To be sure the number she wrote was prime, she would need to test each prime divisor from 2-29. What is the smallest number she could've written?

Question

A teacher wrote a number on the blackboard. She indicated that to be sure whether or not the number she wrote was prime, she would need to test each prime divisor from 2-29. What is the smallest number that she could have written on the board?

Answer 1

29²=841 is the smallest number she could have written on the board

if she wrote 840, then 840 is composite because it's even

if she wrote 839, then √839=28.96549 and you would then test each prime divisor from 23 down to 2 (28,27,26,25, and 24 are all composite)

however, if the teacher wrote 841 on the board without any other numbers and asked you to determine if the number was prime or composite, the first thing that you would do is take the square root of the number 841 and you would see right away that 841 is composite because √841=29 and therefore 841 is divisible by 1, 841, and 29