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.