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.