# Prime-square or prime-squared? [on hold]

I am not so sure which one is the correct spelling. When we try to say a square/cube of a prime, we should call it a "prime-squared/cubed" or a "prime-square/cube" number?

It sounds to me that "prime-squared/cubed" is the right choice as we are squaring/cubing the number. But I found both versions in different webpages, so I get confused. Are they both acceptable or it was a typo?

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## put on hold as off-topic by Hot Licks, Jason Bassford, Cascabel, jimm101, Edwin Ashworth2 days ago

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• This question belongs on another site in the Stack Exchange network: MathsSE. – Edwin Ashworth 2 days ago

In the expression "a prime-square", the hyphenated word is a noun, whereas in "a prime-squared number" the hyphenated word is an adjective. Both are correct in the context they're being used for.

Thus it would be correct to say:

A prime-square is also called a prime-squared number and refers to a prime number that has been squared. Similarly, a prime that has been cubed is a prime-cube.

However, the above is an example of correct grammar rather than preferred usage. The terms themselves don't seem to be very common: Google Ngram Viewer returned a null result for each of the hyphenated forms. A broader search through Google Books shows mixed results, but it seems that the unhyphenated expressions are also used: this book uses both prime squared and a prime squared number.

The most common expression is neither of these but the square of a prime. See Google Ngrams.

In fact, the Google Ngram overestimates the use of prime square for this concept because most of the hits use prime square for something else.

In the noun "prime-squared", the word "prime" acts as a noun (it is shorthand for "prime number"). It would be my preferred choice by far, referring to a "prime number that has been squared". I would argue that the second formulation is actually wrong and should be avoided! Indeed, as a "prime" is a noun referring to a "prime-number", a "prime-square" seems, in this context, to refer to a "prime-square number", i.e. a number which is both a prime and a square (which obviously cannot exist).

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In fact, such terms are commonly used in mathematical society. And that is why I am asking this question. I just searched through MathSciNet (you might have no access) and it seems that native English speakers all used "prime-squared" and other people use both. (See a screenshot as follows) So I guess "prime-squared" should be more appropriate?

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