Consecutive zeros in decimal expansion of $\pi$

Question

Is it known whether or not there exist arbitrarily long sequences of consecutive zeros in the decimal expansion of $\pi$?

Answer 1

It is "known" but not known. It is "known" because $\pi$ is expected to be normal. Almost all reals are and there is no known reason for $\pi$ not to be. Being normal implies (among many other things) that sequences of zeros occur at their statistical expectation-that a string of $n$ zeros will occur on average every $10^{n}$ digits. But the normality of $\pi$ has not been proven.

Answer 2

There are conjectures saying so. The result is unknown. Anyway, taking a random number in every interval without preference, you find such a number with probability one. There are known nombers with such a property, such as the Champernowne constant