Commentary: Wonders - Numbers: Prime or Choice?; November 1998; Scientific American Magazine; by Morrison; 2 Page(s)

The simplest infinity is the one already recognized by many a curious young girl or boy counting 1, 2, 3, 4. . .. My friend Carl Sagan recalled a Sunday long ago when at age six he had delighted in newfound counting skills. His father explained to him that there need be no end to the count. Why stop? Just add one more. Gung ho, the boy set out to write integers that very evening all the way up to a big--if finite--1,000! His father generously wrote on for the boy during the time lost to Carl¿s customary evening bath. Together father and son completed their kilocount by bedtime, an experience Carl never forgot.

Positive integers are an infinite family whose kinship is wonderfully intricate. Most integers can be generated by multiplying together enough smaller integers, called factors. Thus, the number 18 = 2 x 3 x 3. (But try 17!) Here a chemical metaphor arises: 18 is a molecule among numbers, a composite of three numberatoms, whereas 17 suggests a pure element, all one kind of atom. It is called a prime number and has as factors only itself and unity.