Primality in Number Theory

Janet Flume
Friedley Senior High School

Abstract

The concept of primality is central to the number theory concepts. Prime numbers are the natural integers with no positive divisors apart from one and itself. Natural numbers greater than one, which are not prime numbers are commonly referred to as composite numbers. For instance, five is a prime number solely because five and one are its lone positive, numerical factors. On the other hand, six is not a prime number because two and three are its divisors in addition to one and itself. The fundamental theorem establishes the principle role of primality in the number theory. It states that integers greater than one may be expressed as products of primes uniquely in terms of ordering. The distinctiveness of the conception requires the exclusion of one as a prime number because of the possibility of including one in factorization. For instance, 3, 1•3, 1• 1 c3 and so on, are legitimate factorization of three. The trial division is a slow but simple approach for the verification of the primality of any given integer. The process entails ascertaining whether an integer is a multiple of any number between two and the root of the integer. However, algorithms are considered to be much more effective in the testing of primality of relatively larger integers. Even numbers greater than two are not considered as prime numbers because, by definition, such numbers have at minimum three discrete divisors, namely one, two, and itself.

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