Is this a valid definition? : A prime number can be constructed from other positive integers by addition, but not by multiplication.

(I am neither a math student nor a professional, but maths somehow got into my head recently. I am trying to understand things in terms which seem as simple as possible to me. Anything beyond quadratic equations rapidly leaves me in the dust. Calculus is way beyond my grasp for now.)

Edit : I guess I am trying to get a handle on the relationship between one and primes by sticking to the numberline and avoiding representing composites as 2d objects as they appear to me when they are a product.

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    $\begingroup$ Welcome to Mathematics Stack Exchange. Perhaps you mean constructed from other positive integers. $3=1\times3$ is prime $\endgroup$ Aug 10 '21 at 13:53
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    $\begingroup$ Unfortunately, it's not a valid definition unless you state precisely what you mean by "construct by addition/multiplication". The usual definition of a prime number is that it is a positive integer with exactly two (positive) factors. That doesn't require knowledge of calculus to understand, does it? :) $\endgroup$
    – Joe
    Aug 10 '21 at 13:55
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    $\begingroup$ A prime number $p$ has only $1$ and itself as positive integer (natural) factors. For various good reasons, the natural number $1$ is defined not to be prime! To talk about construction, you should know that any composite number (non-prime), is composable - hence the name - as the product of two or more primes. This is called the Fundamental Theorem of Arithmetic. For example, $24=3\times2\times2\times2$; this works for any positive integer, of any size, other than $1$, but I suppose $1$ is considered an "empty product". $\endgroup$
    – FShrike
    Aug 10 '21 at 14:06
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    $\begingroup$ No. Prime numbers can be constructed by division of other numbers. For example, $3=18/6$. $11=1100/100$ etc. $\endgroup$ Aug 10 '21 at 14:14
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    $\begingroup$ @ToMath: The term "factor" is standard mathematical terminology that will be familiar to the vast majority of my audience; this is not so with "construction by addition/multiplication". It's for the same reason that I didn't feel the need to define what "positive" meant when I was giving the definition. $\endgroup$
    – Joe
    Aug 10 '21 at 19:41

As Joe said in his comment, a prime number is a positive integer with exactly two distinct (positive integer) factors.


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