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?

Aside from the mathematical answers provided by others, the computational verification of the Collatz problem is a good exercise for programmers. There are many optimization opportunities (e.g., time-space trade-off using lookup tables, parallelism), many pitfalls (e.g., integer type overflow), possibilities of exploiting various implementation tricks (e.g., count trailing zeros instructions available in modern hardware), etc. It is a simple task where you can practice many basic programming constructions (branching the program, do-while loops, recursion). And for these reasons, this is arguably the most common task you can find in many online or university courses (e.g., Harvard University's CS50 course).
