"Proth number" meaning in English

{
  "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": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
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          "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": "quotation"
        },
        {
          "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": "quotation"
        }
      ],
      "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 entries with language name categories using raw markup",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with non-redundant non-automated sortkeys",
        "English terms with quotations",
        "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": "quotation"
        },
        {
          "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": "quotation"
        }
      ],
      "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"
}