 223 and 223 BC __NOTOC__ Year 223 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Flaminus and Philus (or, less frequently, year 531 '' Ab urbe condita''). The denomination 223 BC for this year has bee ... * The number of synodic months of a Saros Referen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
225 (number)
225 (two hundred ndtwenty-five) is the natural number following 224 and preceding 226. In mathematics 225 is the smallest number that is a polygonal number in five different ways. It is a square number , an octagonal number, and a squared triangular number . As the square of a double factorial, counts the number of permutations of six items in which all cycles have even length, or the number of permutations in which all cycles have odd length. And as one of the Stirling numbers of the first kind, it counts the number of permutations of six items with exactly three cycles. 225 is a highly composite odd number, meaning that it has more divisors than any smaller odd numbers. After 1 and 9, 225 is the third smallest number ''n'' for which , where ''σ'' is the sum of divisors function and ''φ'' is Euler's totient function. 225 is a refactorable number. 225 is the smallest square number to have one of every digit in some number base (225 is 3201 in base 4) 225 is the fir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Practical Number
In number theory, a practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of n. For example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its divisors 1, 2, 3, 4, and 6: as well as these divisors themselves, we have 5 = 3 + 2, 7 = 6 + 1, 8 = 6 + 2, 9 = 6 + 3, 10 = 6 + 3 + 1, and 11 = 6 + 3 + 2. The sequence of practical numbers begins Practical numbers were used by Fibonacci in his Liber Abaci (1202) in connection with the problem of representing rational numbers as Egyptian fractions. Fibonacci does not formally define practical numbers, but he gives a table of Egyptian fraction expansions for fractions with practical denominators.. The name "practical number" is due to . He noted that "the subdivisions of money, weights, and measures involve numbers like 4, 12, 16, 20 and 28 which are usually supposed to be so inconvenient as to dese ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carmichael Function
In number theory, a branch of mathematics, the Carmichael function of a positive integer is the smallest positive integer such that :a^m \equiv 1 \pmod holds for every integer coprime to . In algebraic terms, is the exponent of the multiplicative group of integers modulo . The Carmichael function is named after the American mathematician Robert Carmichael who defined it in 1910. It is also known as Carmichael's λ function, the reduced totient function, and the least universal exponent function. The following table compares the first 36 values of with Euler's totient function (in bold if they are different; the s such that they are different are listed in ). Numerical examples # Carmichael's function at 5 is 4, , because for any number 0 |
Alex Bellos
Alexander Bellos (born 1969) is a British writer, broadcaster and mathematics communicator.Alex Bellos He is the author of books about Brazil and mathematics, as well as having a column in ''The Guardian'' newspaper. Education and early life Alex Bellos was born in Oxford and grew up in Edinburgh and Southampton. He was educated at Hampton Park Comprehensive School and Richard Taunton Sixth Form College in Southampton. He went on to study mathematics and philosophy at Corpus Christi College, Oxford, where he was the editor of the student paper ''Cherwell''. Career Bellos's first job was working for '' The Argus'' in Brighton before moving to ''The Guardian'' in London. From 1998 to 2003 he was South America correspondent of ''The Guardian'', and wrote ''Futebol: the Brazilian Way of Life''. The book was well received in the UK, where it was nominated for sports book of the year at the British Book Awards. In the US, it was included as one of '' Publishers Weekly's'' books ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interesting Number Paradox
The interesting number paradox is a humorous paradox which arises from the attempt to classify every natural number as either "interesting" or "uninteresting". The paradox states that every natural number is interesting. The " proof" is by contradiction: if there exists a non-empty set of uninteresting natural numbers, there would be a smallest uninteresting number – but the smallest uninteresting number is itself interesting because it is the smallest uninteresting number, thus producing a contradiction. "Interestingness" concerning numbers is not a formal concept in normal terms, but an innate notion of "interestingness" seems to run among some number theorists. Famously, in a discussion between the mathematicians G. H. Hardy and Srinivasa Ramanujan about interesting and uninteresting numbers, Hardy remarked that the number 1729 of the taxicab he had ridden seemed "rather a dull one", and Ramanujan immediately answered that it is interesting, being the smallest number that is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English Wikipedia
