According to Dr. Dillon Mayhew, of the Victoria University of Wellington (New Zealand), "modern mathematicians define a number as prime if it is divided by exactly two numbers. For example: 13 is prime, because it can be divided by exactly two numbers, 1 and 13. Six (6) is not prime, because it can be divided by four numbers, 1, 2, 3 and 6. One (1) can only be divided by one number, 1 itself, so with this definition 1 is not a prime number."
Dr. Mayhew goes on to explain that 1 has been deliberately excluded from the set of prime numbers, for the convenience of mathematicians. The reason is that if 1 is not a prime, every non–prime number can be formed by multiplying primes together "in a unique way". For example: the number 325 can be formed by multiplying 5 by 5 by 13, and this is the only way that this number can be formed by multiplying primes (except by rearranging the order, for example 5 by 13 by 5; but this, according to Dr. Mayhew, is "pretty cosmetic"). If 1 is a prime, 325 can be formed by multiplying (for example) 1 by 1 by 5 by 5 by 13; there is no longer a unique way of forming the number 325 by multiplying primes together.
© Haydn Thompson 2023