Primality proof for n = 998970029:
Take b = 2.
b^(n-1) mod n = 1.
35677501 is prime. b^((n-1)/35677501)-1 mod n = 268435455, which is a unit, inverse 70923276.
(35677501) divides n-1.
(35677501)^2 > n.
n is prime by Pocklington's theorem.