Composite number is translated as 合成数 (by google translation to Japanese),
which makes sense.

Prime number is called 素数, but what does 素 means here?

I am trying to trace the source of it. We borrowed the translation of it
decades ago, so it does not very conceivable to illustrate it by the Chinese
dictionary items.

I would appreciate it very much if answered in English.
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question
etymology compounds mathematics
what does 素 mean in 素数?
From an etymological standpoint, the character 素 itself originates from China.
In about the 5th century AD, Japan started using Chinese characters. Before
this point, there was no Japanese writing system, and modern hiragana and
katakana are derived from the Kanji that was first introduced to Japan around
this time period.

From what I understand the Japanese language obtained most of their Kanji from
China between the [5th and 9th centuries](https://www.sljfaq.org/afaq/kanji-
pronunciation.html#:~:targetText=For%20example%20the%20character%20%E6%9C%A8,read%20as%20moku%20or%20ki.&targetText=The%20on%2Dyomi%20is%20an,have%20multiple%20on%2Dyomi%20readings.).

Over the centuries, there were many Japanese scholars that went to either
Korea or China to study, and they returned with additional Kanji characters
that they then introduced to the Japanese language. Due to the lack of
detailed records about what character came when, I cannot be more specific
than this: The character started being used in the Japanese language sometime
during or even after the 5th century AD.

The thing is, the scholars that went to China had their disagreements about
the meaning and pronunciation of the Chinese characters. These disagreements
can be derived from one of a number of factors including the region the
scholar studied, or when the scholar studied (things change with time). This
is why we sometimes see multiple Chinese readings for characters. A classic
example is [人](https://jisho.org/search/%E4%BA%BA%20%23kanji), which has the
Chinese readings ジン, and ニン. This discrepancy likely stems from the fact that
two different scholars disagreed on how the character was truly pronounced (or
they were confused), and so they taught what they understood. As the language
developed both readings became accepted.

Just as Kanji can have multiple ON-readings, the same issues sprouted up about
what the characters actually meant. Remember, that Chinese was not the
Japanese scholar's first language, [so at times the meaning of words and
characters were occasionally garbled by the translation attempts of the
scholars](https://www.sljfaq.org/afaq/kanji-
pronunciation.html#:~:targetText=For%20example%20the%20character%20%E6%9C%A8,read%20as%20moku%20or%20ki.&targetText=The%20on%2Dyomi%20is%20an,have%20multiple%20on%2Dyomi%20readings.).
In addition, as characters were re-introduced into the Japanese language, the
pronunciation of the Chinese reading also occasionally evolved. Though I do
not speak Chinese personally, I have seen cases where characters will take a
different meaning in Japan.

So to answer more directly, the character 素 likely was introduced to Japan
between the 5th and 9th century AD. Due to the complexities of learning
foreign languages, the meaning and ON-readings of the character were probably
the source of some discrepancies between early scholars, so the Japanese
language evolved to accept the opinions of all the scholars involved.

* * *

**Edit:**

I realized that I did not answer what 素 means in this context. According to
the online dictionaries that I use, [素 can
mean](https://jisho.org/search/%E7%B4%A0%20%23kanji): elementary, principle,
naked, or uncovered.

In the context of prime numbers, I would take this to mean elementary or
principle, as prime numbers cannot be divided into whole numbers.
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answer