We can factor $2^8-1$ as $(2^4+1)(2^4-1)$.
Continuing to factor, we have $(2^4+1)(2^2+1)(2^2-1)$.
This simplifies to $(16+1)(4+1)(4-1)$, or $17\cdot5\cdot3$.
The sum of the three prime numbers is $17+5+3=\boxed{25}$.
The answer is: 25
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
The value $2^8 -1$ is divisible by 3 prime numbers. What is the sum of the three prime numbers?

### Answer:
