Take b = 2.

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

146621177686829237856559365192161554600556965873 is prime.
b^((n-1)/146621177686829237856559365192161554600556965873)-1 mod n = 589995763880780869378788646762296025909929232245451970016033283528758235401, which is a unit, inverse 166232847777896122236128377062190324574156871914668297420848732064386467839.

(146621177686829237856559365192161554600556965873) divides n-1.

(146621177686829237856559365192161554600556965873)^2 > n.

n is prime by Pocklington's theorem.