Using For loop to determine if a number is prime

Could someone help me with this problem: "Use a for loop combined with an if statement to whether 3257861 is prime."

My professor also gave the hint but it just made me more confused: "To determine if a number n is prime, you have to check every number up to and including sqrt(n) and see whether that number is a divisor of n. Also, you will need to create a variable that tells you whether you have found a divisor of 3257861 (in which case 3257861 is not prime). This variable should start at 0, and if you find a divisor, change it to 1."

Answer 1

[Matt J]

To determine if a number n is prime, you have to check every number up to and including sqrt(n) and see whether that number is a divisor of n.

The reason this is true is because suppose a number n is not prime. There therefore exists two integer divisors a>=b>1 such that n=a*b. Then,

n=a*b>=b^2

and therefore b<=sqrt(n). Therefore, if n is not prime, you should have found one of its divisors if you checked all b from 2 to floor(sqrt(n)).

[Vy Do]

so how do you write the code then?

[Matt J]

As you have been instructed, with a for-loop and an if statement. You can use rem() or mod() to check whether a number b is a divisor of n.