# How do you make Prime “COMPUTERS”?

$$Given$$:

$$COMPUTERS$$ 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?

• Enough info given... – Uvc Jun 29 at 10:39

$$1$$
$$COMPUTERS=123456789$$, $$V\ne\{2,4,6,8\}$$ (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.