Primality proof for n = 912026155762311229:

Take b = 2.

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

16064717743999 is prime.
b^((n-1)/16064717743999)-1 mod n = 813929617109191379, which is a unit, inverse 371448305354204680.

(16064717743999) divides n-1.

(16064717743999)^2 > n.

n is prime by Pocklington's theorem.