### Instruction: What is the smallest prime whose digits sum to $19$?### Response: A prime number is a positive integer that has exactly two factors: $1$ and itself.
To find the smallest prime with a given property, it is often helpful to start with the smallest possible number that satisfies the property and then check if it is prime.
In this case, the smallest possible number whose digits sum to $19$ is $199$, because we want to use as few digits as possible and make them as small as possible.
To check if $199$ is prime, we can try to divide it by some small primes, such as $2, 3, 5, 7, 11, 13, 17, 19$.
$199$ is not divisible by $2, 3, 5, 7, 11, 13, 17$, or $19$, because none of these numbers are factors of $199$.
Therefore, $199$ is prime, and it is the smallest prime whose digits sum to $19$.