Primality proof for n = 73827037:

Take b = 2.

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

43633 is prime.
b^((n-1)/43633)-1 mod n = 43099735, which is a unit, inverse 60151063.

(43633) divides n-1.

(43633)^2 > n.

n is prime by Pocklington's theorem.