Cover illustration: The cover shows a magnified view—through a watchmaker’s loupe—of a very small portion of an actual poster giving the 7.2 million decimal digits of the prime 2 24036583-1. Ifthe entire one-meter tall poster were thus magnified, it would be the size of a baseball diamond.

Building upon the work of Carl Pomerance and others, the central purpose of this discourse is to discuss the distribution of base-2 pseudoprimes, as well as improve upon Pomerance's conjecture regarding the Carmichael number counting function [8]. All conjectured formulas apply to any base b ≥ 2 for x ≥ x0(b). A table of base-2 pseudoprime, 2-strong pseudoprime, and Carmichael number counts up to 10 15 from [4] is included in the Appendix. We also discuss strong pseudoprimes and probabilistic primality testing. 1