Irregular, there is a definite trend to its values. Now back up and view a larger portion of the graph of π( x). Sub-section.) Look at the following graph and notice how irregular the Π( x) = the number of primes less than or equal to x. Primes are there less than x?' has been asked so frequently that its π( x) is the number of primes less than or equal to x The second question isĭiscussed on the page ' How Big of an Infinity?.' 1.1. This document will focus on the first question. There are infinitely many primes, but how big of an infinity?.How many primes are there less than the number x? Number of primes is infinite, so two possible questions come to mind: Over 2,300 years ago Euclid proved that the Introduction: Asking the Correct Question History of the Prime Number Theorem and other approximationsġ.Consequence Three: The chance of a random integer x being prime is about 1/ln x.Consequence Two: The nth prime is about n ln n.Consequence One: You can Approximate π( x) with x/(ln x - 1).π( x) is the number of primes less than or.Introduction: Asking the Correct Question.
