Primality proof for n = 71741:

Take b = 2.

b^(n-1) mod n = 1.

211 is prime.
b^((n-1)/211)-1 mod n = 12880, which is a unit, inverse 27510.

17 is prime.
b^((n-1)/17)-1 mod n = 69378, which is a unit, inverse 44933.

(17 * 211) divides n-1.

(17 * 211)^2 > n.

n is prime by Pocklington's theorem.