mersenne number: meaning, definition, pronunciation and examples
RareAcademic, Technical, Specialised
Quick answer
What does “mersenne number” mean?
A number that is one less than a power of two, expressed as M_n = 2^n – 1.
Audio
Pronunciation
Definition
Meaning and Definition
A number that is one less than a power of two, expressed as M_n = 2^n – 1.
In mathematics, a number of the form 2^n – 1. When such a number is prime, it is known as a Mersenne prime. Named after the 17th-century French mathematician Marin Mersenne.
Dialectal Variation
British vs American Usage
Differences
No significant spelling or usage differences exist between British and American English. Both use the capitalised 'M' as a proper noun derivative.
Connotations
No connotative differences. Purely technical and referential.
Frequency
The term is equally rare and specialised in both varieties, confined to advanced mathematical discourse.
Grammar
How to Use “mersenne number” in a Sentence
The Mersenne number M_n is...A Mersenne number of the form...to check/primality test a Mersenne numberVocabulary
Collocations
Examples
Examples of “mersenne number” in a Sentence
adjective
British English
- The Mersenne-number search is a major computational project.
- He specialises in Mersenne-number theory.
American English
- The Mersenne number search is a major computational project.
- He specializes in Mersenne number theory.
Usage
Meaning in Context
Business
Not used.
Academic
Used in advanced mathematics, particularly in number theory papers and lectures.
Everyday
Not used in everyday conversation.
Technical
The primary domain of use, in mathematical literature, computational number theory, and related software documentation.
Vocabulary
Synonyms of “mersenne number”
Neutral
Weak
Watch out
Common Mistakes When Using “mersenne number”
- Pronouncing it as 'mer-seen' (correct is closer to 'mer-sen').
- Omitting the capital 'M' as it's a proper noun derivative.
- Assuming all Mersenne numbers are primes.
- Incorrectly writing the formula as 2^(n-1) instead of (2^n) – 1.
FAQ
Frequently Asked Questions
No, not every Mersenne number is prime. For example, M_11 = 2047, which is 23 * 89. When a Mersenne number is prime, it is called a Mersenne prime.
Mersenne primes are important in number theory and are often the largest known primes due to the efficient Lucas-Lehmer primality test, which works specifically for numbers of this form.
Marin Mersenne (1588–1648) was a French polymath, mathematician, music theorist, and theologian. He studied numbers of the form 2^n – 1, though he did not discover all their properties.
GIMPS stands for the Great Internet Mersenne Prime Search. It is a collaborative volunteer computing project dedicated to finding new Mersenne primes using distributed software.
A number that is one less than a power of two, expressed as M_n = 2^n – 1.
Mersenne number is usually academic, technical, specialised in register.
Mersenne number: in British English it is pronounced /mɛəˈsɛn ˈnʌmbə/, and in American English it is pronounced /mɛrˈsɛn ˈnʌmbər/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Remember 'Mersenne' as 'Mere-SEN', like 'sent' from the centre. Think: 'Marin Mersenne's special numbers are one LESS than a power of TWO'.
Conceptual Metaphor
A numerical quarry; a specific, defined shape (2^n - 1) within the infinite landscape of numbers, which may sometimes yield the precious gem of a prime.
Practice
Quiz
Which of the following is a property of a Mersenne number M_n?