law of small numbers (another Prime Pages' Glossary entries) The
Prime Glossary Glossary: Prime Pages: Top 5000: Richard Guy
often refers to the law of small numbers which states that there
are not enough small numbers to satisfy all the demands placed
on them. What this means is that we will often see things happen
with small numbers that are not normative, that is, often small
numbers do not well represent the behavior of large numbers. I
think this demands a few examples before we discuss it further.
1. Let's start real small: the first four odd numbers are 1, 3,
5, 7; so should we conclude all odd numbers are either one or
prime? I'd hope not!   2. Look at the remainders when the first
few primes are divided by four     2, 3, 1, 3, 3, 1, 1, 3, 3, 1,
3, 1, 1, 3, 3, 1, 3, 1, 3, 3, 1, 3, 3, 1, 1, 1, 3, 3, 1, 1, . .
.     It looks like if we stop this list at any point, there are
always at least as many 3's as there are 1's. This pattern would
hold even if we looked at the first 25000 terms of this sequence