The English Wikipedia is, along with the Simple English Wikipedia, one of two English-language editions of Wikipedia, an online encyclopedia. It was founded on January 15, 2001, as Wikipedia's first edition, and, as of , has the most articles of any edition, at . As of , of articles in all Wikipedias belong to the English-language edition; this share was more than 50% in 2003. The edition's one-billionth edit was made on January 13, 2021. Articles The English Wikipedia has pioneered some ideas as conventions, policies or features which were later adopted by Wikipedia editions in some of the other languages. These ideas include "featured articles", the neutral-point-of-view policy, navigation templates, the sorting of short "stub" articles into sub-categories, dispute resolution mechanisms such as mediation and arbitration, and weekly collaborations. It surpassed six million articles on 23 January 2020. In November 2022, the total volume of the compressed texts of it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SHA-2
SHA-2 (Secure Hash Algorithm 2) is a set of cryptographic hash functions designed by the United States National Security Agency (NSA) and first published in 2001. They are built using the Merkle–Damgård construction, from a one-way compression function itself built using the Davies–Meyer structure from a specialized block cipher. SHA-2 includes significant changes from its predecessor, SHA-1. The SHA-2 family consists of six hash functions with digests (hash values) that are 224, 256, 384 or 512 bits: SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224, SHA-512/256. SHA-256 and SHA-512 are novel hash functions computed with eight 32-bit and 64-bit words, respectively. They use different shift amounts and additive constants, but their structures are otherwise virtually identical, differing only in the number of rounds. SHA-224 and SHA-384 are truncated versions of SHA-256 and SHA-512 respectively, computed with different initial values. SHA-512/224 and SHA-512/256 are also trunca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptographic Hash Function
A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with fixed size of n bits) that has special properties desirable for cryptography: * the probability of a particular n-bit output result (hash value) for a random input string ("message") is 2^ (like for any good hash), so the hash value can be used as a representative of the message; * finding an input string that matches a given hash value (a ''pre-image'') is unfeasible, unless the value is selected from a known pre-calculated dictionary (" rainbow table"). The ''resistance'' to such search is quantified as security strength, a cryptographic hash with n bits of hash value is expected to have a ''preimage resistance'' strength of n bits. A ''second preimage'' resistance strength, with the same expectations, refers to a similar problem of finding a second message that matches the given hash value when one message is already known; * finding any pair of different messa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triple DES
In cryptography, Triple DES (3DES or TDES), officially the Triple Data Encryption Algorithm (TDEA or Triple DEA), is a symmetric-key block cipher, which applies the DES cipher algorithm three times to each data block. The Data Encryption Standard's (DES) 56-bit key is no longer considered adequate in the face of modern cryptanalytic techniques and supercomputing power. A CVE released in 2016, CVE-2016-2183' disclosed a major security vulnerability in DES and 3DES encryption algorithms. This CVE, combined with the inadequate key size of DES and 3DES, NIST has deprecated DES and 3DES for ''new'' applications in 2017, and for ''all'' applications by the end of 2023. It has been replaced with the more secure, more robust AES. While the government and industry standards abbreviate the algorithm's name as TDES (Triple DES) and TDEA (Triple Data Encryption Algorithm), RFC 1851 referred to it as 3DES from the time it first promulgated the idea, and this namesake has since come into wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shekel
Shekel or sheqel ( akk, 𒅆𒅗𒇻 ''šiqlu'' or ''siqlu,'' he, שקל, plural he, שקלים or shekels, Phoenician: ) is an ancient Mesopotamian coin, usually of silver. A shekel was first a unit of weight—very roughly —and became currency in ancient Tyre and ancient Carthage and then in ancient Israel under the Maccabees. Name The word is based on the Semitic verbal root for "weighing" (''Š-Q-L''), cognate to the Akkadian or , a unit of weight equivalent to the Sumerian . Use of the word was first attested in during the Akkadian Empire under the reign of Naram-Sin, and later in in the Code of Hammurabi. The ''Š-Q-L'' root is found in the Hebrew words for "to weigh" (), "weight" () and "consideration" (). It is cognate to the Aramaic root ''T-Q-L'' and the Arabic ''root Θ-Q-L'' ''ثقل'', in words such as (the weight), (heavy) or (unit of weight). The famous writing on the wall in the Biblical Book of Daniel includes a cryptic use of the word in Aram ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Silver
Silver is a chemical element with the Symbol (chemistry), symbol Ag (from the Latin ', derived from the Proto-Indo-European wikt:Reconstruction:Proto-Indo-European/h₂erǵ-, ''h₂erǵ'': "shiny" or "white") and atomic number 47. A soft, white, lustrous transition metal, it exhibits the highest electrical conductivity, thermal conductivity, and reflectivity of any metal. The metal is found in the Earth's crust in the pure, free elemental form ("native silver"), as an alloy with gold and other metals, and in minerals such as argentite and chlorargyrite. Most silver is produced as a byproduct of copper, gold, lead, and zinc Refining (metallurgy), refining. Silver has long been valued as a precious metal. Silver metal is used in many bullion coins, sometimes bimetallism, alongside gold: while it is more abundant than gold, it is much less abundant as a native metal. Its purity is typically measured on a per-mille basis; a 94%-pure alloy is described as "0.940 fine". As one of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
