Is -1 Prime?
Date: 10/20/2000 at 09:57:04 From: Tom Nesbitt Subject: Is -1 Prime? My class discussed prime numbers. The class noted that -1 has exactly two factors (namely 1 and -1) and asked why it wasn't listed as a prime number. I reiterated the definition, but they weren't satisfied. Do you have any further information on this topic?
Date: 10/20/2000 at 12:28:25 From: Doctor Peterson Subject: Re: Is -1 Prime? Hi, Tom. Did you check our FAQ on Primes, or search our archives for "negative prime"? Here is one answer I found there: Why Aren't There Negative Prime Numbers? http://mathforum.org/dr.math/problems/lopez.12.10.99.html I assume that your definition of prime includes the word "positive," as in our FAQ. If the students are asking why the definition doesn't allow for negative primes, then this and other answers we have given should help. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 10/20/2000 at 13:07:15 From: Tom Nesbitt Subject: Re: Is -1 Prime? Thanks for writing back, Dr. Peterson. After writing you, students found the FAQ you enclosed and were appeased. The book we are using, Glencoe, defines a prime number as "A number that has exactly two factors, 1 and the number itself." I showed them a couple of other definitions that include natural numbers, counting numbers, or positive integers. They now want to write to the company and suggest a correction. One of the authors teaches in nearby Unionville-Chaddsford, so we may make this a letter-writing lesson too. Thanks for your help.
Date: 10/21/2000 at 03:33:50 From: Doctor Floor Subject: Re: Is -1 Prime? Dear Tom, I read the discussion you had with Dr. Peterson. Indeed it is true that in the usual definition of a prime, the prime is supposed to be a positive integer, or natural number. However, there are people, and not the least, who do consider -1 to be a prime. Professor John Conway of Princeton is one of them. Although I don't suppose it is desirable to have this in high school textbooks, I would like to point you to a newsgroup discussion thread about this subject: -1 as a Prime (geometry-research, Math Forum) http://mathforum.org/kb/message.jspa?messageID=1093170 A lot of this thread is useless, but the first (and later) messages by John Conway do explain why he considers -1 a prime, and why this is useful in his opinion. I hope you appreciate this addition. Best regards, - Doctor Floor, The Math Forum http://mathforum.org/dr.math/
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