Primality proof for n = 1947073:
Take b = 2.
b^(n-1) mod n = 1.
10141 is prime. b^((n-1)/10141)-1 mod n = 1057824, which is a unit, inverse 104252.
(10141) divides n-1.
(10141)^2 > n.
n is prime by Pocklington's theorem.