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11 (number)
11 (eleven) is the natural number following 10 and preceding 12 (number), 12. It is the smallest number whose name has three syllables. Name "Eleven" derives from the Old English ', which is first attested in Bede's late 9th-century ''Ecclesiastical History of the English People''. It has cognates in every Germanic language (for example, German ), whose Proto-Germanic language, Proto-Germanic ancestor has been linguistic reconstruction, reconstructed as , from the prefix (adjectival "1 (number), one") and suffix , of uncertain meaning. It is sometimes compared with the Lithuanian language, Lithuanian ', though ' is used as the suffix for all numbers from 11 to 19. The Old English form has closer cognates in Old Frisian, Old Saxon, Saxon, and Old Norse, Norse, whose ancestor has been reconstructed as . This was formerly thought to be derived from Proto-Germanic ("10 (number), ten"); it is now sometimes connected with or ("left; remaining"), with the implicit meaning that "one is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proto-Germanic Language
Proto-Germanic (abbreviated PGmc; also called Common Germanic) is the reconstructed proto-language of the Germanic branch of the Indo-European languages. Proto-Germanic eventually developed from pre-Proto-Germanic into three Germanic branches during the fifth century BC to fifth century AD: West Germanic, East Germanic and North Germanic. North Germanic remained in contact with the other branches over a considerable time, especially with the Ingvaeonic languages (including English), which arose from West Germanic dialects, and had remained in contact with the Norse. A defining feature of Proto-Germanic is the completion of the process described by Grimm's law, a set of sound changes that occurred between its status as a dialect of Proto-Indo-European and its gradual divergence into a separate language. The end of the Common Germanic period is reached with the beginning of the Migration Period in the fourth century AD. The alternative term " Germanic parent langua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brocard's Problem
Brocard's problem is a problem in mathematics that seeks integer values of n such that n!+1 is a perfect square, where n! is the factorial. Only three values of n are known — 4, 5, 7 — and it is not known whether there are any more. More formally, it seeks pairs of integers n and m such thatn!+1 = m^2.The problem was posed by Henri Brocard in a pair of articles in 1876 and 1885, and independently in 1913 by Srinivasa Ramanujan. Brown numbers Pairs of the numbers (n,m) that solve Brocard's problem were named Brown numbers by Clifford A. Pickover in his 1995 book ''Keys to Infinity'', after learning of the problem from Kevin S. Brown. As of October 2022, there are only three known pairs of Brown numbers: based on the equalities Paul Erdős conjectured that no other solutions exist. Computational searches up to one quadrillion have found no further solutions. Connection to the abc conjecture It would follow from the abc conjecture ABC are the first three letter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mersenne Prime
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If is a composite number then so is . Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form for some prime . The exponents which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, ... and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... . Numbers of the form without the primality requirement may be called Mersenne numbers. Sometimes, however, Mersenne numbers are defined to have the additional requirement that should be prime. The smallest composite Mersenne number with prime exponent ''n'' is . Mersenne primes were studied in antiquity because of their close connection to perfect numbers: the Euclid–Eule ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sexy Prime
In number theory, sexy primes are prime numbers that differ from each other by . For example, the numbers and are a pair of sexy primes, because both are prime and 11 - 5 = 6. The term "sexy prime" is a pun stemming from the Latin word for six: . If or (where is the lower prime) is also prime, then the sexy prime is part of a prime triplet. In August 2014, the Polymath group, seeking the proof of the twin prime conjecture, showed that if the generalized Elliott–Halberstam conjecture is proven, one can show the existence of infinitely many pairs of consecutive primes that differ by at most 6 and as such they are either twin, cousin A cousin is a relative who is the child of a parent's sibling; this is more specifically referred to as a first cousin. A parent of a first cousin is an aunt or uncle. More generally, in the kinship system used in the English-speaking world, ... or sexy primes. The sexy primes (sequences and in OEIS) below 500 are: :(5,11), (7,13) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
13 (number)
13 (thirteen) is the natural number following 12 (number), 12 and preceding 14 (number), 14. Folklore surrounding the number 13 appears in many cultures around the world: one theory is that this is due to the cultures employing lunar-solar calendars (there are approximately 12.41 lunations per solar year, and hence 12 "true months" plus a smaller, and often portentous, thirteenth month). This can be witnessed, for example, in the "Twelve Days of Christmas" of Western European tradition. In mathematics The number 13 is a prime number, happy number and a lucky number. It is a twin prime with 11 (number), 11, as well as a cousin prime with 17 (number), 17. It is the second of only 3 Wilson prime, Wilson primes: 5, 13, and 563 (number), 563. A 13-sided regular polygon is called a tridecagon. List of basic calculations In languages Grammar * In all Germanic languages, 13 is the first Compound (linguistics), compound number; the numbers 