The local newspaper has letters to the editor from 60 people. If this number represents 4​% of all of the​ newspaper's readers, how many readers does the newspaper​ have?

Let's call the total number of readers x.

The number of readers represented by the 60 people who wrote letters to the editor is 4/100 * x = <<4/100*+x=0.04x>>0.04x.

Since 0.04x = 60, we can divide both sides of the equation by 0.04 to find x: x = 60 / 0.04 = 1500.

Therefore, the newspaper has 1500 readers. Answer: \boxed{1500}.