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179 (number)
179 (one hundred ndseventy-nine) is the natural number following 178 and preceding 180. In mathematics 179 is part of the Cunningham chain of prime numbers 89, 179, 359, 719, 1439, 2879, in which each successive number is two times the previous number, plus one. Among Cunningham chains of this length, this one has the smallest numbers. Because 179 is neither the start nor the end of this chain, it is both a safe prime and a Sophie Germain prime. It is also a super-prime number, because it is the 41st smallest prime and 41 is also prime. Since 971 (the digits of 179 reversed) is prime, 179 is an emirp. In other fields Astronomers have suggested that sunspot frequency undergoes a cycle of approximately 179 years in length. See also * AD 179 and 179 BC __NOTOC__ Year 179 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Flaccus and Fulvianus (or, less frequently, year 575 ''Ab urbe condita''). The denomination 179 BC for ... [...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 always pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal number, cardinal numbers'', and numbers used for ordering are called ''Ordinal number, ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports Number (sports), jersey numbers). Some definitions, including the standard ISO/IEC 80000, ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
178 (number)
178 (one hundred ndseventy-eight) is the natural number following 177 and preceding 179. In mathematics There are 178 biconnected graphs with six vertices, among which one is designated as the root and the rest are unlabeled. There are also 178 median graph In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertices ''a'', ''b'', and ''c'' have a unique ''median'': a vertex ''m''(''a'',''b'',''c'') that belongs to shortest paths between each pair o ...s on nine vertices. 178 is one of the indexes of the smallest triple of dodecahedral numbers where one is the sum of the other two: the sum of the 46th and the 178th dodecahedral numbers is the 179th. See also * The year 178 AD or 178 BC * List of highways numbered 178 * References {{DEFAULTSORT:178 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
180 (number)
180 (one hundred ndeighty) is the natural number following 179 and preceding 181. In mathematics 180 is an abundant number, with its proper divisors summing up to 366. 180 is also a highly composite number, a positive integer with more divisors than any smaller positive integer. One of the consequences of 180 having so many divisors is that it is a practical number, meaning that any positive number smaller than 180 that is not a divisor of 180 can be expressed as the sum of some of 180's divisors. 180 is a Harshad number and a refactorable number. 180 is the sum of two square numbers: 122 + 62. It can be expressed as either the sum of six consecutive prime numbers: 19 + 23 + 29 + 31 + 37 + 41, or the sum of eight consecutive prime numbers: 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37. 180 is an Ulam number, which can be expressed as a sum of earlier terms in the Ulam sequence only as 177 + 3. 180 is a 61- gonal number. Half a circle has 180 degrees, and thus a U-turn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cunningham Chain
In mathematics, a Cunningham chain is a certain sequence of prime numbers. Cunningham chains are named after mathematician A. J. C. Cunningham. They are also called chains of nearly doubled primes. Definition A Cunningham chain of the first kind of length ''n'' is a sequence of prime numbers (''p''1, ..., ''p''''n'') such that ''p''''i''+1 = 2''p''''i'' + 1 for all 1 ≤ ''i'' < ''n''. (Hence each term of such a chain except the last is a , and each term except the first is a ). It follows that : or, by setting (the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Safe Prime
In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 + 1 = 23 is its associated safe prime. Sophie Germain primes are named after French mathematician Sophie Germain, who used them in her investigations of Fermat's Last Theorem. One attempt by Germain to prove Fermat’s Last Theorem was to let ''p'' be a prime number of the form 8''k'' + 7 and to let ''n'' = ''p'' – 1. In this case, x^n + y^n = z^n is unsolvable. Germain’s proof, however, remained unfinished. Through her attempts to solve Fermat's Last Theorem, Germain developed a result now known as Germain's Theorem which states that if ''p'' is an odd prime and 2''p'' + 1 is also prime, then ''p'' must divide ''x'', ''y'', or ''z.'' Otherwise, x^n + y^n \neq z^n. This case where ''p'' does not divide ''x'', ''y'', or ''z'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sophie Germain Prime
