The first 25 prime numbers are two, three, five, seven, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. A prime number is a positive value only divisible by itself and the number one. For instance, the number 11 has two factors: one and 11.
Greek mathematicians studied prime numbers as far back as 300 BCE when Euclid published a series of theorems in his treatise "Elements." Euclid's work demonstrated that all non-prime numbers, or composites, are made up of a unique combination of prime numbers. In other words, a series of prime numbers can be multiplied to produce each composite number. For example, 2 x 3 = 6, and 2 x 2 x 3 = 12.
Mathematician Eratosthenes designed a rudimentary algorithm in 200 BCE that used a grid system to quickly sort out divisible numbers. The series of prime numbers is considered infinite, and as of May 2013, the largest one discovered contained 17,425,170 digits.
In modern society, prime numbers are used for security encryption, especially in banking and Internet commerce. Large composite numbers are difficult to break down to individual factors, creating a time-consuming roadblock for codebreakers.