## Prime Number

What is the last digit $\textit{d}$ of the 9-digit number $19700019\textit{d}$, given that the number is prime?
Source: NCTM Mathematics Teacher, November 2006

SOLUTION
The last digit $\textit{d}$ could be $1,3,7$, or $9$.
$\textit{d}$ cannot be $3$ because $197000193\div 3=65666731$.
$\textit{d}$ cannot be $9$ because $197000199\div 9=21888911$.
$197000197=197000000+197$
$=197(10^6+1)$
$\textit{d}$ cannot be $7$ because $197000197$ is divisible by $197$.
The last digit $\textit{d}$ must be $1$.

Answer: $1$