# Issue involving primes.

1. Jan 1, 2015

### Calu

1. The problem statement, all variables and given/known data

We have n ≥ 2, n not prime, n ∈ ℤ. Take the smallest such n. n is not prime and as such n is not irreducible and can be written as n = n1.n2; n1, n2 not units. We may take n1, n2 ≥ 2. However we have n > n1, n > n2 so n1, n2 have prime factors.

I'm not sure how n > n1, n > n2 implies that n1, n2 have prime factors.

2. Relevant equations
I'm not sure what's relevant here.

3. The attempt at a solution

From what I can see, the lowest possible n which meets the criteria is 6. 6 has the prime factors 2 and 3, which means that obviously what is stated is true. I'm just not sure how n > n1, n > n2 implies that its true.

2. Jan 1, 2015

### Orodruin

Staff Emeritus
6 is not the smallest non-prime integer larger than or equal to 2, 4 is.

Anyway, if n is the smallest non-prime integer and n1 < n, what does this imply?

3. Jan 1, 2015

### haruspex

Do you mean, "n1, n2 are prime factors"?