How many composite numbers are between 1 and 100?

##74##.

Let's count the primes up to ##100##.

##2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97.##

There are ##25## primes less than ##100##. Since ##1## is neither prime nor composite, and there are ##100## numbers total between ##1## and ##100## (inclusive), there are ##100-25-1=74## composite numbers between ##1## and ##100##.