Why do we need to use 2 nominalizers もの and こと in the following sentence?
素数とは、1 より大きい自然数で、正の約数が 1 と自分自身のみであるもののことである。
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「素数{そすう}とは、1 より大{おお}きい自然数{しぜんすう}で、正{せい}の約数{やくすう}が 1 と自分自身{じぶんじしん}のみであるもののことである。」
In this sentence, neither the 「もの」 nor 「こと」 is a nominalizer.
The 「もの」 here just means "the ones" or "those" and it refers to "those/the ones among the natural numbers greater than 1 that have no positive divisors other than 1 and themselves." That, of course, is the definition of prime numbers.
To call a word a "nominalizer", it needs to be nominalizing a verb. 「もの」 is not nominalizing a verb here.
「～～のことである」 is a set phrase meaning "it is said that ~~~" or "it is defined that ~~". Again, 「こと」 is not nominalizing a verb here.
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1I thought ある is a verb that もの nominalizes. – Second Person Shooter Dec 31 '17 at 22:56
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2@ArtificialStupidity Nominalizing refers to the process of treating a verb as a noun. ある is not itself being treated as a noun rather it is modifying もの to mean "things that are". You would nominalize ある if you were talking about "being" or "existing" in general as opposed to a specific thing that exists (as in this case). – G-Cam Jan 01 '18 at 00:21
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This 「もの」 is not a nominalizer. It is a noun in the full sense of the word, meaning "thing" or the pronominal "one" (in this case I think the latter is more applicable), which is here modified by the relative clause 「1 より大きい自然数で、正の約数が 1 と自分自身のみである」.
So 「1 より大きい自然数で、正の約数が 1 と自分自身のみであるもの」 means:
one (i.e. a number) which is a natural number greater than 1 and have no positive divisors other than one and themselves
As for the こと, it seems to be one indeed, according to デジタル大辞泉.
Under the subhead 「2⃣他の語句をうけて、その語句の表す行為や事態を体言化する形式名詞。」（”a formal noun that nominalizes the action or state expressed by another word or phrase”）, there's this subentry:
㋕（「…のことだ」などの形で）ある言葉の指し示す対象である意を表す。「九郎判官とは源義経の事だ」
This says that the function of this particular use 「事/こと」, in formulations like 「...のことだ」, is to state that a given word refers to some entity.
All in all, a translation of the whole sentence would be something like this:
素数とは1 より大きい自然数で、正の約数が 1 と自分自身のみであるものであるもののことである。
"Prime number" refers to one (i.e. a number) that is a natural number greater than 1 and have no positive divisors other than 1 and themselves.
(Compare: 素数とは...であるものである。→ A prime number is one (i.e. numbers) that is...)
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So, this sentence in Japanese is not a definition of prime numbers? I am confused with prime numbers or a prime number a little bit in both answer. Anyway, 今年もよろしくお願いします。 – Jan 01 '18 at 01:16
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I'm not proposing to make a distinction between the reference and the definition of a noun. When I wrote "'Prime number' refers to..." I meant it as synonymous with "'Prime number' means..." and I consider "'Prime number' means..." to be mostly the same thing as "The definition of 'prime number' is ...". – goldbrick Jan 01 '18 at 02:16
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つまり、定義としては複数形より "a"を使う方が自然かなと思ったのですが、 "The definition of 'prime number' is ..."は次のように、 "The definition of a prime number' is a natural number which is greater than 1 and has no positive divisors other than 1 and itself." ここに書いてある定冠詞の使い分けの説明からするとhttps://ell.stackexchange.com/questions/30999/the-articles-a-and-the-in-generic-statements?rq=1 まあ、とにかくあけましておめでとうございます。 – Jan 01 '18 at 02:50
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As @goldbrick noted correctly もの is preceded by an attributive phrase, wich together with もの becomes a nominal phrase, which in the end makes もの a nominalizer. Arguing if もの nominalizer or not is futile, it is all a matter of prospective. – user1602 Jan 03 '18 at 02:08