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: Pierre-Simon Laplace has an Erdős number of at most 14! More information: According to "The Erdös number project" a path to Laplace was found by Leonid Yanushevich giving the famous mathematician an Erdös number of at most 14.

Answer: 3 More information: Of course, as time passes, the smallest Erdős number that can still be achieved will necessarily increase, as mathematicians with low Erdős numbers die and become unavailable for collaboration.

Answer: 5 More information: Portman collaborated (using her birth name, Natalie Hershlag) with Abigail A. Baird, who has a collaboration path (Gazzaniga, Michael S. -> Victor, Jonathan D.) leading to Joseph Gillis, who has an Erdős number of 1.

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: Leonhard Euler. More information: Swiss-born Euler is held to be one of the greatest mathematicians in history. He made pioneering contributions to several branches of mathematics and introduced much of the modern mathematical terminology and notation.

Answer: Paul Erdős More information: Erdős published at least 1,525 mathematical papers during his lifetime. He engaged more than 500 collaborators and devoted most of his time to mathematics up until his death in 1996 at the age of 83 years old.

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".