C ++如何使用返回布尔值的函数确定素数

Question

I am suppose to make a program that asks a user to input an integer 'n' between 1 and 100, and have an input validation loop. The program will then calculate the first 'n' prime numbers and print them. So I figured out how to calculate the prime numbers and display them, 10 numbers per line, all in the main function. What I have to do is to have a function called isPrime() that takes an integer and returns true if it is prime and false otherwise. I'm not sure how to go about this. This is the code I have for function main().

#include <iostream>
#include <iomanip>
using namespace std;

int  main()
{
   int  number;
   int count = 0;

   cout << "Enter an integer between 1 and 100: ";
   cin >> number;

   while (number < 0 || number > 100)
   {
      cout << "Invalid number." << endl;
      cout << "Enter an integer between 1 and 100: ";
      cin >> number;
   }

   cout << "The first " << number << " primes: \n" << endl;

   for (int i = 2; number > 0; ++i)
   {
      bool  isPrime = true;
      for (int j = 2; j < i; ++j)
      {
         if (i  % j == 0)
         {
            isPrime = false;
            break;
         }
      }
      if (isPrime)
      {
         count++;
         --number;
         cout << setw(5) << i;
         if (count % 10 == 0)
            cout << endl;
      }
   }
   cout << endl;
   system("pause");
   return 0;
}

Any help is good, thanks in advance.

Answer 1

You seem to be testing i % j for every j lower then i. But if you tested for j = 3 then you can exclude all multiples of 3. When a number can't be divided by 3 it can't be divided by 6. This will improve performance.

You can also implement the AKS primalty test https://en.wikipedia.org/wiki/AKS_primality_test This might be a little more work. I don't know the details of this test but it is deterministic and works on all numbers.

If you want a function bool isPrime(int number) you can just extract this code from your main method, it looks something like this:

bool isPrime(int number){
    for (int j = 2; j < number/2; ++j)
    {
        if (number % j == 0)
        {
            return false;
        }
    }
    return true;
}

The for loop in the main function will be something like:

   for (int i = 2; number > 0; ++i)
   {
      if (isPrime(i))
      {
         count++;
         --number;
         cout << setw(5) << i;
         if (count % 10 == 0)
            cout << endl;
      }
   }