Primality proof for n = 5741:

Take b = 2.

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

41 is prime.
b^((n-1)/41)-1 mod n = 370, which is a unit, inverse 5260.

7 is prime.
b^((n-1)/7)-1 mod n = 456, which is a unit, inverse 1750.

(7 * 41) divides n-1.

(7 * 41)^2 > n.

n is prime by Pocklington's theorem.