Primality proof for n = 186062272787:

Take b = 2.

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

550480097 is prime.
b^((n-1)/550480097)-1 mod n = 126376036753, which is a unit, inverse 143409991108.

(550480097) divides n-1.

(550480097)^2 > n.

n is prime by Pocklington's theorem.