C++ Prime Numbers program [closed] - c++

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Closed 10 years ago.
I'm working on a C++ program that determines and prints the prime numbers between 3 and an integer 'x' the user inputs. I'm assuming that I need a double nested loop for this, one to iterate from 3 to x and the other to check if the number is prime. I think it needs to do something like go from 2 to x-1? I'm just really not sure how to do this syntax-wise. Thanks for any help! :)
EDIT:
This is what I have:
#include <iostream>
#include <cmath>
using std::cout;
using std::endl;
using std::cin;
int main(){
int x;
int i;
int j;
cout << "Please enter an integer 'x' greater than 3: " << endl;
cin >> x;
if (x <= 3){
cout << "Please enter new value 'x' greater than 3: " << endl;
cin >> x;
}
for(int i=3; i<=x; i++){
for(j=2; j<i; j++){
if(i%j == 0)
break;
else if(i == j+1);
cout << i << endl;
}
}
return 0;
}
And I when I enter 10 as 'x' I get the output:
3
5
5
5
7
7
7
7
7
9
Can anyone tell me how to fix this?

Answer 1

Provided your X is small enough, you can use the Sieve of Eratosthenes to do it more efficiently. This is ideal for the "primes up to X" case since it maintains a memory of previously discarded primes. It does so by keeping a set of flags for each candidate number, all initially set to true (except for 1, of course).
Then you take the first true value (2), output that as a prime, and then set the flags for all multiples of that to false.
Then carry on with:
3;
5 (since 4 was a multiple of 2);
7 (since 6 was a multiple of 2 and 3);
11 (since 8 and 10 were multiples of 2 and 9 was a multiple of 3);
13 (since 12 was a multiple of 2);
17 (since 14 and 16 were multiples of 2 and 15 was a multiple of 3 and 5);
and so on.
Pseudo-code would be similar to:
def showPrimesUpTo (num):
// create array of all true values
array isPrime[2..num] = true
// start with 2 and go until finished
currNum = 2
while currNum <= num:
// if prime, output it
if isPrime[currNum]:
output currNum
// also flag all multiples as nonprime
clearNum = currNum * 2
while clearNum <= num:
isprime[clearNum] = false
clearNum = clearNum + currNum
// advance to next candidate
currNum = currNum + 1
Otherwise, you can do trial division as per your suggestion. The basic idea is to check each number from 2 up to the square root of your target number to see if it's a multiple. In pseudo-code, that would be something like:
def isPrime (num):
// val is the value to check for factor
val = 2
// only need to check so far
while val * val <= num:
// check if an exact multiple
if int (num / val) * val == num:
return false
// no, carry on
val = val + 1
// if no factors found, it is a prime
return true
The reason you only need to check up to the square root is because, if you find a factor above there, you would have already found the corresponding factor below the square root.
For example, 3 x 17 is 51. If you're checking the numbers from 2 through 50 to see if 51 is prime, you'll find 3 first, meaning you never need to check 17.

Answer 2

int main (char argv)
{
int tempNum = atoi(argv);
for (int i=3; i<=tempNum; i++)
for (int j=2; j*j<=i; j++)
{
if (i % j == 0)
break;
else if (j+1 > sqrt(i)) {
cout << i << " ";
}
}
return 0;
}
Printing prime numbers from 1 through 100
Basically this, but modified

Answer 3

I find this one pretty fast and efficient
int main(){
for(int i=3; i<=X; i++)
if(IsPrime(i)){
cout<<i<<endl;
}
}
bool IsPrime(int num){
/* use commented part if want from 2
if(num<=1)
return false;
if(num==2)
return true;
*/
if(num%2==0)
return false;
int sRoot = sqrt(num*1.0);
for(int i=3; i<=sRoot; i+=2)
{
if(num%i==0)
return false;
}
return true;
}