sieve method

The sieve prime method is a fast method to find all prime numbers less than N, and the time is very short.

accomplish

We first use the simulation method to find all prime numbers within 10000:

for(i=2;i<10000;i++)
{
	for(j=2;j<=i/2;j++)
	{
		if(i%j==0) //If i is divisible by the number j less than it, then i must not be prime
			break;
	}
	if(j>i/2)
		printf("%d ",i);
}

Use the sieve method below:

const int N=10001;

int p[N];
memset(p,0,sizeof(p)); //The initialization is all 0, 1 means it is not a prime number
p[0]=p[1]=1;
for(i=2;i<N;i++)
{
	if(!p[i]) //If the current p[i] of i is not 0, i.e. i is a prime number
	{
		for(j=i+i;j<N;j+=i) //Then all multiples of i must not be prime numbers, so all their multiples are marked as 1
			p[j]=1;
	}
}
for(i=0;i<N;i++) //Print a prime number, 0 means it is a prime number
{
	if(!p[i])
		printf("%d ",i);
}

Compared with the simulation method, the time complexity of the sieve method is close to O(n) from O(n*n).