Data update

Task/Home-primes/Java/home-primes.java

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+import java.math.BigInteger;
+import java.util.ArrayList;
+import java.util.BitSet;
+import java.util.Collections;
+import java.util.List;
+import java.util.concurrent.ThreadLocalRandom;
+import java.util.stream.Collectors;
+import java.util.stream.Stream;
+
+public final class HomePrimes {
+
+	public static void main(String[] aArgs) {
+		listPrimes(PRIME_LIMIT);
+		
+		List<Integer> values = List.of( 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 65 );
+		for ( int value : values ) {
+			BigInteger number = BigInteger.valueOf(value);
+			List<BigInteger> previousNumbers = Stream.of( number ).collect(Collectors.toList());
+			boolean searching = true;
+			while ( searching ) {
+				number = concatenate(primeFactors(number));
+				previousNumbers.add(number);
+				if ( number.isProbablePrime(CERTAINTY_LEVEL) ) {
+					final int lastIndex = previousNumbers.size() - 1;
+					for ( int k = lastIndex; k >= 1; k-- ) {
+						System.out.print("HP" + previousNumbers.get(lastIndex - k) + "(" + k + ") = ");
+					}
+					System.out.println(previousNumbers.get(lastIndex));
+					searching = false;
+				}
+			}
+		}
+	}
+	
+	private static List<BigInteger> primeFactors(BigInteger aNumber) {		
+		List<BigInteger> result = new ArrayList<BigInteger>();
+		
+		if ( aNumber.compareTo(BigInteger.valueOf(PRIME_LIMIT * PRIME_LIMIT)) <= 0 ) {
+			return smallPrimeFactors(aNumber);
+		}	
+		
+		if ( aNumber.isProbablePrime(CERTAINTY_LEVEL) ) {
+			result.add(aNumber);
+			return result;
+		}
+		
+		BigInteger divisor = pollardRho(aNumber);
+    	result.addAll(primeFactors(divisor));
+    	aNumber = aNumber.divide(divisor);    	
+    	result.addAll(primeFactors(aNumber));
+		Collections.sort(result);
+		return result;
+	}
+	
+	private static List<BigInteger> smallPrimeFactors(BigInteger aNumber) {
+		int number = aNumber.intValueExact();
+		List<BigInteger> result = new ArrayList<BigInteger>();
+	
+		for ( int i = 0; i < primes.size() && number > 1; i++ ) {
+			while ( number % primes.get(i) == 0 ) {
+				result.add(BigInteger.valueOf(primes.get(i)));
+				number /= primes.get(i);
+			}
+		}
+		
+		if ( number > 1 ) {
+			result.add(BigInteger.valueOf(number));
+		}
+		return result;
+	}
+
+	private static BigInteger pollardRho(BigInteger aNumber) {
+		if ( ! aNumber.testBit(0) ) {
+			return BigInteger.TWO;
+		}		
+		
+		final BigInteger constant  = new BigInteger(aNumber.bitLength(), RANDOM);
+		BigInteger x  = new BigInteger(aNumber.bitLength(), RANDOM);
+		BigInteger y = x;
+		BigInteger divisor = null;		
+		
+		do {
+			x = x.multiply(x).add(constant).mod(aNumber);
+			y = y.multiply(y).add(constant).mod(aNumber);
+			y = y.multiply(y).add(constant).mod(aNumber);
+			divisor = x.subtract(y).gcd(aNumber);
+		} while ( divisor.compareTo(BigInteger.ONE) == 0 );
+		return divisor;
+	}
+	
+	private static BigInteger concatenate(List<BigInteger> aList) {
+		String number = aList.stream().map(String::valueOf).collect(Collectors.joining());
+		return new BigInteger(number);
+	}
+	
+	public static void listPrimes(int aNumber) {
+		BitSet sieve = new BitSet(aNumber + 1);
+		sieve.set(2, aNumber + 1);		
+		for ( int i = 2; i <= Math.sqrt(aNumber); i = sieve.nextSetBit(i + 1) ) {
+			for ( int j = i * i; j <= aNumber; j = j + i ) {
+				sieve.clear(j);
+			}
+		}
+		
+		primes = new ArrayList<Integer>(sieve.cardinality());
+		for ( int i = 2; i >= 0; i = sieve.nextSetBit(i + 1) ) {
+			primes.add(i);
+		}
+	}
+	
+	private static List<Integer> primes;
+	
+	private static final int CERTAINTY_LEVEL = 20;
+	private static final int PRIME_LIMIT = 10_000;
+	private static final ThreadLocalRandom RANDOM = ThreadLocalRandom.current();
+	
+}