A new definition of primes

I had a discussion over email a while ago with someone I finally met today about whether the number 2 is prime.  Let’s call him James.  His real name is James.

A prime is usually defined as a number greater than or equal to two that is divisble by 1 and itself.  People often take issue with the arbitrary lower limit set, which is there to avoid 1 being prime which would almost certainly cause the world to end—the likely wider consequences are far greater.  But I’ve never had a discussion with anyone about whether 2 is prime.  It just is.

To avoid any doubt over 1’s primeness (and indeed that of its next door neighbour, 2), I’ve never understood why the definition isn’t changed to the following:

Any number divisible by exactly two positive integers.

It would work wonderfully and save all sorts of deep and meaningfuls among mathematicians.  Actually, maybe that’s why the definition’s never been changed.


2 Responses to “A new definition of primes”

  1. The Caped Crusader on July 30th, 2009 11:00

    Perhaps because no self-respecting mathematician would publish a formal definition with a spelling mistake in it, never mind two? A better definition might be

    “Any number divisible by exactly two positive integers.”

    What do you think?

  2. Dan on July 30th, 2009 11:50

    Updated and suitably shamed.

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