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Year 7 Question I got asked and had to admit I didn't know the answer.

Discussion in 'Mathematics' started by adismale, Feb 10, 2011.

  1. I was taking the register the other day and instead of answering their names I challenged them to answer with a prime number that wasn't up on my wall (2 - 37). I got right up to the end when one child said -2.
    He then asked if you could have negative prime numbers and I had to admit that I didn't know for sure but that I would find out for him.
    I knew exactly where to ask! Here. Anbody know?
     
  2. Not certain, but I thought primes had to be integers? Plus, even if there were neg prime numbers, wouldn't they just be the same as the positive ones, but negative?
     
  3. In the more general setting of a ring (the integers are an example of a ring), then yes, -2 would count as a prime.
    But when dealing with the integers, we usually restrict primes to positive numbers, and so -2 would not normally be described as a prime.
     
  4. PaulDG

    PaulDG Occasional commenter

    There can be no negative prime numbers as, if there were, the fundamental theorem of arithmetic would no longer be true.
    It says that every number can only be factorised into prime numbers one way.
    So the ONLY prime factorisation of 4 is 2x2.
    If negatives could be prime, then there would be 2 solutions: 2x2 and (-2)x(-2) (and for larger numbers, the number of possibilities could be huge).
     
  5. David Getling

    David Getling Senior commenter

    every natural number

    If n is a negative integer then clearly, we need to include at least one negative prime, and so we could have more than one factorisation. However, we consider all factorisations that differ only by unities to be the same.

    See section 12.4 of An Introduction to the Theory of Numbers by Hardy and Wright, where a restatement of the fundamental theorem allows for negative primes.
     
  6. I usually use the definition that prime numbers are numbers which have exactly 2 factors (hence 1 not being). Which would mean you couldn't have negative primes. (although you would have to accept that factors are positive)
     

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