Primality proof for n = 734273:

Take b = 2.

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

149 is prime.
b^((n-1)/149)-1 mod n = 572495, which is a unit, inverse 602626.

11 is prime.
b^((n-1)/11)-1 mod n = 563782, which is a unit, inverse 485744.

(11 * 149) divides n-1.

(11 * 149)^2 > n.

n is prime by Pocklington's theorem.