# Number and sum of prime factors of a number

1. Mar 22, 2013

### suchith

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. Mar 22, 2013

### MrAnchovy

If such a formula $f(N)$ exists, what would $f(N) = 1$ mean?

3. Mar 22, 2013

### uperkurk

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.

4. Mar 22, 2013

### MrAnchovy

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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