Subject: Negative primes

I have received the following question via e-mail from my granddaughter: "Can negative numbers (like -7) be prime? If not, why not?"

Name: Paul as agent for Leah 8th grade

Thanks for your help

Hi Leah and Paul

The foundations to the theory of numbers were developed by the ancient Greeks during the centuries before Euclid wrote his famous geometry text (around 300 BC). In Book 7 of that text, Euclid summarized all that was then known about prime numbers. To the Greeks, numbers represented measurements, so only positive numbers made sense. The Greeks thought geometrically: "28 divided by 12" would correspond to something like "27 inches equals 2 feet with 3 inches left over." They would think of a prime number as one being "measured only by units", as opposed to a composite number such as 21 which "can be measured by a ruler that is 3 units long." It seems that 1 was not a number, but a unit, while a number was something composed of two or more units. It is possible to wonder what would have happened had negative numbers been invented before prime numbers, but the fact is that we have been using the same definition of a prime number for more than 2000 years, and nobody is going to change it.

Cheers,

Chris

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