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Super-Poulet Number
A super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor ''d'' divides :2''d'' − 2. For example, 341 is a super-Poulet number: it has positive divisors and we have: :(211 - 2) / 11 = 2046 / 11 = 186 :(231 - 2) / 31 = 2147483646 / 31 = 69273666 :(2341 - 2) / 341 = 13136332798696798888899954724741608669335164206654835981818117894215788100763407304286671514789484550 When \frac is not prime, then it and every divisor of it are a pseudoprime to base 2, and a super-Poulet number. The super-Poulet numbers below 10,000 are : Super-Poulet numbers with 3 or more distinct prime divisors It is relatively easy to get super-Poulet numbers with 3 distinct prime divisors. If you find three Poulet numbers with three common prime factors, you get a super-Poulet number, as you built the product of the three prime factors. Example: 2701 = 37 * 73 is a Poulet number, 4033 = 37 * 109 is a Poulet number, 7957 = 73 * 109 is a Poulet number; so 294409 = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poulet Number
Poulet is a French surname, meaning chicken. Notable people with the name include: * Anne Poulet (born 1942), American art historian * Gaston Poulet (1892–1974), French violinist and conductor * Georges Poulet (1902–1991), Belgian literary critic * J. Poulet (fl. 1811–1818), English cricketer * Olivia Poulet (born 1978), English actress and screenwriter * Paul Poulet (1887–1946), Belgian mathematician * Quentin Poulet (fl. 1477–1506), Burgundian Catholic priest, scribe, illuminator, and librarian * Robert Poulet (1893–1989), Belgian writer, literary critic and journalist * William Poulet (publisher), pseudonym used by Jean-Paul Wayenborgh to write his History of Spectacles "Die Brille" * Auguste Poulet-Malassis (1825–1878), French printer and publisher See also * Poulett Poulett is a surname and given name. Notable people with the name include: Surname * Anne Poulett (1711–1785), fourth son of John Poulett, 1st Earl Poulett, was a British Member of Parliament * G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder. Definition An integer is divisible by a nonzero integer if there exists an integer such that n=km. This is written as :m\mid n. Other ways of saying the same thing are that divides , is a divisor of , is a factor of , and is a multiple of . If does not divide , then the notation is m\not\mid n. Usually, is required to be nonzero, but is allowed to be zero. With this convention, m \mid 0 for every nonzero integer . Some definitions omit the requirement that m be nonzero. General Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4; they ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Factor
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 pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
