Why 1 is not a prime number?

On : 3:41 PM

We know that the prime numbers are 2, 3,5, 7, 11, 13, … … …, it starts from 2 because One is not a prime number.

Why one is not a prime number?

It explanation is on the following.

The fundamental theorem of arithmetic Or Factorization Theorem: The fundamental theorem of arithmetic states that every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of one or more primes (MathWorld)

From the definition we got two factors

  1. product of one or more primes
  2. can be represented in exactly one way

Lets consider 12, the factors of 12 are 1, 2, 3, 4,6 and 12. So if we represent 12 as the product of primes then 12= 2x2x3
But we can not take 1x2x2x3(Extra 1 is multiplied)
Or we can’t take 1x1x2x2x3 (Extra two 1’s is multiplied)
or even we can’t take 1x1x1x2x2x3 (Extra three 1’s is multiplied). Though all these makes 12.

Thus we can represent 12 in many ways if take ‘1’ as a prime number. We cant take these because it violates our second factor "can be represented in exactly one way". So excluding the ‘1’ we represent 12 in exactly one way as a product of three primes(2,2,3).

More example 14=2x7 not (1x2x7 or 1x1x2x7)
51 =3x17 not (1x3x17 or 1x1x317)
So to maintain The fundamental theorem of arithmetic Or Factorization Theorem formula we apart ‘1’ from series of prime numbers.

But, is ‘1’ is a compound number? Nope!! as we know that compound number are those which can be represent as the product of integer number. Example 24 is a compound number as it can be written as 4x6.

So what is ‘1’ actually? According to mathematician we can define it as “Unit Number”


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