What is the importance of the Collatz conjecture? I have been fascinated by the Collatz problem since I first heard about it in high school.

Take any natural number $n$. If $n$ is even, divide it by $2$ to get $n / 2$, if $n$ is odd multiply it by $3$ and add $1$ to obtain $3n + 1$. Repeat the process indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach $1$. [...]
Paul Erdős said about the Collatz conjecture: "Mathematics is not yet ready for such problems." He offered $500 USD for its solution.

QUESTIONS:
How important do you consider the answer to this question to be? Why?
Would you speculate on what might have possessed Paul Erdős to make such an offer?
EDIT: Is there any reason to think that a proof of the Collatz Conjecture would be complex (like the FLT) rather than simple (like PRIMES is in P)?  And can this characterization of FLT vs. PRIMES is in P be made more specific than a bit-length comparison?

I will answer to this question:
Question: How important do you consider the answer to this question to be? Why?
See the given below Reason given by mathematician Terence Tao here:

See Terence Tao you tube video on Collatz Conjecture where you will understand it's more application.
EDIT:
Also see this pdf which contains all the things discussed by professor Terence Tao in this video.
