Primality proof for n = 1046598874349470040812238544166825597307092300404591085307326405812564486341:
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.