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RE: [PrimeNumbers] Are Big Numbers More Likely To Be Prime?

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  • Chris Caldwell
    ... increases as A increases. QED. Alan pointed out the Prime Number Theorem, which is truly important, but also consider common sense: past 2, half of the
    Message 1 of 4 , May 23, 2010
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      > This is tantamount to saying that the probability that A is prime
      increases as A increases. QED.

      Alan pointed out the Prime Number Theorem, which is truly important, but
      also consider common sense: past 2, half of the numbers composites
      divisible by 2. Past 3, half of those remaining numbers are divisible
      3, past 5, 1/5 are divisible by 5... obviously the density is going down
      (on the average).

      Good luck!
    • Peter Kosinar
      ... So far okay... ... ... but why exactly would this ratio describe the probability of a number being a prime? Peter
      Message 2 of 4 , May 23, 2010
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        > Let A be a natural number. Let S be the set of all prime numbers such
        > that any element of S is less than the step function of the square root
        > of A.

        So far okay...

        > Define the probability that A is a prime number as the quotient (A-S)/A.

        ... but why exactly would this ratio describe the probability of a number
        being a prime?

        Peter
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