Data commit

Task/Meissel-Mertens-constant/Java/meissel-mertens-constant.java

@@ -0,0 +1,41 @@
+import java.util.ArrayList;
+import java.util.BitSet;
+import java.util.List;
+
+/**
+ * Calculates the Meissel-Mertens constant correct to 9 s.f. in approximately 15 seconds.
+ */
+public final class MeisselMertensConstant {
+	
+	public static void main(String[] aArgs) {
+		List<Double> primeReciprocals = listPrimeReciprocals(1_000_000_000);
+		final double euler = 0.577_215_664_901_532_861;
+		double sum = 0.0;
+	    for ( double reciprocal : primeReciprocals ) {
+	    	sum +=  reciprocal + Math.log(1.0 - reciprocal);
+	    }	
+	
+	    final double constant = euler + sum;	
+	    System.out.println("The Meissel-Mertens constant = " + constant);
+	}	
+	
+	private static List<Double> listPrimeReciprocals(int aLimit) {
+		BitSet sieve = new BitSet(aLimit + 1);
+		sieve.set(2, aLimit + 1);
+		
+		final int squareRoot = (int) Math.sqrt(aLimit);
+		for ( int i = 2; i <= squareRoot; i = sieve.nextSetBit(i + 1) ) {
+			for ( int j = i * i; j <= aLimit; j += i ) {
+				sieve.clear(j);
+			}
+		}
+		
+		List<Double> result = new ArrayList<Double>(sieve.cardinality());
+		for ( int i = 2; i >= 0; i = sieve.nextSetBit(i + 1) ) {
+			result.add(1.0 / i);
+		}
+		
+		return result;
+	}
+
+}