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.