Primality proof for n = 1758043857162342261873808298370022542631:

Take b = 2.

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

20850849555552798305550425353 is prime.
b^((n-1)/20850849555552798305550425353)-1 mod n = 143474615280513417131591198718868674150, which is a unit, inverse 1168314827224465584194020774540379565234.

(20850849555552798305550425353) divides n-1.

(20850849555552798305550425353)^2 > n.

n is prime by Pocklington's theorem.