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.