Primality proof for n = 42110248155485387:

Take b = 2.

b^(n-1) mod n = 1.

4537129159 is prime.
b^((n-1)/4537129159)-1 mod n = 35113962048643419, which is a unit, inverse 38392188826897504.

(4537129159) divides n-1.

(4537129159)^2 > n.

n is prime by Pocklington's theorem.