"prime decomposition" meaning in English

{
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    {
      "form": "prime decompositions",
      "tags": [
        "plural"
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      "expansion": "prime decomposition (plural prime decompositions)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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          "name": "English entries with incorrect language header",
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          "source": "w"
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      ],
      "glosses": [
        "Synonym of prime factorization"
      ],
      "id": "en-prime_decomposition-en-noun-Z6Rfsm9Z",
      "links": [
        [
          "prime factorization",
          "prime factorization#English"
        ]
      ],
      "raw_glosses": [
        "(rare) Synonym of prime factorization"
      ],
      "synonyms": [
        {
          "tags": [
            "synonym",
            "synonym-of"
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          "word": "prime factorization"
        }
      ],
      "tags": [
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    }
  ],
  "word": "prime decomposition"
}

{
  "forms": [
    {
      "form": "prime decompositions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "expansion": "prime decomposition (plural prime decompositions)",
      "name": "en-noun"
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  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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      ],
      "glosses": [
        "Synonym of prime factorization"
      ],
      "links": [
        [
          "prime factorization",
          "prime factorization#English"
        ]
      ],
      "raw_glosses": [
        "(rare) Synonym of prime factorization"
      ],
      "synonyms": [
        {
          "tags": [
            "synonym",
            "synonym-of"
          ],
          "word": "prime factorization"
        }
      ],
      "tags": [
        "rare"
      ]
    }
  ],
  "word": "prime decomposition"
}