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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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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.

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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.

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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?enter image description here

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