Primality proof for n = 3352477528785765665039059407454939:

Take b = 2.

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

7721623655416232036046857 is prime.
b^((n-1)/7721623655416232036046857)-1 mod n = 1702772252460998175687948914025928, which is a unit, inverse 1572491714075284957010858542447266.

(7721623655416232036046857) divides n-1.

(7721623655416232036046857)^2 > n.

n is prime by Pocklington's theorem.