Primality proof for n = 290064143:

Take b = 2.

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

3739 is prime.
b^((n-1)/3739)-1 mod n = 283265731, which is a unit, inverse 25524567.

491 is prime.
b^((n-1)/491)-1 mod n = 211463535, which is a unit, inverse 48832013.

(491 * 3739) divides n-1.

(491 * 3739)^2 > n.

n is prime by Pocklington's theorem.