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191 (number)
191 (one hundred ndninety-one) is the natural number following 190 and preceding 192. In mathematics 191 is a prime number, part of a prime quadruplet of four primes: 191, 193, 197, and 199. Because doubling and adding one produces another prime number (383), 191 is a Sophie Germain prime. It is the smallest prime that is not a full reptend prime in ''any'' base from 2 to 10; in fact, the smallest base for which 191 is a full period prime is base 19 There are many different numeral systems, that is, writing systems for expressing numbers. By culture / time period By type of notation Numeral systems are classified here as to whether they use positional notation (also known as place-value ....Wolfram MathWorldPrimitive Root/ref> See also * 191 (other) References Integers {{num-stub ... [...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] |
190 (number)
190 (one hundred ndninety) is the natural number following 189 and preceding 191. In mathematics 190 is a triangular number, a hexagonal number, and a centered nonagonal number, the fourth figurate number (after 1, 28, and 91) with that combination of properties. It is also a truncated square pyramid number. Integers from 191 to 199 ;191 : 191 is a prime number. ;192 : 192 = 26 × 3 is a 3-smooth number, the smallest number with 14 divisors. ;193 : 193 is a prime number. ;194 : 194 = 2 × 97 is a Markov number, the smallest number written as the sum of three squares in five ways, and the number of irreducible representations of the Monster group. ;195 : 195 = 3 × 5 × 13 is the smallest number expressed as a sum of distinct squares in 16 different ways. ;196 :196 = 22 × 72 is a square number. ;197 :197 is a prime number and a Schröder–Hipparchus number. ;198 :198 = 2 × 32 × 11 is the smallest number written as the sum of four squares in ten ways :No integer factorial eve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
192 (number)
192 (one hundred ndninety-two) is the natural number following 191 and preceding 193. In mathematics 192 has the prime factorization 2^6\times 3. Because it has so many small prime factors, it is the smallest number with 14 divisors, namely 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, and 192 itself. Because its only prime factors are 2 and 3, it is a 3-smooth number. 192 is the sum of ten consecutive prime 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 ...s ( 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37). 192 is a Leyland number of the second kind. See also * 192 (other) References {{Integers, 1 Integers ... [...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] |
Prime Quadruplet
In number theory, a prime quadruplet (sometimes called prime quadruple) is a set of four prime numbers of the form This represents the closest possible grouping of four primes larger than 3, and is the only prime constellation of length 4. Prime quadruplets The first eight prime quadruplets are: , , , , , , , All prime quadruplets except are of the form for some integer ''n''. (This structure is necessary to ensure that none of the four primes are divisible by 2, 3 or 5). A prime quadruplet of this form is also called a prime decade. A prime quadruplet can be described as a consecutive pair of twin primes, two overlapping sets of prime triplets, or two intermixed pairs of sexy primes. It is not known if there are infinitely many prime quadruplets. A proof that there are infinitely many would imply the twin prime conjecture, but it is consistent with current knowledge that there may be infinitely many pairs of twin primes and only finitely many prime quadruplets. The n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
193 (number)
193 (one hundred ndninety-three) is the natural number following 192 and preceding 194. In mathematics 193 is a prime number, and a Pierpont prime, implying that a 193-gon can be constructed using a compass, straightedge, and angle trisector. It is the only odd prime p known for which 2 is not a primitive root of 4p^2 + 1. It is the number of compositions of 14 into distinct parts. It is also part of the prime quadruplet (191, 193, 197, 199). See also * 193 (other) 193 A.D. is a year. 193 may also refer to: * 193 Ambrosia * Connecticut Route 193 * Maryland Route 193 * West Virginia Route 193 * Alabama State Route 193 * California State Route 193 * Ohio State Route 193 * Georgia State Route 193 * Maine S ... References {{DEFAULTSORT:193 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
197 (number)
197 (one hundred ndninety-seven) is the natural number following 196 and preceding 198. In mathematics * 197 is a prime number, the third of a prime quadruplet: 191, 193, 197, 199 * 197 is the smallest prime number that is the sum of 7 consecutive primes: 17 + 19 + 23 + 29 + 31 + 37 + 41, and is the sum of the first twelve prime numbers: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 * 197 is a centered heptagonal number, a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers * 197 is a Schröder–Hipparchus number, counting for instance the number of ways of subdividing a heptagon by a non-crossing set of its diagonals. In other fields 197 is also: * A police emergency telephone number in Tunisia * Number enquiry telephone number in Nepal * a song by Norwegian alternative rock group Major Parkinson Major Parkinson is a Norwegian rock group currently based in Berge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
199 (number)
199 (one hundred ndninety-nine) is the natural number following 198 and preceding 200. In mathematics 199 is a centered triangular number. It is a prime number and the fourth part of a prime quadruplet: 191, 193, 197, 199. It is an emirp, given that the reversal of its digits is also prime (991). 199 is the smallest natural number that takes more than two iterations to compute its digital root as a repeated digit sum: \begin 199&\mapsto 1+9+9=19\\ &\mapsto 1+9=10\\ &\mapsto 1+0=1. \end Thus, its additive persistence is three, and it is the smallest number of persistence three. See also * The year AD 199 or 199 BC __NOTOC__ Year 199 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Lentulus and Tappulus (or, less frequently, year 555 '' Ab urbe condita''). The denomination 199 BC for this year has be ... * List of highways numbered 199 * References {{Integers, 1 Integers ... [...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] |
Full Reptend Prime
In number theory, a full reptend prime, full repetend prime, proper primeDickson, Leonard E., 1952, ''History of the Theory of Numbers, Volume 1'', Chelsea Public. Co. or long prime in base ''b'' is an odd prime number ''p'' such that the Fermat quotient : q_p(b) = \frac (where ''p'' does not divide ''b'') gives a cyclic number. Therefore, the base ''b'' expansion of 1/p repeats the digits of the corresponding cyclic number infinitely, as does that of a/p with rotation of the digits for any ''a'' between 1 and ''p'' − 1. The cyclic number corresponding to prime ''p'' will possess ''p'' − 1 digits if and only if ''p'' is a full reptend prime. That is, the multiplicative order = ''p'' − 1, which is equivalent to ''b'' being a primitive root modulo ''p''. The term "long prime" was used by John Conway and Richard Guy in their ''Book of Numbers''. Confusingly, Sloane's OEIS refers to these primes as "cyclic numbers". Base 10 Base 10 may be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Base 19
There are many different numeral systems, that is, writing systems for expressing numbers. By culture / time period By type of notation Numeral systems are classified here as to whether they use positional notation (also known as place-value notation), and further categorized by radix or base. Standard positional numeral systems The common names are derived somewhat arbitrarily from a mix of Latin and Greek, in some cases including roots from both languages within a single name. There have been some proposals for standardisation. Non-standard positional numeral systems Bijective numeration Signed-digit representation Negative bases The common names of the negative base numeral systems are formed using the prefix ''nega-'', giving names such as: Complex bases Non-integer bases ''n''-adic number Mixed radix * Factorial number system * Even double factorial number system * Odd double factorial number system * Primorial number system * Fibonorial n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
191 (other)
{{Number disambiguation ...
191 A.D. is a year. 191 may also refer to: * 191 BC * 191 (number) * Jordan 191 * VF-191 See also *Flight 191 (other) *List of highways numbered 191 The following highways are numbered 191: Canada *''New Brunswick Route 191'' * Quebec Route 191 Japan * Japan National Route 191 Philippines * N191 highway (Philippines) United States * U.S. Route 191 * Alabama State Route 191 * Arkansas High ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
