Primality proof for n = 74058212732561358302231226437062788676166966415465897661863160754340907:

Take b = 2.

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

75445702479781427272750846543864801 is prime.
b^((n-1)/75445702479781427272750846543864801)-1 mod n = 69490809710348678725736597923071784769591275419387514694139338586948359, which is a unit, inverse 70463328703800545008217672123162676565183935400628861884889913886334520.

31757755568855353 is prime.
b^((n-1)/31757755568855353)-1 mod n = 50366660687963342066214195241331738400016478712605795091965648721912164, which is a unit, inverse 18232248056023258384404751131439975669387062239511397558448549501188471.

(31757755568855353 * 75445702479781427272750846543864801) divides n-1.

(31757755568855353 * 75445702479781427272750846543864801)^2 > n.

n is prime by Pocklington's theorem.