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Super-Poulet Number
In number theory, 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 (1, 11, 31, 341), 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory can often be understood through the study of Complex analysis, analytical objects, such as the Riemann zeta function, that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, as for instance how irrational numbers can be approximated by fractions (Diophantine approximation). Number theory is one of the oldest branches of mathematics alongside geometry. One quirk of number theory is ... [...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 (pronounced ) 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudoprime
A pseudoprime is a probable prime (an integer that shares a property common to all prime numbers) that is not actually prime. Pseudoprimes are classified according to which property of primes they satisfy. Some sources use the term pseudoprime to describe all probable primes, both composite numbers and actual primes. Pseudoprimes are of primary importance in public-key cryptography, which makes use of the difficulty of factoring large numbers into their prime factors. Carl Pomerance estimated in 1988 that it would cost $10 million to factor a number with 144 digits, and $100 billion to factor a 200-digit number (the cost today is dramatically lower but still prohibitively high). But finding two large prime numbers as needed for this use is also expensive, so various probabilistic primality tests are used, some of which in rare cases inappropriately deliver composite numbers instead of primes. On the other hand, deterministic primality tests, such as the AKS primality test, do not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radix
In a positional numeral system, the radix (radices) or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal system (the most common system in use today) the radix is ten, because it uses the ten digits from 0 through 9. In any standard positional numeral system, a number is conventionally written as with ''x'' as the string of digits and ''y'' as its base. For base ten, the subscript is usually assumed and omitted (together with the enclosing parentheses), as it is the most common way to express value. For example, (the decimal system is implied in the latter) and represents the number one hundred, while (100)2 (in the binary system with base 2) represents the number four. Etymology ''Radix'' is a Latin word for "root". ''Root'' can be considered a synonym for ''base,'' in the arithmetical sense. In numeral systems Generally, in a system with radix ''b'' (), a string of digits denotes the number , ... [...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 n is divisible by a nonzero integer m if there exists an integer k such that n=km. This is written as : m\mid n. This may be read as that m divides n, m is a divisor of n, m is a factor of n, or n is a multiple of m. If m does not divide n, then the notation is m\not\mid n. There are two conventions, distinguished by whether m is permitted to be zero: * With the convention without an additional constraint on m, m \mid 0 for every integer m. * With the convention that m be nonzero, m \mid 0 for every nonzero integer m. General Divisors can be negative as well as positive, although often the term is restricted to posi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Composite Number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime number, prime, or the Unit (ring theory), unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit. E.g., the integer 14 is a composite number because it is the product of the two smaller integers 2 × 7 but the integers 2 and 3 are not because each can only be divided by one and itself. The composite numbers up to 150 are: :4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, ... [...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 , called trial division, tests whether is a multiple of any integer between 2 and . 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] |
