Introduction
A prime number is “a natural number greater than 1 that can be divided evenly only by 1 and itself” (Alfeld). There are great many of prime numbers, the smallest one is 1 and the largest known prime number on the moment of webpage creation is m39 = 213,466,917-1 (Alfeld). A prime counting function π(x) “counts the number of primes that are less than or equal” to x (Bose 292). Considering the prime counting function π(x), it may be concluded that the value of π(x) increases only when x encounters the prime number. Thus, the function π(x) can be characterized as monotonically increasing one.
Defining the prime number theorem, it is significant to notice that it was conjectured by Legendre and Gauss. To the word, they worked on the theorem separately and managed to achieve the same results independently. A prime number theorem is the statement that “the relative error in the approximation π(x) ~ Li(x) approaches zero as x → ∞” (Edwards 68). The following statement can be illustrated as follows,
The non-linear equation can be characterized as “one that represents a relationship whose graph is not a straight line (with two variables), a plane (with three) or a hyperplane (with four or more)” (Parkhurst 229). The examples of non-linear equations are numerous, such as logarithmic and trigonometric functions, power functions (axb), exponentials (aebx) and many others (Parkhurst 229).
Thus, when the theoretical information is checked, it is high time to turn to the practical assignment. Still, there is one more question that can be interesting for students is why the prime numbers should be considered and whether they are really important.
Theory
Prime numbers play significant role in different spheres of people’s life, both scientific and social. Related to mathematics, prime numbers are important is developing new theories, in convergent or divergent of certain series, for finite field creation, and many others that are connected with calculation. It should be highlighted that prime numbers play a significant role in coding and computation algorithms and circuits.
Prime numbers in practical life
As it was mentioned above, prime numbers are used in practical life. Using computers and calculators, people usually turn to Binary operation that is characterized by 2 that is a prime number. Internet shops became an essential part of people’s life. Not many people know that buying products online, they use prime numbers via credit card. Prime numbers in the credit card are created with the aim of security not to deliver the message to a strange person, except for intended recipient. In other words, buying furniture, for example, a person sends a credit card number and PIN to online furniture shop and no any other person is able to read this information (Bose 243).
Still, this use prime numbers is practical, thus not really interesting. There is one more opportunity to use prime numbers in everyday life that is to solve the problems they give us. In fact, there are some problems connected to prime numbers that are not solved yet and these problems give scientist food for thoughts, such as Goldbach’s conjecture that relates to the question whether there is an even number greater than two and that at the same time cannot be written a sum of two primes and other problems. Apostol once said, “Solve any of the above, and your name, too, shall live forever in the mathematical hall of fame!” (in Peterson 125). Is not this the main background for prime numbers consideration?
Works Cited
Alfeld, Peter. Understanding Mathematics. University of Utah, 2003. Web.
Bose, Ranjan. Information theory, coding and cryptography. Noida: Tata McGraw-Hill, 2008. Print.
Edwards, Harold M. Riemann’s zeta function. Dover: Courier Dover Publications, 2001. Print.
Parkhurst, David F. Introduction to applied mathematics for environmental science. New York: Springer, 2006. Print.
Peterson, Ivars. Mathematical treks: from surreal numbers to magic circles. New York: MAA, 2002. Print.