Number theory, or the study of integers (the counting numbers 1, 2, 3..., their opposites –1, –2, –3..., and 0), has fascinated mathematicians for years. Prime numbers, a concept introduced to most students in Grades 4 and up, are fundamental to number theory. They form the basic building blocks for all integers.
A prime number is a counting number that only has two factors, itself and one. Counting numbers which have more than two factors (such as 6, whose factors are 1, 2, 3, and 6), are said to be composite numbers. The number 1 only has one factor and usually isn't considered either prime or composite.
- Key standard: Determine whether a given number is prime or composite, and find all factors for a whole number. (Grade 4)
Why Do Prime Factors Matter?
It's the age-old question that math teachers everywhere must contend with. When will I use this? One notable example is with cryptography, or the study of creating and deciphering codes. With the help of a computer, it is easy to multiply two prime numbers. However, it can be extremely difficult to factor a number. Because of this, when a website sends and receives information securely—something especially important for financial or medical websites, for example—you can bet there are prime numbers behind the scenes. Prime numbers also show up in a variety of surprising contexts, including physics, music, and even in the arrival of cicadas!
There is another place where prime numbers show up often, and it's easy to overlook when discussing applications: math! The study of pure mathematics is a topic that people practice, study, and share without worrying about where else it might apply, similar to how a musician does not need to ask how music applies to the real world. Number theory is an extremely rich topic that is central to college courses, research papers, and other branches of mathematics. Mathematicians of all stripes no doubt encounter number theory many times along their academic and professional journeys.
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