The mathematical community has different opinions throughout history. Before the twentieth century, most mathematicians considered 1 prime but now due to some current conventions including cryptography has taken the position that it is not, because the primes are defined for non-invertible elements, and Z the 1 is invertible. Also does not meet certain requirements like a prime in the Euler function (the number of relatively prime to n). Despite this today in many areas the prime number 1 is considered prime number and many mathematicians with less conventionalist character they are in favor of 1 is a prime number.

Let’s discuss some definitions of prime numbers to be closer to an answer:

An integer is called a prime number if you only have as positive divisors (factors) itself and unity.

1 has factors the itself and the unit (although they are the same) therefore satisfies the condition because the definition does not make clear that the dividers have to be different, so in this definition one is prime.

A number is prime if it has two dividers (the drive and the same).

In this case it’s required that there are two dividers. Therefore for this definition one is not prime.

Prime number is one that can not be obtained by the multiplication of two numbers other than itself and unity.

The definition is valid since the two numbers can be 1 and 1 For this definition one is prime.

A number has a unique prime factorization. (T.Fundamental arithmetic)

By this definition if number 1 was cousin exist infinite factorizations (7 = 7×1 = 7x1x1). For this definition one is not prime.

As we see there are differing voluntary or involuntary definitions including or excluding this number.

Do you think that 1 is a prime number? Explain your answer!