To decide whether 541 is prime you divide it by every prime up to its square root. What is the largest prime you actually need to try?

Since √541 ≈ 23.26, the largest prime worth testing is 23. Nothing beyond it can help: if 541 had a factor larger than 23.26 it would need a partner smaller than 23.26, and the earlier tests would already have caught that partner. Working through 2, 3, 5, 7, 11, 13, 17, 19 and 23, none divides 541, so 541 is prime. The trap 19 stops one prime too soon — $19^2=361$ is still short of 541, so the job is not finished. Going on to 29 or 31 only wastes effort, since $29^2=841$ has already overshot.