Primality proof for n = 1364367483307:

Take b = 2.

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

56767 is prime.
b^((n-1)/56767)-1 mod n = 87947923949, which is a unit, inverse 794600744371.

5077 is prime.
b^((n-1)/5077)-1 mod n = 214374611272, which is a unit, inverse 1020293145660.

(5077 * 56767) divides n-1.

(5077 * 56767)^2 > n.

n is prime by Pocklington's theorem.