Primality proof for n = 9610823281:
Take b = 2.
b^(n-1) mod n = 1.
3931 is prime.
b^((n-1)/3931)-1 mod n = 8940185587, which is a unit, inverse 9486107731.
167 is prime.
b^((n-1)/167)-1 mod n = 3907843733, which is a unit, inverse 9481220143.
(167 * 3931) divides n-1.
(167 * 3931)^2 > n.
n is prime by Pocklington's theorem.