"primorial" meaning in All languages combined

{
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        "2": "prime",
        "3": "factorial"
      },
      "expansion": "Blend of prime + factorial",
      "name": "blend"
    }
  ],
  "etymology_text": "Blend of prime + factorial. Coined by American engineer and mathematician Harvey Dubner.",
  "forms": [
    {
      "form": "primorials",
      "tags": [
        "plural"
      ]
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  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "_dis1": "0 0",
      "word": "primorial prime"
    }
  ],
  "senses": [
    {
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          "kind": "topical",
          "langcode": "en",
          "name": "Number theory",
          "orig": "en:Number theory",
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      "examples": [
        {
          "ref": "2017, Kevin Broughan, Equivalents of the Riemann Hypothesis: Volume 1, Arithmetic Equivalents, Cambridge University Press, page 97",
          "text": "For example, up to 10⁹, every positive integer which is a multiple of a primorial and is less than the following primorial satisfies the given inequality. There has also been little discussion on which primorials qualify in the different situations when RH fails.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Any number belonging to the integer sequence whose nth element is the product of the first n primes."
      ],
      "id": "en-primorial-en-noun-2MzgC-zZ",
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        [
          "sequence",
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        ],
        [
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        ]
      ],
      "raw_glosses": [
        "(number theory) Any number belonging to the integer sequence whose nth element is the product of the first n primes."
      ],
      "synonyms": [
        {
          "word": "primorial number"
        }
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ]
    },
    {
      "categories": [
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          "kind": "topical",
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        {
          "_dis": "31 69",
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          "name": "English blends",
          "parents": [],
          "source": "w+disamb"
        },
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          "_dis": "24 76",
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          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
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          "source": "w+disamb"
        }
      ],
      "examples": [
        {
          "text": "The primorial of 6 is #x5C;textstyle 6#x5C;#x23;#x3D;2#x5C;times 3#x5C;times 5#x3D;30.",
          "type": "example"
        },
        {
          "text": "2020, Rong Pan, Qinheping Hu, Rishabh Singh, Loris D'Antoni, Solving Problem Sketches with Large Integer Values, Peter Müller (editor), Programming Languages and Systems: 29th European Symposium, Proceedings, Springer, LNCS 12075, page 587,\nThe following number theory result relates the primorial to the Chebyshev function.\nθ(n)= log (n#)= log 2⁽¹⁺ᵒ⁽ⁿ⁾⁾ⁿ=(1+o(n))n"
        }
      ],
      "glosses": [
        "A unary operation, denoted by the postfix symbol # and defined on the nonnegative integers, which maps 0 to 1, 1 to 1, and each subsequent number to the product of all primes less than or equal to it; the value mapped to by said operation for a given input."
      ],
      "id": "en-primorial-en-noun-6X1rFs5i",
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          "number theory",
          "number theory"
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          "unary operation",
          "unary operation"
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          "postfix",
          "postfix"
        ],
        [
          "nonnegative",
          "nonnegative"
        ],
        [
          "integers",
          "integers"
        ],
        [
          "less than",
          "less than"
        ],
        [
          "equal",
          "equal"
        ]
      ],
      "raw_glosses": [
        "(number theory) A unary operation, denoted by the postfix symbol # and defined on the nonnegative integers, which maps 0 to 1, 1 to 1, and each subsequent number to the product of all primes less than or equal to it; the value mapped to by said operation for a given input."