In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 + 1 = 23 is its associated safe prime. Sophie Germain primes are named after French mathematician Sophie Germain, who used them in her investigations of Fermat's Last Theorem. One attempt by Germain to prove Fermat’s Last Theorem was to let ''p'' be a prime number of the form 8''k'' + 7 and to let ''n'' = ''p'' – 1. In this case, x^n + y^n = z^n is unsolvable. Germain’s proof, however, remained unfinished. Through her attempts to solve Fermat's Last Theorem, Germain developed a result now known as Germain's Theorem which states that if ''p'' is an odd prime and 2''p'' + 1 is also prime, then ''p'' must divide ''x'', ''y'', or ''z.'' Otherwise, x^n + y^n \neq z^n. This case where ''p'' does not divide ''x'', ''y'', or ''z'' i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emirp
An emirp (''prime'' spelled backwards) is a prime number that results in a different prime when its decimal digits are reversed. This definition excludes the related palindromic primes. The term ''reversible prime'' is used to mean the same as emirp, but may also, ambiguously, include the palindromic primes. The sequence of emirps begins 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 991, ... . All non-palindromic permutable primes are emirps. , the largest known emirp is 1010006+941992101×104999+1, found by Jens Kruse Andersen in October 2007. The term 'emirpimes' (singular) is used also in places to treat semiprimes in a similar way. That is, an emirpimes is a semiprime that is also a (distinct) semiprime upon reversing its digits. It is an open problem whether there are infinitely many emirps. Other bases The emirps in base 12 are (using rotated ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sunspot
Sunspots are phenomena on the Sun's photosphere that appear as temporary spots that are darker than the surrounding areas. They are regions of reduced surface temperature caused by concentrations of magnetic flux that inhibit convection. Sunspots appear within active regions, usually in pairs of opposite magnetic polarity. Their number varies according to the approximately 11-year solar cycle. Individual sunspots or groups of sunspots may last anywhere from a few days to a few months, but eventually decay. Sunspots expand and contract as they move across the surface of the Sun, with diameters ranging from to . Larger sunspots can be visible from Earth without the aid of a telescope. They may travel at relative speeds, or proper motions, of a few hundred meters per second when they first emerge. Indicating intense magnetic activity, sunspots accompany other active region phenomena such as coronal loops, prominences, and reconnection events. Most solar flares and coronal mas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
179 BC
__NOTOC__ Year 179 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Flaccus and Fulvianus (or, less frequently, year 575 ''Ab urbe condita''). The denomination 179 BC for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Republic * Tiberius Sempronius Gracchus goes to Hispania as Roman governor to deal with uprisings there. * The Pons Aemilius is completed across the Tiber River in Rome. It is regarded as the world's first stone bridge. * Marcus Aemilius Lepidus is appointed both censor and princeps senatus. Greece * Philip V of Macedon dies at Amphipolis in Macedonia, remorseful for having put his younger son Demetrius to death, at the instigation of his older son Perseus. Nevertheless, he is succeeded by his son Perseus. Asia Minor * Eumenes II of Pergamum defeats Pharnaces I of Pontus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Highways Numbered 179
The following highways are numbered 179: Canada * Prince Edward Island Route 179 Ireland * R179 road (Ireland) Japan * Japan National Route 179 Malaysia * Malaysia Federal Route 179 United Kingdom * A179 road United States * Interstate 179 (former) * Alabama State Route 179 * Arizona State Route 179 * Arkansas Highway 179 * California State Route 179 * Connecticut Route 179 * Florida State Road 179 (former) * Georgia State Route 179 (former) * Illinois Route 179 (former) * K-179 (Kansas highway) * Kentucky Route 179 * Maine State Route 179 * Maryland Route 179 * M-179 (Michigan highway) * Missouri Route 179 * New Jersey Route 179 * New Mexico State Road 179 * New York State Route 179 * North Carolina Highway 179 * Ohio State Route 179 * Pennsylvania Route 179 * Rhode Island Route 179 * South Carolina Highway 179 * Tennessee State Route 179 * Texas State Highway 179 ** Texas State Highway Loop 179 ** Farm to Market Road 179 (Texas) * Utah State Route 179 (for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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