How do you make Prime “COMPUTERS”?

Question

$Given$:

$COMPUTERS$ is the smallest Pan Digital containing all the digits 1 to 9 occurring only once.

$COMPUTERSV$ is a Prime only when one of the correct digit ($V$)is added at the end.

Also,

$COMPUTERSE$ = $CE$ * $EOTOCTPC$

What is the digit $V$ that has to be added to make $COMPUTERS$ A Prime?

Answer 1

V=

$1$

because:

$COMPUTERS=123456789$, $V\ne\{2,4,6,8\}$ (even), $V\ne\{3,6,9\}$ (multiple of $3$), $V\ne\{5\}$ (multiple of $5$). So $V=1$ or $V=7$. But $E=7$ and this is not prime, as given later. Therefore $V=1$. And indeed $1234567891$ is prime.