Primality proof for n = 2862218959:
Take b = 2.
b^(n-1) mod n = 1.
2213 is prime.
b^((n-1)/2213)-1 mod n = 2146665760, which is a unit, inverse 1800090976.
1373 is prime.
b^((n-1)/1373)-1 mod n = 1370959119, which is a unit, inverse 1473717517.
(1373 * 2213) divides n-1.
(1373 * 2213)^2 > n.
n is prime by Pocklington's theorem.