Primality proof for n = 62417726963:

Take b = 2.

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

73043 is prime.
b^((n-1)/73043)-1 mod n = 30862096064, which is a unit, inverse 41154654475.

2237 is prime.
b^((n-1)/2237)-1 mod n = 44153049734, which is a unit, inverse 58548552422.

(2237 * 73043) divides n-1.

(2237 * 73043)^2 > n.

n is prime by Pocklington's theorem.