Answer: 312211 More information: John Conway's "look and say" sequence has no digits other than 1, 2, and 3 in it, unless the seed number contains such a digit or a run of more than three of the same digit. A degenerate sequence appears with the seed of 22.

Answer: 3 More information: Russell collaborated very little and no Erdös number can be found using research articles. But, as pointed out by Sachi Sri Kantha at "the Erdös number project" Russell and Albert Einstein did coauthor the Russell-Einstein "Peace" Manifesto of 1955.

Answer: Paul Erdős, of course! More information: As the Erdős number describes the "collaborative distance" in authorship of mathematical papers between mathematician Paul Erdős and another person it is only natural that Paul Erdős holds this position.

Answer: A perfect number. More information: You might also think of a perfect number as a number that is half the sum of all of its positive divisors, including itself! This definition is at least 2300 years old as it appears in Euclid's "Elements".