"Mersenne prime" meaning in English

{
  "etymology_templates": [
    {
      "args": {},
      "expansion": ",",
      "name": ","
    },
    {
      "args": {
        "1": "theologian, philosopher, mathematician, and music theorist",
        "2": "",
        "3": "",
        "4": "",
        "5": ""
      },
      "expansion": "theologian, philosopher, mathematician, and music theorist",
      "name": "named-after/list"
    },
    {
      "args": {},
      "expansion": "|",
      "name": "!"
    },
    {
      "args": {
        "1": "en",
        "2": "Marin Mersenne"
      },
      "expansion": "Marin Mersenne",
      "name": "lang"
    },
    {
      "args": {
        "1": "en",
        "2": "Marin Mersenne",
        "born": "1588",
        "died": "1648",
        "nat": "French",
        "occ": "theologian, philosopher, mathematician, and music theorist",
        "wplink": "="
      },
      "expansion": "Named after French theologian, philosopher, mathematician, and music theorist Marin Mersenne (1588–1648)",
      "name": "named-after"
    }
  ],
  "etymology_text": "Named after French theologian, philosopher, mathematician, and music theorist Marin Mersenne (1588–1648).",
  "forms": [
    {
      "form": "Mersenne primes",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Mersenne prime (plural Mersenne primes)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Number theory",
          "orig": "en:Number theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2004, Sheldon Axler, “3: Mathematicians Versus the Silicon Age: Who Wins?”, in David F. Hayes, Tatiana Shubin, editors, Mathematical Adventures for Students and Amateurs, American Mathematical Society, page 20",
          "text": "In addition to being the largest known Mersenne prime, this number is also currently the largest known prime number of any type.",
          "type": "quotation"
        },
        {
          "text": "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,\nMersenne 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)."
        },
        {
          "ref": "2013, Louis Komzsik, Magnificent Seven: The Happy Number, Trafford Publishing, page 71",
          "text": "Mersenne primes, named after the French priest first describing them in the 17th century, are of the form of 2ᵖ-1, where the exponent p is a prime itself. Obviously 7 is a Mersenne prime, since 2³-1#x3D;7, and 3 is a prime. The interesting twist comes in the fact that there are certain primes that are double Mersenne primes. These are of the form 2#x7B;2ᵖ-1#x7D;-1, meaning that the exponent now is not just a prime, but it is itself a Mersenne prime. Since 2#x7B;2²-1#x7D;-1#x3D;7, 7 is the very first double Mersenne prime.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "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)."
      ],
      "id": "en-Mersenne_prime-en-noun-pJcmglO3",
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "prime number",
          "prime number"
        ]
      ],
      "raw_glosses": [
        "(number theory) 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)."
      ],
      "related": [
        {
          "word": "Mersenne number"
        },
        {
          "word": "Mersenne twister"
        },
        {
          "word": "perfect number"
        }
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "wikipedia": [
        "Mersenne prime"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/mɛə(ɹ)ˈsɛn ˈpɹaɪm/"
    }
  ],
  "word": "Mersenne prime"
}

{
  "etymology_templates": [
    {
      "args": {},
      "expansion": ",",
      "name": ","
    },
    {
      "args": {
        "1": "theologian, philosopher, mathematician, and music theorist",
        "2": "",
        "3": "",
        "4": "",
        "5": ""
      },
      "expansion": "theologian, philosopher, mathematician, and music theorist",
      "name": "named-after/list"
    },
    {
      "args": {},
      "expansion": "|",
      "name": "!"
    },
    {
      "args": {
        "1": "en",
        "2": "Marin Mersenne"
      },
      "expansion": "Marin Mersenne",
      "name": "lang"
    },
    {
      "args": {
        "1": "en",
        "2": "Marin Mersenne",
        "born": "1588",
        "died": "1648",
        "nat": "French",
        "occ": "theologian, philosopher, mathematician, and music theorist",
        "wplink": "="
      },
      "expansion": "Named after French theologian, philosopher, mathematician, and music theorist Marin Mersenne (1588–1648)",
      "name": "named-after"
    }
  ],
  "etymology_text": "Named after French theologian, philosopher, mathematician, and music theorist Marin Mersenne (1588–1648).",
  "forms": [
    {
      "form": "Mersenne primes",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Mersenne prime (plural Mersenne primes)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "Mersenne number"
    },
    {
      "word": "Mersenne twister"
    },
    {
      "word": "perfect number"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with IPA pronunciation",
        "English terms with quotations",
        "en:Number theory"
      ],
      "examples": [
        {
          "ref": "2004, Sheldon Axler, “3: Mathematicians Versus the Silicon Age: Who Wins?”, in David F. Hayes, Tatiana Shubin, editors, Mathematical Adventures for Students and Amateurs, American Mathematical Society, page 20",
          "text": "In addition to being the largest known Mersenne prime, this number is also currently the largest known prime number of any type.",
          "type": "quotation"
        },
        {
          "text": "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,\nMersenne 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)."
        },
        {
          "ref": "2013, Louis Komzsik, Magnificent Seven: The Happy Number, Trafford Publishing, page 71",
          "text": "Mersenne primes, named after the French priest first describing them in the 17th century, are of the form of 2ᵖ-1, where the exponent p is a prime itself. Obviously 7 is a Mersenne prime, since 2³-1#x3D;7, and 3 is a prime. The interesting twist comes in the fact that there are certain primes that are double Mersenne primes. These are of the form 2#x7B;2ᵖ-1#x7D;-1, meaning that the exponent now is not just a prime, but it is itself a Mersenne prime. Since 2#x7B;2²-1#x7D;-1#x3D;7, 7 is the very first double Mersenne prime.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "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)."
      ],
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "prime number",
          "prime number"
        ]
      ],
      "raw_glosses": [
        "(number theory) 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)."
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "wikipedia": [
        "Mersenne prime"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/mɛə(ɹ)ˈsɛn ˈpɹaɪm/"
    }
  ],
  "word": "Mersenne prime"
}