Quandaries and Queries


Dear Math Central,
My name is Joshua and I am a 5th grade student. We have been
learning about prime and composite numbers. Unfortunately no one in
our class, including the teacher, can answer this question: "if 1
is neither prime nor composite...what is it called?"

Please let me know ASAP, our class is waiting for an answer.

Thank you,



Hi Joshua,

Actually, these definitions date from at least two thousand years. In book VII of Euclid's Elements, the following definitions are given:

Definition 1
A unit is that by virtue of which each of the things that exist is called one.

Definition 2
A number is a multitude composed of units.
Definition 11
A prime number is that which is measured by a unit alone.

...Definition 13
A composite number is that which is measured by some number.
I am not sure what to make of the definition of "unit'', but I think that calling a number a "multitude composed of units'' meant that Euclid does not consider 1 as a number!

Nowadays, we do consider 1, 0, and negatives as "numbers'', but the tradition concerning the definition of "primes'' and "composites'' has been passed on down to us. The everyday langage is also full of expressions that we still use but that made sense in the past. For example, we still say `"you sound like a broken record'' to somebody who always repeats the same thing, but only the older adults have actually heard a ``broken record'' who always repeats the same thing.

There is also at least one other instances in Mathematics where we seem to split the numbers into two sets, but one number gets left unaccounted for. I am thinking about positive and negative integers. The positive integers are larger than zero, the negative numbers are less than zero, and zero in niether positive nor negative.

Claude and Penny


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