A prime number is a natural number greater than 1 that cannot be written as the product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. In other words, a prime number is only divisible by 1 and itself, and if you divide a prime number by a number other than 1 and itself, you will get a non-zero remainder. The first 25 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. The central importance of prime numbers to number theory and mathematics in general stems from the fundamental theorem of arithmetic, which states that every integer larger than 1 can be written as a product of one or more primes.