Expert: David Hemmer - 7/10/2007

Question
QUESTION: Hello:

Can a fraction be a prime number? If not, why, and if none are prime numbers, are they considered composite numbers?

I thank you for your reply.


ANSWER: No, "prime numbers" are a subset of 1,2,3,4,5,6,7 ... which have only 1 and themselves as factors. Thus the prime numbers are 2, 3, 5, 7, 11, 13, ... Fractions are not "prime".

There is a generalization of "prime" to different rings, other than the integers. If you are interested ask me a followup question. (This is if you are, for example, a senior math major.)

---------- FOLLOW-UP ----------

QUESTION: I want to thank you for your reply. I do have a follow-up question.
If they are not considered to be prime numbers, are they composite numbers or just in the category of rational numbers?

I thank you for your follow-up reply.

Answer
They are rational numbers, I would not call them composite or prime. You might want to call fractions like 11/7 prime but that wouldn't be good because they can factor in many nontrivial ways:

11/7= 33/14 * 2/3  for example.

"Prime" and "composite" refer only to integers!