Is there a way to check if a number is prime with only a few details about the number?

I need to find a prime with the info, the sum of all its digits, the first and last digit and how much digits the number has.

For example, lets check if $13$ is prime.

First digit: 1

Last digit: 3

Sum of all digits: 13 -> 1 + 3 = 4

Amount of digits: 2

How can I be sure that this number is 100% prime by only using this info?

Answer

Unfortunately no, you cannot deduce the primality of a number from the number and sum of its digits, in general. The best one can achieve, currently, is a polynomial time algorithm. There is more information on Wikipedia.

However, you can use the so-called divisibility criteria, to weed out composite numbers that have those factors for which you have a criterion.