Minimal Prime/Examples

Examples of Minimal Primes
$857$ is a minimal prime in base $10$ because there is no prime greater than $10$ among the shorter subsequences of the digits $8$, $5$, $7$, $85$, $87$, $57$.

The subsequence does not have to consist of consecutive digits, so $149$ is not a minimal prime in base $10$ (because $19$ is prime and $19 > 10$).

But it does have to be in the same order.

So, for example, $991$ is still a minimal prime in base $10$, even though a subset of the digits can form the shorter prime $19 > 10$ by changing the order.