Primality proof for n = 1861:
Take b = 2.
b^(n-1) mod n = 1.
31 is prime.
b^((n-1)/31)-1 mod n = 1546, which is a unit, inverse 449.
5 is prime.
b^((n-1)/5)-1 mod n = 757, which is a unit, inverse 1802.
(5 * 31) divides n-1.
(5 * 31)^2 > n.
n is prime by Pocklington's theorem.