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Number and sum of prime factors of a number

  1. Mar 22, 2013 #1
    Given a large number N, do we have any formula to find the number of prime factors and their sum like τ(N) and σ(N) functions?

    CONDITION: One should not list the factors of N or is not allowed to factorize N since afterwards it would be just a matter of counting and addition
  2. jcsd
  3. Mar 22, 2013 #2
    If such a formula ## f(N) ## exists, what would ## f(N) = 1 ## mean?
  4. Mar 22, 2013 #3
    I believe if such a formula does exist then the entire internet would be vulnerable. The internet is secure because of prime number factorisation. See RSA Algorithm

    There is a formula to find if a number is prime or not, but not the factors.

  5. Mar 22, 2013 #4
    That actually looks like a "formula" to find the ## n ##th prime, but such "formulas" are really just symbolic descriptions of (very ineffecient) algorithms and of no practical importance.
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