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.