Primality proof for n = 1736389:

Take b = 2.

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

347 is prime.
b^((n-1)/347)-1 mod n = 1514888, which is a unit, inverse 46604.

139 is prime.
b^((n-1)/139)-1 mod n = 859161, which is a unit, inverse 1231532.

(139 * 347) divides n-1.

(139 * 347)^2 > n.

n is prime by Pocklington's theorem.