输出素数的代码优化

输出100到200的素数

#include<stdio.h>
int main()
{
int num = 0;
int count = 0;
for (num = 100; num <= 200; num++)
{
int number = 0;
for (number = 2; number <= num - 1; number++)
{
if (num%number == 0)
{
break;
}
}
if (num == number)
{
printf("%d\n", num);
count++;
}

}
printf("count=%d", count);
system("pause");
return 0;
}

</pre><pre class="objc" name="code">对代码进行的优化：根据数学分析，偶数都不是素数，所以只考虑奇数的情况

<pre class="objc" name="code">#include<stdio.h>
int main()
{
int num = 0;
int count = 0;
for (num = 101; num <= 200; num+=2)
{
int number = 0;
for (number = 2; number <= num - 1; number++)
{
if (num%number == 0)
{
break;
}
}
if (num == number)
{
printf("%d\n", num);
count++;
}
}
printf("count=%d", count);
system("pause");
return 0;
}

在只考虑奇数的情况下，奇数肯定不能被偶数整除，所以除数也可以只考虑在奇数情况下

#include<stdio.h>
int main()
{
int num = 0;
int count = 0;
for (num = 101; num <= 200; num+=2)
{
int number = 0;
for (number = 3; number <= num - 1; number+=2)
{
if (num%number == 0)
{
break;
}
}
if (num == number)
{
printf("%d\n", num);
count++;
}
}
printf("count=%d", count);
system("pause");
return 0;
}

如果一个数能被其他数整除，那么这个数的两个除数中肯定有一个小于等于这个数的开平方数。（16=2*8,16=4*4，）

#include<stdio.h>
#include<math.h>
int main()
{
int num = 0;
int count = 0;
for (num = 101; num <= 200; num+=2)
{
int number = 0;
for (number = 3; number <= sqrt(num); number+=2)
{
if (num%number == 0)
{
break;
}
}
if (number > sqrt(num))
{
printf("%d\n", num);
count++;
}
}
printf("count=%d", count);
system("pause");
return 0;
}