Question

To test whether an integer, $n$, is prime, it is enough to be sure that none of the primes less than or equal to the square root of $n$ divide $n$. If you want to check that a number between 900 and 950 is prime with this rule, what is the largest prime divisor you need to test

Answer 1

the largest divisor is less than the square root of that number

Explanation:

Pick any number between 900 and 950 . For example I choose 937 . Now taking the square root of 937 would give 30.61

So divide 937 with all the primes less than 30.61

937/2, 937/3, 937/5,...................937/29

29 would be the largest divisor which is less than the square root of 937 .

29< 30.61

But if you check 937 does not divide wholly with any of the primes hence it is a prime number itself.

If any number such 925 is chosen and it gets divided wholly by another prime like 5

925 /5= 185 so it is not a prime number