"Fermat prime" meaning in All languages combined

{
  "etymology_templates": [
    {
      "args": {
        "1": "lawyer and amateur mathematician",
        "2": "",
        "3": "",
        "4": "",
        "5": ""
      },
      "expansion": "lawyer and amateur mathematician",
      "name": "named-after/list"
    },
    {
      "args": {},
      "expansion": "|",
      "name": "!"
    },
    {
      "args": {
        "1": "en",
        "2": "Pierre de Fermat"
      },
      "expansion": "Pierre de Fermat",
      "name": "lang"
    },
    {
      "args": {
        "1": "en",
        "2": "Pierre de Fermat",
        "born": "1601",
        "died": "1665",
        "nat": "French",
        "occ": "lawyer and amateur mathematician",
        "wplink": "="
      },
      "expansion": "Named after French lawyer and amateur mathematician Pierre de Fermat (1601–1665)",
      "name": "named-after"
    }
  ],
  "etymology_text": "Named after French lawyer and amateur mathematician Pierre de Fermat (1601–1665).",
  "forms": [
    {
      "form": "Fermat primes",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Fermat prime (plural Fermat 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": "2001, I. Martin Isaacs, Geometry for College Students, American Mathematical Society, page 201",
          "text": "It is not hard to prove that the only way that the number 1#x2B;2ᵉ can possibly be prime is when e is a power of 2, and so all Fermat primes must have the form 1#x2B;2#x7B;2ᵃ#x7D; for integers a#x5C;ge 0. The numbers F#x5F;a#x3D;1#x2B;2#x7B;2ᵃ#x7D; are called Fermat numbers, and although it is true that every Fermat prime is a Fermat number, it is certainly not true that every Fermat number is prime.",
          "type": "quotation"
        },
        {
          "ref": "2004, T. W. Müller, “12: Parity patterns in Hecke groups and Fermat primes”, in Thomas Wolfgang Müller, editor, Groups: Topological, Combinatorial and Arithmetic Aspects, Cambridge University Press, page 327",
          "text": "Rather surprisingly, it turns out that Fermat primes play an important special role in this context, a phenomenon hitherto unobserved in the arithmetic theory of Hecke groups, and, as a byproduct of our investigation, several new characterizations of Fermat primes are obtained.",
          "type": "quotation"
        },
        {
          "ref": "2013, Dean Hathout, Wearing Gauss’s Jersey, Taylor & Francis (CRC Press), page xi, Believe it or not, so far only five Fermat primes are known",
          "text": "F₀ = 3, F₁ = 5, F₂ = 17, F₃ = 257, and F₄ = 65537.\nThe next 28 Fermat numbers, F₅ through F₃₂, are known to be composite."
        }
      ],
      "glosses": [
        "A Fermat number that is prime."
      ],
      "id": "en-Fermat_prime-en-noun-DOi2jgj7",
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "Fermat number",
          "Fermat number"
        ],
        [
          "prime",
          "prime"
        ]
      ],
      "raw_glosses": [
        "(number theory) A Fermat number that is prime."
      ],
      "related": [
        {
          "word": "Fermat number"
        }
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "wikipedia": [
        "Fermat number"
      ]
    }
  ],
  "word": "Fermat prime"
}

{
  "etymology_templates": [
    {
      "args": {
        "1": "lawyer and amateur mathematician",
        "2": "",
        "3": "",
        "4": "",
        "5": ""
      },
      "expansion": "lawyer and amateur mathematician",
      "name": "named-after/list"
    },
    {
      "args": {},
      "expansion": "|",
      "name": "!"
    },
    {
      "args": {
        "1": "en",
        "2": "Pierre de Fermat"
      },
      "expansion": "Pierre de Fermat",
      "name": "lang"
    },
    {
      "args": {
        "1": "en",
        "2": "Pierre de Fermat",
        "born": "1601",
        "died": "1665",
        "nat": "French",
        "occ": "lawyer and amateur mathematician",
        "wplink": "="
      },
      "expansion": "Named after French lawyer and amateur mathematician Pierre de Fermat (1601–1665)",
      "name": "named-after"
    }
  ],
  "etymology_text": "Named after French lawyer and amateur mathematician Pierre de Fermat (1601–1665).",
  "forms": [
    {
      "form": "Fermat primes",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Fermat prime (plural Fermat primes)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "Fermat number"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "en:Number theory"
      ],
      "examples": [
        {
          "ref": "2001, I. Martin Isaacs, Geometry for College Students, American Mathematical Society, page 201",
          "text": "It is not hard to prove that the only way that the number 1#x2B;2ᵉ can possibly be prime is when e is a power of 2, and so all Fermat primes must have the form 1#x2B;2#x7B;2ᵃ#x7D; for integers a#x5C;ge 0. The numbers F#x5F;a#x3D;1#x2B;2#x7B;2ᵃ#x7D; are called Fermat numbers, and although it is true that every Fermat prime is a Fermat number, it is certainly not true that every Fermat number is prime.",
          "type": "quotation"
        },
        {
          "ref": "2004, T. W. Müller, “12: Parity patterns in Hecke groups and Fermat primes”, in Thomas Wolfgang Müller, editor, Groups: Topological, Combinatorial and Arithmetic Aspects, Cambridge University Press, page 327",
          "text": "Rather surprisingly, it turns out that Fermat primes play an important special role in this context, a phenomenon hitherto unobserved in the arithmetic theory of Hecke groups, and, as a byproduct of our investigation, several new characterizations of Fermat primes are obtained.",
          "type": "quotation"
        },
        {
          "ref": "2013, Dean Hathout, Wearing Gauss’s Jersey, Taylor & Francis (CRC Press), page xi, Believe it or not, so far only five Fermat primes are known",
          "text": "F₀ = 3, F₁ = 5, F₂ = 17, F₃ = 257, and F₄ = 65537.\nThe next 28 Fermat numbers, F₅ through F₃₂, are known to be composite."
        }
      ],
      "glosses": [
        "A Fermat number that is prime."
      ],
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "Fermat number",
          "Fermat number"
        ],
        [
          "prime",
          "prime"
        ]
      ],
      "raw_glosses": [
        "(number theory) A Fermat number that is prime."
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "wikipedia": [
        "Fermat number"
      ]
    }
  ],
  "word": "Fermat prime"
}