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".

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: 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: 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: 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.