Primality proof for n = 112704357986686512751543694400357156875971984515762587440143302448053844671:

Take b = 2.

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

351209660225850764954644159 is prime.
b^((n-1)/351209660225850764954644159)-1 mod n = 44631786968122106405569920885137117232158880512446639213053264538036040125, which is a unit, inverse 37726362921483518915026327004763388357531135117237681327781775177581569083.

597386494759892631967 is prime.
b^((n-1)/597386494759892631967)-1 mod n = 58586370292017069013514585484198025959211441804503004207984968639071953128, which is a unit, inverse 48468826611125281551812612774204553586671800426925358294114450150161622379.

(597386494759892631967 * 351209660225850764954644159) divides n-1.

(597386494759892631967 * 351209660225850764954644159)^2 > n.

n is prime by Pocklington's theorem.