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.