### Spiral primes题号：58 难度： 5 中英对照

Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed.

37 36 35 34 33 32 31
38 17 16 15 14 13 30
39 18  5  4  3 12 29
40 19  6  1  2 11 28
41 20  7  8  9 10 27
42 21 22 23 24 25 26
43 44 45 46 47 48 49

It is interesting to note that the odd squares lie along the bottom right diagonal, but what is more interesting is that 8 out of the 13 numbers lying along both diagonals are prime; that is, a ratio of 8/13 ≈ 62%.

If one complete new layer is wrapped around the spiral above, a square spiral with side length 9 will be formed. If this process is continued, what is the side length of the square spiral for which the ratio of primes along both diagonals first falls below 10%?

### Code


import java.math.BigInteger;

public final class p058 {

public static void main(String[] args) {
long start = System.nanoTime();
long result = run();
long end = System.nanoTime();
System.out.println(result);
System.out.println((end - start) / 1000000 + "ms");
}

public static long run() {
int numPrimes = 0;
int n=3;
while(true){
for (int i = 0; i <= 3; i++) {
if (isPrime(n * n - i * (n - 1))) {
numPrimes++;
}
}
if (numPrimes * 10 < n * 2 - 1) {
return n;
}
n+=2;
}
}

public static boolean isPrime(int x) {
if (x < 0) {
throw new IllegalArgumentException("Negative number");
}
if (x == 0 || x == 1) {
return false;
} else if (x == 2) {
return true;
} else {
if (x % 2 == 0) {
return false;
}
int max = (int)Math.sqrt(x);
for (int i = 3; i<= max; i += 2) {
if (x % i == 0) {
return false;
}
}
return true;
}
}
}

26241
263ms