"Proth number" meaning in All languages combined

{
  "etymology_text": "After French mathematician François Proth (1852-1879).",
  "forms": [
    {
      "form": "Proth numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Proth number (plural Proth numbers)",
      "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": "other",
          "name": "Entries with translation boxes",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Italian translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Number theory",
          "orig": "en:Number theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "2006, B. Grégoire, L. Théry, B. Werner, A Computational Approach to Pocklington Certificates, Masami Hagiya, Philip Wadler (editors), Functional and Logic Programming: 8th International Symposium, Proceedings, Springer, LNCS 3945, page 109,\nTo generate Pocklington certificates for Proth number we add a new entry to the oracle: pocklington -proth k p."
        },
        {
          "ref": "2016, Abhijit Das, Computational Number Theory, Taylor & Francis (CRC Press / Chapman & Hall), page 295:",
          "text": "Suppose that a Proth number n#x3D;k2ʳ#x2B;1 satisfies the condition that a#x7B;(n-1)#x2F;2#x7D;#x5C;equiv-1#x5C;pmodn for some integer a. Prove that n is prime.",
          "type": "quote"
        },
        {
          "ref": "2014, Adam Spencer, Adam Spencer's Big Book of Numbers, Brio Books, page 388:",
          "text": "If a Proth number is prime, we call it a Proth prime.",
          "type": "quote"
        }
      ],
      "glosses": [
        "Any number of the form k·2ⁿ + 1, where k is odd, n is a positive integer, and 2ⁿ > k."
      ],
      "hyponyms": [
        {
          "word": "Cullen number"
        },
        {
          "word": "Proth prime"
        }
      ],
      "id": "en-Proth_number-en-noun-bFEA2H59",
      "links": [
        [
          "number theory",
          "number theory"
        ]
      ],
      "raw_glosses": [
        "(number theory) Any number of the form k·2ⁿ + 1, where k is odd, n is a positive integer, and 2ⁿ > k."
      ],
      "related": [
        {
          "word": "Sierpinski number"
        }
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "translations": [
        {
          "code": "it",
          "lang": "Italian",
          "sense": "number of the form k×2^n + 1",
          "tags": [
            "masculine"
          ],
          "word": "numero di Proth"
        }
      ],
      "wikipedia": [
        "François Proth",
        "Proth number"
      ]
    }
  ],
  "word": "Proth number"
}

{
  "etymology_text": "After French mathematician François Proth (1852-1879).",
  "forms": [
    {
      "form": "Proth numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Proth number (plural Proth numbers)",
      "name": "en-noun"
    }
  ],
  "hyponyms": [
    {
      "word": "Cullen number"
    },
    {
      "word": "Proth prime"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "Sierpinski 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",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with Italian translations",
        "en:Number theory"
      ],
      "examples": [
        {
          "text": "2006, B. Grégoire, L. Théry, B. Werner, A Computational Approach to Pocklington Certificates, Masami Hagiya, Philip Wadler (editors), Functional and Logic Programming: 8th International Symposium, Proceedings, Springer, LNCS 3945, page 109,\nTo generate Pocklington certificates for Proth number we add a new entry to the oracle: pocklington -proth k p."
        },
        {
          "ref": "2016, Abhijit Das, Computational Number Theory, Taylor & Francis (CRC Press / Chapman & Hall), page 295:",
          "text": "Suppose that a Proth number n#x3D;k2ʳ#x2B;1 satisfies the condition that a#x7B;(n-1)#x2F;2#x7D;#x5C;equiv-1#x5C;pmodn for some integer a. Prove that n is prime.",
          "type": "quote"
        },
        {
          "ref": "2014, Adam Spencer, Adam Spencer's Big Book of Numbers, Brio Books, page 388:",
          "text": "If a Proth number is prime, we call it a Proth prime.",
          "type": "quote"
        }
      ],
      "glosses": [
        "Any number of the form k·2ⁿ + 1, where k is odd, n is a positive integer, and 2ⁿ > k."
      ],
      "links": [
        [
          "number theory",
          "number theory"
        ]
      ],
      "raw_glosses": [
        "(number theory) Any number of the form k·2ⁿ + 1, where k is odd, n is a positive integer, and 2ⁿ > k."
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "wikipedia": [
        "François Proth",
        "Proth number"
      ]
    }
  ],
  "translations": [
    {
      "code": "it",
      "lang": "Italian",
      "sense": "number of the form k×2^n + 1",
      "tags": [
        "masculine"
      ],
      "word": "numero di Proth"
    }
  ],
  "word": "Proth number"
}