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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 bee ... * List of highways numbered 199 * References {{Integers, 1 Integers ... [...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 numbers'', and numbers used for ordering are called ''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 jersey numbers). Some definitions, including the standard 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 numbers form a set. Many other number sets are built by succ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
200 (number)
200 (two hundred) is the natural number following 199 and preceding 201. 200 is an abundant number, as 265, the sum of its proper divisors, is greater than itself. The number appears in the Padovan sequence, preceded by 86, 114, 151 (it is the sum of the first two of these). The sum of Euler's totient function φ(''x'') over the first twenty-five integers is 200. 200 is the smallest base 10 unprimeable number – it cannot be turned into a prime number by changing just one of its digits to any other digit. It is also a Harshad number. 200 is an Achilles number. Two hundred is also: * A common ISO-standard film speed for photographic films. However, 200 speed film is being phased out in consumer films in favor of faster films. * A denomination of the euro note. The 200 euro note was designed by Robert Kalina. * 200 MeV is the temperature of quark–gluon plasma phase transition. * An HTTP status code indicating a successful connection; the code is " 200 OK". * The sum of po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Triangular Number
A centered (or centred) triangular number is a centered figurate number that represents an equilateral triangle with a dot in the center and all its other dots surrounding the center in successive equilateral triangular layers. The following image shows the building of the centered triangular numbers by using the associated figures: at each step, the previous triangle (shown in red) is surrounded by a triangular layer of new dots (in blue). Properties *The gnomon of the ''n''-th centered triangular number, corresponding to the (''n'' + 1)-th triangular layer, is: ::C_ - C_ = 3(n+1). *The ''n''-th centered triangular number, corresponding to ''n'' layers ''plus'' the center, is given by the formula: ::C_ = 1 + 3 \frac = \frac. *Each centered triangular number has a remainder of 1 when divided by 3, and the quotient (if positive) is the previous regular triangular number. *Each centered triangular number from 10 onwards is the sum of three consecutive regular triangular ... [...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 alway ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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.Wolfram MathWorldPrimitive Root/ref> See also * 191 (other) 191 A.D. is a year. 191 may also refer to: * 191 BC * 191 (number) * Jordan 191 * VF-191 Fighter Squadron 191 (VF-191) was an aviation unit of the United States Navy. It was established in 1943 and disestablished in 1978. The squadron was nickna ... References Integers {{num-stub ... [...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 from their self-titled debut album See also * The year AD 197 or ... [...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] |
Digital Root
The digital root (also repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached. For example, in base 10, the digital root of the number 12345 is 6 because the sum of the digits in the number is 1 + 2 + 3 + 4 + 5 = 15, then the addition process is repeated again for the resulting number 15, so that the sum of 1 + 5 equals 6, which is the digital root of that number. In base 10, this is equivalent to taking the remainder upon division by 9 (except when the digital root is 9, where the remainder upon division by 9 will be 0), which allows it to be used as a divisibility rule. Formal definition Let n be a natural number. For base b > 1, we define the digit sum F_ : \mathbb \rightarrow \mathbb to be the following: :F_(n) = \sum_^ d_i where k = \lfloor \lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Persistence Of A Number
In mathematics, the persistence of a number is the number of times one must apply a given operation to an integer before reaching a fixed point at which the operation no longer alters the number. Usually, this involves additive or multiplicative persistence of a non-negative integer, which is how often one has to replace the number by the sum or product of its digits until one reaches a single digit. Because the numbers are broken down into their digits, the additive or multiplicative persistence depends on the radix. In the remainder of this article, base ten is assumed. The single-digit final state reached in the process of calculating an integer's additive persistence is its digital root. Put another way, a number's additive persistence counts how many times we must sum its digits to arrive at its digital root. Examples The additive persistence of 2718 is 2: first we find that 2 + 7 + 1 + 8 = 18, and then that 1 + 8&n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 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 * The Roman general Gnaeus Baebius Tamphilus attacks the Insubres in Gaul, but loses over 6,700 soldiers in the process. * Scipio Africanus becomes censor and princeps Senatus (the titular head of the Roman Senate The Roman Senate ( la, Senātus Rōmānus) was a governing and advisory assembly in ancient Rome. It was one of the most enduring institutions in Roman history, being established in the first days of the city of Rome (traditionally founded in ...). * The Roman law, Lex Porcia, is proposed by the tribune P. Porcius Laeca to give Roman citizens in Italy an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
