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Re: [PrimeNumbers] New guy test drive

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  • Andy Swallow
    ... etc But read what I said. The number of squares *LESS THAN N* is of order N^(1/2), whereas the number of primes *LESS THAN N* is of order N/log N. I wasn t
    Message 1 of 6 , Dec 27, 2003
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      > Hi,
      > I am new too. However, since I can square every prime number, there are as
      > many square
      > numbers as there are prime numbers. I can also square every composite number
      > to get
      > even more squares but it doesn't matter. Indeed, since there is a 1 to 1
      > correspondence
      > between the positive integers and primes ie., every prime has an index,
      > threre are as many
      > primes as there are numbers. This takes care of every composite number
      > squared.
      etc

      But read what I said. The number of squares *LESS THAN N* is of order
      N^(1/2), whereas the number of primes *LESS THAN N* is of order N/log N.
      I wasn't talking about infinity, since that is a dangerous concept to
      mess around with. If you're unsure of what I mean by order, and if you
      want to talk about prime distribution, then I suggest you look up order
      notation.

      It all depends how you look at it, I guess. But the old paradox of
      "there are as many squares as integers" doesn't help much.

      Andy
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