|
11th Century In Serbia
11 (eleven) is the natural number following 10 and preceding 12. It is the first repdigit. In English, it is the smallest positive integer 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 ancestor has been reconstructed as , from the prefix (adjectival "one") and suffix , of uncertain meaning. It is sometimes compared with the Lithuanian ', though ' is used as the suffix for all numbers from 11 to 19 (analogously to "-teen"). The Old English form has closer cognates in Old Frisian, Saxon, and Norse, whose ancestor has been reconstructed as . This was formerly thought to be derived from Proto-Germanic (" ten"); it is now sometimes connected with or ("left; remaining"), with the implicit meaning that "one is left" after counting to ten.''Oxford English Dict ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which alw ... [...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, which however remained in contact over a considerable time, especially the Ingvaeonic languages (including English), which arose from West Germanic dialects and remained in continued contact with North Germanic. 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. As it is probable that the development of this sound shift spanned a considerable time (several centuries), Proto-Germanic cannot adequately be reconstructed as a simple node in a tree ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Good Prime
A good prime is a prime number whose square is greater than the product of any two primes at the same number of positions before and after it in the sequence of primes. That is, good prime satisfies the inequality :p_n^2 > p_ \cdot p_ for all 1 ≤ ''i'' ≤ ''n''−1, where ''pk'' is the ''k''th prime. Example: the first primes are 2, 3, 5, 7 and 11. Since for 5 both the conditions :5^2 >3 \cdot 7 :5^2 >2 \cdot 11 are fulfilled, 5 is a good prime. There are infinitely many good primes. The first good primes are: : 5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 97, 101, 127, 149, 179, 191, 223, 227, 251, 257, 269, 307, 311, 331, 347, 419, 431, 541, 557, 563, 569, 587, 593, 599, 641, 727, 733, 739, 809, 821, 853, 929, 937, 967 . An alternative version takes only ''i'' = 1 in the definition. With that there are more good primes: : 5, 11, 17, 29, 37, 41, 53, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 157, 163, 173, 179, 191, 197, 211, 223, 227, 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.PNG "Click for more on -> Proto-Germanic Language")