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17th Century In Ireland
17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number. Seventeen is the sum of the first four prime numbers. In mathematics 17 is the seventh prime number, which makes seventeen the fourth super-prime, as seven is itself prime. The next prime is 19, with which it forms a twin prime. It is a cousin prime with 13 and a sexy prime with 11 and 23. It is an emirp, and more specifically a permutable prime with 71, both of which are also supersingular primes. Seventeen is the sixth Mersenne prime exponent, yielding 131,071. Seventeen is the only prime number which is the sum of four consecutive primes: 2, 3, 5, 7. Any other four consecutive primes summed would always produce an even number, thereby divisible by 2 and so not prime. Seventeen can be written in the form x^y + y^x and x^y - y^x, and, as such, it is a Leyland prime and Leyland prime of the second kind: :17=2^+3^=3^-4^. 17 is one of seven lucky numbers of Euler which produ ... [...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] |
Lucky Numbers Of Euler
Euler's "lucky" numbers are positive integers ''n'' such that for all integers ''k'' with , the polynomial produces a prime number. When ''k'' is equal to ''n'', the value cannot be prime since is divisible by ''n''. Since the polynomial can be written as , using the integers ''k'' with produces the same set of numbers as . These polynomials are all members of the larger set of prime generating polynomials. Leonhard Euler published the polynomial which produces prime numbers for all integer values of ''k'' from 1 to 40. Only 7 lucky numbers of Euler exist, namely 1, 2, 3, 5, 11, 17 and 41 . Note that these numbers are all prime numbers except for 1. The primes of the form ''k''2 − ''k'' + 41 are :41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281, 313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971, ... .See also the sieve algorithm for all such primes: Euler's lucky numbers are unrelated to the "lucky numbers" defined by a sieve a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
