Primality proof for n = 734647:

Take b = 2.

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

11131 is prime.
b^((n-1)/11131)-1 mod n = 196233, which is a unit, inverse 422044.

(11131) divides n-1.

(11131)^2 > n.

n is prime by Pocklington's theorem.