Note: The assertion that the digits of pi are normal is widely conjectured but unproven. (Also note that random is not the same thing as normal. Hate to hairsplit, but the digits of pi are certainly not random). It is important to note that the digits of certain other irrational numbers appear to be normal to a superficial inspection but in fact are not (such as root three, for instance. at least, so I've heard.)

An actual proof that the digits of pi are in fact normal would make big waves in the math circles.