Phrase guide

Mersenne prime

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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  • /mɛə(ɹ)ˈsɛn ˈpɹaɪm/
  • rhymes with -aɪm

1

noun

Meaning 1

A prime number which is one less than a power of two (i.e., is expressible in the form 2n-1; for example, 31=25-1).

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, number-theory, sciences

Examples

  • 2005, Jean-Claude Bajard, Laurent Imbert, Thomas Plantard, Modular Number Systems: Beyond the Mersenne Family, Helena Handschuh, M. Anwar Hasan (editors), Selected Areas in Cryptography: 11th International Workshop, SAC 2004, Revised Selected Papers, Springer, LNCS 3357, page 159, Mersenne numbers of the form 2m-1 are well known examples, but they are not useful for cryptography because there are only a few primes (the first Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, etc).

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

Named after French theologian, philosopher, mathematician, and music theorist Marin Mersenne (1588–1648).

Across languages

Translations

2 source translations are retained for this English entry.

  • Bulgarian: про́сто число́ на Мерсе́н (prósto čisló na Mersén) — prime number which is one less than a power of two
  • Polish: liczba Mersenne'a — prime number which is one less than a power of two