Primality proof for n = 107361793816595537:

Take b = 2.

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

4681609 is prime.
b^((n-1)/4681609)-1 mod n = 10202789421650174, which is a unit, inverse 44826003584452600.

85831 is prime.
b^((n-1)/85831)-1 mod n = 101608383539442155, which is a unit, inverse 89382073196192802.

(85831 * 4681609) divides n-1.

(85831 * 4681609)^2 > n.

n is prime by Pocklington's theorem.