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Re: [PrimeNumbers] Probability of a number being a mobius number...

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  • Sarad AV
    hi Sudarshan, ... You might also like to try out MIRACL s factoring package below. http://indigo.ie/~mscott/#other ... According to mathworld (URL below) the
    Message 1 of 2 , Jul 8 11:12 AM
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      hi Sudarshan,

      > Its been a thrill to me to use the pari to factorize
      > large numbers.

      You might also like to try out MIRACL's factoring
      package below.

      http://indigo.ie/~mscott/#other

      > The question:-
      > The probability that a given big number n is a
      > mobius number is very
      > high. What is the mathematical reasoning behind
      > this.

      According to mathworld (URL below) the asymptotic
      density of square free numbers is 6/(pi^2) which is
      approximately 60%. So you should hit a squareful
      number nearly 40% of the time. With what probability
      did you find that the number under test to be
      squarefree and for how many integers did you test?

      http://mathworld.wolfram.com/Squarefree.html


      Sarad.




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