Data update

Task/Ramanujan-primes-twins/Java/ramanujan-primes-twins.java

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+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+
+public final class RamanujanPrimesTwins {
+
+	public static void main(String[] aArgs) {
+		final int limit = 1_000_000;
+		final int[] primePi = initialisePrimePi(ramanujanMaximum(limit) + 1);
+		final int millionthRamanujanPrime = ramanujanPrime(primePi, limit);
+		System.out.println("The 1_000_000th Ramanujan prime is " + millionthRamanujanPrime);
+		
+		List<Integer> primes = listPrimesLessThan(millionthRamanujanPrime);		
+		int[] ramanujanPrimeIndexes = new int[primes.size()];
+		for ( int i = 0; i < ramanujanPrimeIndexes.length; i++ ) {
+			ramanujanPrimeIndexes[i] = primePi[primes.get(i)] - primePi[primes.get(i) / 2];
+		}
+		int lowerLimit = ramanujanPrimeIndexes[ramanujanPrimeIndexes.length - 1];
+		for ( int i = ramanujanPrimeIndexes.length - 2; i >= 0; i-- ) {
+			if ( ramanujanPrimeIndexes[i] < lowerLimit ) {
+				lowerLimit = ramanujanPrimeIndexes[i];
+			} else {
+				ramanujanPrimeIndexes[i] = 0;
+			}
+		}
+		
+		List<Integer> ramanujanPrimes = new ArrayList<Integer>();
+		for ( int i = 0; i < ramanujanPrimeIndexes.length; i++ ) {
+			if ( ramanujanPrimeIndexes[i] != 0 ) {
+				ramanujanPrimes.add(primes.get(i));
+			}
+		}
+		
+		int twinsCount = 0;
+        for ( int i = 0; i < ramanujanPrimes.size() - 1; i++ ) {
+            if ( ramanujanPrimes.get(i) + 2 == ramanujanPrimes.get(i + 1) ) {
+                twinsCount += 1;
+            }
+        }
+		System.out.println("There are " + twinsCount + " twins in the first " + limit + " Ramanujan primes.");
+	}
+	
+	private static List<Integer> listPrimesLessThan(int aLimit) {
+		boolean[] composite = new boolean[aLimit + 1];
+		int n = 3;
+		int nSquared = 9;
+		while ( nSquared <= aLimit ) {
+		    if ( ! composite[n] ) {
+		    	for ( int k = nSquared; k < aLimit; k += 2 * n ) {
+		    		composite[k] = true;
+		    	}
+		    }
+		    nSquared += ( n + 1 ) << 2;
+		    n += 2;
+		}
+		
+		List<Integer> result = new ArrayList<Integer>();
+		result.add(2);
+		for ( int i = 3; i < aLimit; i += 2 ) {
+		    if ( ! composite[i] ) {
+		    	result.add(i);
+		    }
+		}
+		return result;
+	}
+
+	private static int ramanujanPrime(int[] aPrimePi, int aNumber) {
+		int maximum = ramanujanMaximum(aNumber);
+		if ( ( maximum & 1) == 1 ) {
+			maximum -= 1;
+		}
+		
+		int index = maximum;
+		while ( aPrimePi[index] - aPrimePi[index / 2] >= aNumber ) {
+			index -= 1;
+		}
+		return index + 1;
+	}
+	
+	private static int[] initialisePrimePi(int aLimit) {
+		int[] result = new int[aLimit];
+        Arrays.fill(result, 1);
+        result[0] = 0;
+        result[1] = 0;
+        for ( int i = 4; i < aLimit; i += 2 ) {
+            result[i] = 0;
+        }
+        for ( int p = 3, square = 9; square < aLimit; p += 2 ) {
+            if ( result[p] != 0 ) {
+                for ( int q = square; q < aLimit; q += p << 1 ) {
+                    result[q] = 0;
+                }
+            }
+            square += ( p + 1 ) << 2;
+        }
+        Arrays.parallelPrefix(result, Integer::sum);
+        return result;
+    }
+	
+	private static int ramanujanMaximum(int aNumber) {
+		return (int) Math.ceil(4 * aNumber * Math.log(4 * aNumber));
+	}
+
+}