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.