1 and 0Date: Fri, 4 Nov 94 08:33:09 +1000 From: - - Subject: maths problems Is 1 or 0 a prime number ? Why ? Please reply ASAP to form 2 maths group1 at St. Michael's Grammar School Melbourne Australia Date: Thu, 3 Nov 1994 19:42:56 -0500 (EST) From: Dr. Ken (dr.math@mathforum.org) Subject: Re: maths problems To: stmg@ozemail.com.au (- -) Hello Melbourne! Technically, neither 1 nor zero is a prime number. It is easiest to see why zero isn't: since a prime number is only divisible by one and itself, let's find all the divisors of zero. Well, since 0 x 1 = 0, and 0 x 2 = 0, and 0 x 3 = 0, and so on, all these numbers divide zero, i.e. zero is divisible by every positive integer. So it isn't a prime number. As for 1, you might want to call it a prime number, since it really _is_ divisible by only one and itself. But then you run into some problems. For instance, you may know that every positive integer can be factored into the product of prime numbers, and that there's only one way to do it for every number. For instance, 280 = 2x2x2x5x7, and there's only one way to factor 280 into prime numbers. But if you let 1 be a prime, then you can get the following factorizations: 1x1x1x2x2x2x5x7, 1x2x2x2x5x7, and so on. The factorization is no longer unique. Furthermore, there are a whole bunch of theorems in Number Theory that tell you something about prime numbers. But most of these theorems just flat out ain't true for the number 1. So in light of these facts, we just declare the number 1 to not be a prime. So that's why we don't WANT 1 to be a prime. Mathematicians have summarized this in a nice neat definition: a prime number is a positive integer which has exactly 2 different positive integers that divide it evenly - no more and no fewer. -Ken |
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