What is a Prime Number?
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. This means that a prime number can only be divided evenly by 1 and itself, showing that it has exactly two distinct positive divisors. For example, the number 2 is considered prime because it can only be evenly divided by 1 and 2. Similarly, numbers like 3, 5, 7, 11, and 13 are also prime numbers.
Characteristics of Prime Numbers
- Prime numbers are greater than 1.
- They have no positive divisors other than 1 and themselves.
- The number 2 is the only even prime number; all other even numbers can be divided by 2, thus having at least three positive divisors.
Significance in Mathematics
Prime numbers are fundamental in number theory due to their role as the "building blocks" of the integers. Every integer greater than 1 can be expressed uniquely as a product of prime numbers, a fact known as the Fundamental Theorem of Arithmetic. This property makes prime numbers particularly interesting and essential in various branches of mathematics, including cryptography, which utilizes prime numbers to secure data.
Examples
Some of the first prime numbers include:
- 2
- 3
- 5
- 7
- 11
- 13
- 17
- 19