11 and 12 have their own names. * The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Twin Prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime'' is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Twin primes become increasingly rare as one examines larger ranges, in keeping with the general tendency of gaps between adjacent primes to become larger as the numbers themselves get larger. However, it is unknown whether there are infinitely many twin primes (the so-called twin prime conjecture) or if there is a largest pair. The breakthrough work of Yitang Zhang in 2013, as well as work by James Maynard, Terence Tao and others, has made substantial progress towards proving that there are infinitely many twin primes, but at present this remains unsolved. Properties Usually the pair is not considered to be a pair of twin primes. Since 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. In other words, if prime numbers are matched with ordinal numbers, starting with prime number 2 matched with ordinal number 1, then the primes matched with prime ordinal numbers are the super-primes. The subsequence begins :3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, 179, 191, 211, 241, 277, 283, 331, 353, 367, 401, 431, 461, 509, 547, 563, 587, 599, 617, 709, 739, 773, 797, 859, 877, 919, 967, 991, ... . That is, if ''p''(''n'') denotes the ''n''th prime number, the numbers in this sequence are those of the form ''p''(''p''(''n'')). In 1975, Robert Dressler and Thomas Parker used a computer-aided proof (based on calculations involving the subset sum problem) to show that every integer greater than 96 may be represented as a sum of distinct super-prime numbers. Their proof ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
10 (number)
10 (ten) is the even natural number following 9 and preceding 11. Ten is the base of the decimal numeral system, the most common system of denoting numbers in both spoken and written language. Name The number "ten" originates from the Proto-Germanic root "*tehun", which in turn comes from the Proto-Indo-European root "*dekm-", meaning "ten". This root is the source of similar words for "ten" in many other Germanic languages, like Dutch, German, and Swedish. The use of "ten" in the decimal system is likely due to the fact that humans have ten fingers and ten toes, which people may have used to count by. Linguistics * A collection of ten items (most often ten years) is called a decade. * The ordinal adjective is ''decimal''; the distributive adjective is ''denary''. * Increasing a quantity by one order of magnitude is most widely understood to mean multiplying the quantity by ten. * To reduce something by one tenth is to '' decimate''. (In ancient Rome, the killing o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Old Norse
Old Norse, also referred to as Old Nordic or Old Scandinavian, was a stage of development of North Germanic languages, North Germanic dialects before their final divergence into separate Nordic languages. Old Norse was spoken by inhabitants of Scandinavia and their Viking expansion, overseas settlements and chronologically coincides with the Viking Age, the Christianization of Scandinavia, and the consolidation of Scandinavian kingdoms from about the 8th to the 15th centuries. The Proto-Norse language developed into Old Norse by the 8th century, and Old Norse began to develop into the modern North Germanic languages in the mid- to late 14th century, ending the language phase known as Old Norse. These dates, however, are not precise, since written Old Norse is found well into the 15th century. Old Norse was divided into three dialects: Old West Norse (Old West Nordic, often referred to as ''Old Norse''), Old East Norse (Old East Nordic), and Old Gutnish. Old West Norse and O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Old Saxon
Old Saxon (), also known as Old Low German (), was a Germanic language and the earliest recorded form of Low German (spoken nowadays in Northern Germany, the northeastern Netherlands, southern Denmark, the Americas and parts of Eastern Europe). It is a West Germanic language, closely related to the Anglo-Frisian languages. It is documented from the 8th century until the 12th century, when it gradually evolved into Middle Low German. It was spoken throughout modern northwestern Germany, primarily in the coastal regions and in the eastern Netherlands by Saxons, a Germanic tribe that inhabited the region of Saxony. It partially shares Anglo-Frisian's ( Old Frisian, Old English) Ingvaeonic nasal spirant law which sets it apart from Low Franconian and Irminonic languages, such as Dutch, Luxembourgish and German. The grammar of Old Saxon was fully inflected with five grammatical cases ( nominative, accusative, genitive, dative, and instrumental), three grammati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Old Frisian
Old Frisian was a West Germanic language spoken between the late 13th century and the end of 16th century. It is the common ancestor of all the modern Frisian languages except for the North Frisian language#Insular North Frisian, Insular North Frisian dialects, with which Old Frisian shares a common ancestor called Pre–Old Frisian or Proto-Frisian. Old Frisian was spoken by contemporary Frisians who comprised a loose confederacy along the North Sea coast from around modern-day Bruges in Belgium to the Weser in modern-day northern Germany, dominating Maritime transport, maritime trade. The vast majority of the surviving literature comprises legal documents and charters, though some poetry, historiographies, and religious documents are attested as well. Old Frisian was Ingvaeonic languages, closely related to and shared common characteristics with the Middle English, forms of English and Middle Low German, Low German spoken during the period. Although earlier scholarship contend ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
