Primality proof for n = 60757:
Take b = 2.
b^(n-1) mod n = 1.
83 is prime.
b^((n-1)/83)-1 mod n = 37315, which is a unit, inverse 47417.
61 is prime.
b^((n-1)/61)-1 mod n = 12714, which is a unit, inverse 41599.
(61 * 83) divides n-1.
(61 * 83)^2 > n.
n is prime by Pocklington's theorem.