Six nines in pi

I myself once learned 380 digits of π, when I was a crazy high-school kid. My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes "999999", so that I could recite it out loud, come to those six 9s, and then impishly say, "and so on!"

This sequence of six nines is colloquially known as the "Feynman point", after physicist Richard Feynman, who allegedly stated this same idea in a lecture. However it is not clear when, or even if, Feynman ever made such a statement, as it is neither mentioned in his memoirs nor is it known to his biographer James Gleick.

Related statistics

It is widely conjectured that π is a normal number. For a normal number sampled uniformly at random, the probability of a specific sequence of six digits occurring this early in the decimal representation is about 0.08%.

The early string of six 9s is also the first occurrence of four and five consecutive identical digits. The next sequence of six consecutive identical digits is again composed of 9s, starting at position 193,034. The next distinct sequence of six consecutive identical digits after that starts with the digit 8 at position 222,299.

The positions of the first occurrence of a string of 1, 2, 3, 4, 5, 6, 7, 8, and 9 consecutive 9s in the decimal expansion are 5; 44; 762; 762; 762; 762; 1,722,776; 36,356,642; and 564,665,206, respectively (sequence A048940 in the OEIS).