Primality proof for n = 107590001:
Take b = 2.
b^(n-1) mod n = 1.
53 is prime.
b^((n-1)/53)-1 mod n = 26896162, which is a unit, inverse 75712971.
29 is prime.
b^((n-1)/29)-1 mod n = 68236645, which is a unit, inverse 100085220.
7 is prime.
b^((n-1)/7)-1 mod n = 95730223, which is a unit, inverse 4923006.
(7 * 29 * 53) divides n-1.
(7 * 29 * 53)^2 > n.
n is prime by Pocklington's theorem.