Problem 58:
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%?
import java.math.BigInteger;
class runner
{
public static void main (String[] args) throws java.lang.Exception
{
long time = System.currentTimeMillis();
int diff_p = 0; int prev = 0;
int i=1;
int numOfPrime = 0;
double totalDiag = 0;
while(true){
int difference = 2*diff_p;//from 8*diff_p/4
for(int j=1;j<5;j++){
BigInteger x = new BigInteger(""+(difference*j+prev));
if(x.isProbablePrime(100)){
numOfPrime++;
}
totalDiag++;
}
double cur = numOfPrime/totalDiag;
if(numOfPrime> 0 && cur < .1){
break;
}
prev = i*i;
diff_p++;
i+=2;
}
System.out.println(i);
System.out.println("time:"+(System.currentTimeMillis()-time));
}
}
Note: Got lazy and ended up using BigInteger for primality test.