Primality proof for n = 2955889:
Take b = 2.
b^(n-1) mod n = 1.
1579 is prime.
b^((n-1)/1579)-1 mod n = 537443, which is a unit, inverse 1897992.
13 is prime.
b^((n-1)/13)-1 mod n = 817126, which is a unit, inverse 1608490.
(13 * 1579) divides n-1.
(13 * 1579)^2 > n.
n is prime by Pocklington's theorem.