Primality proof for n = 2305472951:
Take b = 2.
b^(n-1) mod n = 1.
1373 is prime.
b^((n-1)/1373)-1 mod n = 319855112, which is a unit, inverse 403552596.
71 is prime.
b^((n-1)/71)-1 mod n = 1508896854, which is a unit, inverse 67666692.
(71 * 1373) divides n-1.
(71 * 1373)^2 > n.
n is prime by Pocklington's theorem.