Primality proof for n = 5271793:

Take b = 2.

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

109829 is prime.
b^((n-1)/109829)-1 mod n = 4548170, which is a unit, inverse 3793698.

(109829) divides n-1.

(109829)^2 > n.

n is prime by Pocklington's theorem.