Primality proof for n = 2749283:
Take b = 2.
b^(n-1) mod n = 1.
1013 is prime.
b^((n-1)/1013)-1 mod n = 2192408, which is a unit, inverse 1111794.
59 is prime.
b^((n-1)/59)-1 mod n = 2489823, which is a unit, inverse 1578692.
(59 * 1013) divides n-1.
(59 * 1013)^2 > n.
n is prime by Pocklington's theorem.