      ],
      "topics": [
        "mathematics",
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    }
  ],
  "translations": [
    {
      "_dis1": "53 47",
      "code": "de",
      "lang": "German",
      "sense": "product of primes",
      "tags": [
        "feminine"
      ],
      "word": "Primorial"
    },
    {
      "_dis1": "53 47",
      "code": "de",
      "lang": "German",
      "sense": "product of primes",
      "tags": [
        "feminine",
        "rare"
      ],
      "word": "Primfakultät"
    },
    {
      "_dis1": "53 47",
      "code": "it",
      "lang": "Italian",
      "sense": "product of primes",
      "tags": [
        "masculine"
      ],
      "word": "primoriale"
    },
    {
      "_dis1": "53 47",
      "code": "tr",
      "lang": "Turkish",
      "sense": "product of primes",
      "word": "primoriyel"
    }
  ],
  "wikipedia": [
    "Harvey Dubner",
    "primorial"
  ],
  "word": "primorial"
}

{
  "categories": [
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    "English entries with incorrect language header",
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    "English nouns"
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  "etymology_templates": [
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      },
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      "name": "blend"
    }
  ],
  "etymology_text": "Blend of prime + factorial. Coined by American engineer and mathematician Harvey Dubner.",
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    {
      "form": "primorials",
      "tags": [
        "plural"
      ]
    }
  ],
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  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "primorial prime"
    }
  ],
  "senses": [
    {
      "categories": [
        "English terms with quotations",
        "en:Number theory"
      ],
      "examples": [
        {
          "ref": "2017, Kevin Broughan, Equivalents of the Riemann Hypothesis: Volume 1, Arithmetic Equivalents, Cambridge University Press, page 97",
          "text": "For example, up to 10⁹, every positive integer which is a multiple of a primorial and is less than the following primorial satisfies the given inequality. There has also been little discussion on which primorials qualify in the different situations when RH fails.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Any number belonging to the integer sequence whose nth element is the product of the first n primes."
      ],
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        [
          "number theory",
          "number theory"
        ],
        [
          "sequence",
          "sequence"
        ],
        [
          "prime",
          "prime"
        ]
      ],
      "raw_glosses": [
        "(number theory) Any number belonging to the integer sequence whose nth element is the product of the first n primes."
      ],
      "synonyms": [
        {
          "word": "primorial number"
        }
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ]
    },
    {
      "categories": [
        "English terms with usage examples",
        "en:Number theory"
      ],
      "examples": [
        {
          "text": "The primorial of 6 is #x5C;textstyle 6#x5C;#x23;#x3D;2#x5C;times 3#x5C;times 5#x3D;30.",
          "type": "example"
        },
        {
          "text": "2020, Rong Pan, Qinheping Hu, Rishabh Singh, Loris D'Antoni, Solving Problem Sketches with Large Integer Values, Peter Müller (editor), Programming Languages and Systems: 29th European Symposium, Proceedings, Springer, LNCS 12075, page 587,\nThe following number theory result relates the primorial to the Chebyshev function.\nθ(n)= log (n#)= log 2⁽¹⁺ᵒ⁽ⁿ⁾⁾ⁿ=(1+o(n))n"
        }
      ],
      "glosses": [
        "A unary operation, denoted by the postfix symbol # and defined on the nonnegative integers, which maps 0 to 1, 1 to 1, and each subsequent number to the product of all primes less than or equal to it; the value mapped to by said operation for a given input."
      ],
      "links": [
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          "number theory",
          "number theory"
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        [
          "unary operation",
          "unary operation"
        ],
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          "postfix"
        ],
        [
          "nonnegative",
          "nonnegative"
        ],
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          "integers",
          "integers"
        ],
        [
          "less than",
          "less than"
        ],
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          "equal",
          "equal"
        ]
      ],
      "raw_glosses": [
        "(number theory) A unary operation, denoted by the postfix symbol # and defined on the nonnegative integers, which maps 0 to 1, 1 to 1, and each subsequent number to the product of all primes less than or equal to it; the value mapped to by said operation for a given input."
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ]
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "product of primes",
      "tags": [
        "feminine"
      ],
      "word": "Primorial"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "product of primes",
      "tags": [
        "feminine",
        "rare"
      ],
      "word": "Primfakultät"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "product of primes",
      "tags": [
        "masculine"
      ],
      "word": "primoriale"
    },
    {
      "code": "tr",
      "lang": "Turkish",
      "sense": "product of primes",
      "word": "primoriyel"
    }
  ],
  "wikipedia": [
    "Harvey Dubner",
    "primorial"
  ],
  "word": "primorial"
}