码迷,mamicode.com
首页 > 其他好文 > 详细

Fermat’s Chirstmas Theorem (素数打表的)

时间:2014-08-09 09:03:57      阅读:258      评论:0      收藏:0      [点我收藏+]

标签:des   style   blog   http   color   io   strong   for   

                                                                         Fermat’s Chirstmas Theorem
Time Limit:1000MS     Memory Limit:65536KB     64bit IO Format:%lld & %llu

Description

In a letter dated December 25, 1640; the great mathematician Pierre de Fermat wrote to Marin Mersenne that he just proved that an odd prime p is expressible as p = a2 + b2 if and only if p is expressible as p = 4c + 1. As usual, Fermat didn’t include the proof, and as far as we know, never
wrote it down. It wasn’t until 100 years later that no one other than Euler proved this theorem.

Input

Your program will be tested on one or more test cases. Each test case is specified on a separate input line that specifies two integers L, U where L ≤ U < 1, 000, 000
The last line of the input file includes a dummy test case with both L = U = −1.

Output

L U x y
where L and U are as specified in the input. x is the total number of primes within the interval [L, U ] (inclusive,) and y is the total number of primes (also within [L, U ]) that can be expressed as a sum of squares.

Sample Input

10 20
11 19
100 1000
-1 -1

Sample Output

10 20 4 2
11 19 4 2
100 1000 143 69
#include<stdio.h>  
#include<string.h>  

#define N 1000005

int prime[100005];  
int flag[1000005];  
int e;
  
void getP()  // 素数打表,找出素数存栈  
{  
	int i, j;  
	e = 0;  
	memset(flag, 0, sizeof(flag) ); //标记初始化
	
	for ( i=2; i<N; i++)  
	{  
		if ( flag[i]==0 ) 
		{
			prime[e++] = i; //进栈  
		}
		for ( j=0; j<e && i*prime[j]<N; j++ )  
		{  
			flag[ i * prime[j] ] = 1;  
		}  
	}  
}  

int main()  
{  
	int l,u,x,y;  

	getP(); 
	int i;
	while(scanf("%d %d",&l,&u))  
	{  
	  
		if(l==-1 && u==-1)  
            break;  
		x=0;  
		y=0;
		for( i=0; i<e; i++)  
		{  
			if(prime[i]>=l && prime[i]<=u )  
			{  
				x++;  
				if(prime[i]%4==1) 
				{
                    y++;  
				}
			}  
			if(prime[i]>u)  
                break;  
		}  
		if(l<=2 && u>=2)
		{
			y++;
		}
		printf("%d %d %d %d\n",l, u, x, y );  
	}  
	return 0;  
}  

 

Fermat’s Chirstmas Theorem (素数打表的),布布扣,bubuko.com

Fermat’s Chirstmas Theorem (素数打表的)

标签:des   style   blog   http   color   io   strong   for   

原文地址:http://www.cnblogs.com/yspworld/p/3900513.html

(0)
(0)
   
举报
评论 一句话评论(0
登录后才能评论!
© 2014 mamicode.com 版权所有  联系我们:gaon5@hotmail.com
迷上了代码!