Primality proof for n = 3972738854007370570932605213:

Take b = 2.

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

49290007066067 is prime.
b^((n-1)/49290007066067)-1 mod n = 3289702716637765437499339632, which is a unit, inverse 752304189260465354422677905.

8097347 is prime.
b^((n-1)/8097347)-1 mod n = 531717846300181929421050333, which is a unit, inverse 228094226755197230112751083.

(8097347 * 49290007066067) divides n-1.

(8097347 * 49290007066067)^2 > n.

n is prime by Pocklington's theorem.