Problem 46

原题：

 //合数是与质数（也叫素数）相对应的概念，即除了1和本身之外，还可以被其它正整数整除的数称为合数。
 //奇合数：既是合数又是奇数的数称为奇合数。例如：9，15，21等等都是奇合数。
 It was proposed by Christian Goldbach that every odd composite number can be written as 
  the sum of a prime and twice a square.

9 = 7 + 2*(1*1)
15 = 7 + 2*(2*2)
21 = 3 + 2*(3*3)
25 = 7 + 2*(3*3)
27 = 19 + 2*(2*2)
33 = 31 + 2*(1*1)

It turns out that the conjecture was false.
What is the smallest odd composite that cannot be written as the sum of a prime and
  twice a square?

 

代码如下：

public class Problem46 { //判断是否为质数 static boolean isPrime(int number){ if(number<=1) return false; for(int i=2;i<=Math.sqrt(number);i++){ if(number%i==0) return false; } return true; } //判断该奇合数是否能写成质数+2*一个数的平方 static boolean isPrimeAddPower(int number){ for(int i=1;i<Math.sqrt(number);i++){ if(isPrime(number-2*i*i)) return true; } return false; } public static void main(String[] args) { for(int i=3;;i=i+2){ if(!isPrime(i)){ if(!isPrimeAddPower(i)){ System.out.println(i); return; } } } } }