Consider the following claim:\\
The difference between two consecutive positive cube numbers is always prime.\\
Here is an attempted proof of this claim:

$$\text { I } \quad ( x + 1 ) ^ { 3 } = x ^ { 3 } + 3 x ^ { 2 } + 3 x + 1$$

II Taking $x$ to be a positive integer, the difference between two consecutive cube numbers can be expressed as $( x + 1 ) ^ { 3 } - x ^ { 3 } = 3 x ^ { 2 } + 3 x + 1$

III It is impossible to factorise $3 x ^ { 2 } + 3 x + 1$ into two linear factors with integer coefficients because its discriminant is negative.

IV Therefore for every positive integer value of $x$ the integer $3 x ^ { 2 } + 3 x + 1$ cannot be factorised.

V Hence, the difference between two consecutive cube numbers will always be prime.\\
Which of the following best describes this proof?

A The proof is completely correct, and the claim is true.\\
B The proof is completely correct, but there are counterexamples to the claim.\\
C The proof is wrong, and the first error occurs on line I.\\
D The proof is wrong, and the first error occurs on line II.\\
E The proof is wrong, and the first error occurs on line III.\\
F The proof is wrong, and the first error occurs on line IV.\\
G The proof is wrong, and the first error occurs on line V.