Maths proof help

Hey I just jotted the mark scheme down on the lines (in red)
The part I don’t understand is why they square rooted 23 and then why they only test 2 and 3?
How does this prove 23 is a prime

(edited 1 year ago)

Reply 1

Saeed23

To prove that 23 is a prime number, we can use the following method:

Take the square root of the number (in this case, the square root of 23 is approximately 4.8).
Test all the prime numbers less than or equal to the square root (in this case, the primes less than or equal to 4 are 2 and 3).
If none of these prime numbers divide the original number (23), then the original number is prime.
Now, let's apply this method to the number 23:

The square root of 23 is approximately 4.8.
We test the primes less than or equal to 4, which are 2 and 3. We can see that neither 2 nor 3 divide 23 without a remainder.
Therefore, 23 is prime.
The reason we take the square root of the number is that any factor of a number greater than its square root must be paired with a factor less than its square root. So, testing all the primes less than or equal to the square root is sufficient to determine whether a number is prime or not.

In this case, since 2 and 3 are the only primes less than or equal to the square root of 23, and neither of them divides 23 without a remainder, we can conclude that 23 is prime number
hope this helps!

(edited 1 year ago)