what is a prime number in maths

A prime number in mathematics is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. Prime numbers are the building blocks of the natural numbers and play a crucial role in number theory and mathematics in general. They are not divisible by any other positive integer without leaving a remainder. For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29 are the first few prime numbers. The concept of prime numbers is fundamental to the fundamental theorem of arithmetic, which states that every integer greater than 1 can be written as a unique product of prime numbers. This theorem is essential in various branches of mathematics and has been generalized in different ways to indicate minimality or indecomposability in an appropriate sense.