Primality proof for n = 27301809421:

Take b = 2.

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

139537 is prime.
b^((n-1)/139537)-1 mod n = 8454877314, which is a unit, inverse 19222083206.

1087 is prime.
b^((n-1)/1087)-1 mod n = 20413604198, which is a unit, inverse 25471735842.

(1087 * 139537) divides n-1.

(1087 * 139537)^2 > n.

n is prime by Pocklington's theorem.