Primality proof for n = 7293089:

Take b = 2.

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

20719 is prime.
b^((n-1)/20719)-1 mod n = 3539901, which is a unit, inverse 6833422.

(20719) divides n-1.

(20719)^2 > n.

n is prime by Pocklington's theorem.