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.