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单词 Mersenne number
释义

Definition of Mersenne number in English:

Mersenne number

nounməːˈsɛnmərˈsen ˌnəmbər
Mathematics
  • A number of the form 2p−1, where p is a prime number. Such a number which is itself prime is also called a Mersenne prime.

    Example sentencesExamples
    • Primes of the form 2 n - 1 are known as Mersenne primes, and these numbers figure prominently in the search for the largest known prime.
    • And the Great Internet Mersenne Prime Search continues to unearth new Mersenne primes.
    • Written in the form 2 p - 1, where the exponent p is a prime number, Mersenne numbers hold a special place in the never-ending pursuit of larger and larger primes.
    • How can you calculate a perfect number from a Mersenne prime?
    • The largest known prime is the 40th Mersenne prime: M 20996011 which has 6320430 decimal digits.
    • ‘Fermat had this idea that there were families of primes other than Mersenne primes, and there would be an infinite number of them,’ he adds.
    • Primes of the form are now known as Mersenne primes, and these numbers figure prominently in the search for the largest known prime.
    • In 1876 he used his methods to prove that the Mersenne number 2 127-1 is prime.
    • This project is seeking the largest Mersenne prime number, which is, at the moment, also the largest prime number of any form.
    • After reading up on how known perfect numbers relate to Mersenne Prime Numbers, I wrote another program, this time to find Mersenne prime numbers and perfect numbers.
    • One must be the Lucas Lehmer primality test which uses the Fermat congruence, and in particular his application to testing whether a Mersenne number was prime.
    • Usually you download a screensaver or something, and when your computer isn't busy it turns itself on and cranks away at calculating a Mersenne prime or a SETI signal or some other worthy semi-scientific endeavor.
    • Primes of the form 2 p - 1 are called Mersenne primes.
    • A few months later an engineer at Cray Research discovered a new record Mersenne prime number, and I wrote a 700-word piece describing the discovery.
    • The divisor itself is the fifth largest known prime number, and it is the largest that is not a Mersenne prime.
    • A computer search turned up the 40th Mersenne prime.
    • Expressed in the form 2 p - 1, where the exponent p is itself prime, Mersenne numbers have characteristics that make it relatively easy to determine whether a candidate is prime.

Origin

Late 19th century: named after Marin Mersenne (1588–1648), French mathematician.

 
 

Definition of Mersenne number in US English:

Mersenne number

nounmərˈsen ˌnəmbər
Mathematics
  • A number of the form 2p−1, where n is a prime number. Such a number which is itself prime is also called a Mersenne prime.

    Example sentencesExamples
    • A computer search turned up the 40th Mersenne prime.
    • Primes of the form are now known as Mersenne primes, and these numbers figure prominently in the search for the largest known prime.
    • Expressed in the form 2 p - 1, where the exponent p is itself prime, Mersenne numbers have characteristics that make it relatively easy to determine whether a candidate is prime.
    • How can you calculate a perfect number from a Mersenne prime?
    • Written in the form 2 p - 1, where the exponent p is a prime number, Mersenne numbers hold a special place in the never-ending pursuit of larger and larger primes.
    • The largest known prime is the 40th Mersenne prime: M 20996011 which has 6320430 decimal digits.
    • ‘Fermat had this idea that there were families of primes other than Mersenne primes, and there would be an infinite number of them,’ he adds.
    • Primes of the form 2 n - 1 are known as Mersenne primes, and these numbers figure prominently in the search for the largest known prime.
    • In 1876 he used his methods to prove that the Mersenne number 2 127-1 is prime.
    • Usually you download a screensaver or something, and when your computer isn't busy it turns itself on and cranks away at calculating a Mersenne prime or a SETI signal or some other worthy semi-scientific endeavor.
    • One must be the Lucas Lehmer primality test which uses the Fermat congruence, and in particular his application to testing whether a Mersenne number was prime.
    • This project is seeking the largest Mersenne prime number, which is, at the moment, also the largest prime number of any form.
    • The divisor itself is the fifth largest known prime number, and it is the largest that is not a Mersenne prime.
    • And the Great Internet Mersenne Prime Search continues to unearth new Mersenne primes.
    • A few months later an engineer at Cray Research discovered a new record Mersenne prime number, and I wrote a 700-word piece describing the discovery.
    • After reading up on how known perfect numbers relate to Mersenne Prime Numbers, I wrote another program, this time to find Mersenne prime numbers and perfect numbers.
    • Primes of the form 2 p - 1 are called Mersenne primes.

Origin

Late 19th century: named after Marin Mersenne (1588–1648), French mathematician.

 
 
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更新时间:2025/2/7 15:33:24