Primality proof for n = 1075060097:

Take b = 2.

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

12517 is prime.
b^((n-1)/12517)-1 mod n = 134734877, which is a unit, inverse 282938091.

61 is prime.
b^((n-1)/61)-1 mod n = 14276112, which is a unit, inverse 551211956.

(61 * 12517) divides n-1.

(61 * 12517)^2 > n.

n is prime by Pocklington's theorem.