Primality proof for n = 2291581:

Take b = 2.

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

439 is prime.
b^((n-1)/439)-1 mod n = 1573630, which is a unit, inverse 564393.

29 is prime.
b^((n-1)/29)-1 mod n = 1566074, which is a unit, inverse 1886820.

(29 * 439) divides n-1.

(29 * 439)^2 > n.

n is prime by Pocklington's theorem.