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.