Primality proof for n = 50520606258875818707470860153287666700917696099933389351507:

Take b = 2.

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

375503554633724504423937478103159147573209 is prime.
b^((n-1)/375503554633724504423937478103159147573209)-1 mod n = 10084247389854643911241542541906780573951372338829511760588, which is a unit, inverse 24137879162838580483631743182491659235880674722528516014804.

(375503554633724504423937478103159147573209) divides n-1.

(375503554633724504423937478103159147573209)^2 > n.

n is prime by Pocklington's theorem.