Wolstenholme numbers: Difference between revisions

=={{header|Java}}==

<syntaxhighlight lang="java">

import java.math.BigInteger;

import java.util.ArrayList;

import java.util.List;

public final class WolstenholmeNumbers {

public static void main(String[] args) {

WolstenholmeIterator iterator = new WolstenholmeIterator();

List<BigInteger> wolstenholmePrimes = new ArrayList<BigInteger>();

System.out.println("Wolstenholme numbers:");

for ( int index = 1; index <= 10_000; index++ ) {

BigInteger wolstenholmeNumber = iterator.next();

if ( wolstenholmePrimes.size() < 15 && wolstenholmeNumber.isProbablePrime(15) ) {

wolstenholmePrimes.add(wolstenholmeNumber);

}

if ( index <= 20 || PRINT_POINTS.contains(index) ) {

System.out.println(String.format("%5d%s%s", index, ": ", abbreviate(wolstenholmeNumber)));

}

}

System.out.println();

System.out.println("Prime Wolstenholme numbers:");

for ( int index = 0; index < wolstenholmePrimes.size(); index++ ) {

System.out.println(String.format("%5d%s%s", index + 1, ": ", abbreviate(wolstenholmePrimes.get(index))));

}

}

private static String abbreviate(BigInteger number) {

String text = number.toString();

int digits = text.length();

return digits <= 20 ?

text : text.substring(0, 20) + " ... " + text.substring(digits - 20) + " (digits: " + digits + ")";

}

private static final List<Integer> PRINT_POINTS = List.of( 500, 1_000, 2_500, 5_000, 10_000 );

}

final class WolstenholmeIterator {

public BigInteger next() {

BigInteger result = secondHarmonic.numerator();

k += 1;

secondHarmonic = secondHarmonic.add( new Rational(BigInteger.ONE, BigInteger.valueOf(k * k)) );

return result;

}

private int k = 1;

private Rational secondHarmonic = new Rational(BigInteger.ONE, BigInteger.ONE);

}

final class Rational {

public Rational(BigInteger aNumerator, BigInteger aDenominator) {

numerator = aNumerator;

denominator = aDenominator;

BigInteger gcd = numerator.gcd(denominator);

numerator = numerator.divide(gcd);

denominator = denominator.divide(gcd);

}

public Rational add(Rational aRational) {

BigInteger numer = numerator.multiply(aRational.denominator).add(aRational.numerator.multiply(denominator));

BigInteger denom = aRational.denominator.multiply(denominator);

return new Rational(numer, denom);

}

public BigInteger numerator() {

return numerator;

}

private BigInteger numerator;

private BigInteger denominator;

}

</syntaxhighlight>

{{ out }}

<pre>

Wolstenholme numbers:

1: 1

2: 5

3: 49

4: 205

5: 5269

6: 5369

7: 266681

8: 1077749

9: 9778141

10: 1968329

11: 239437889

12: 240505109

13: 40799043101

14: 40931552621

15: 205234915681

16: 822968714749

17: 238357395880861

18: 238820721143261

19: 86364397717734821

20: 17299975731542641

500: 40989667509417020364 ... 48084984597965892703 (digits: 434)

1000: 83545938483149689478 ... 99094240207812766449 (digits: 866)

2500: 64537911900230612090 ... 12785535902976933153 (digits: 2164)

5000: 34472086597488537716 ... 22525144829082590451 (digits: 4340)

10000: 54714423173933343999 ... 49175649667700005717 (digits: 8693)

Prime Wolstenholme numbers:

1: 5

2: 266681

3: 40799043101

4: 86364397717734821

5: 36190908596780862323 ... 79995976006474252029 (digits: 104)

6: 33427988094524601237 ... 48446489305085140033 (digits: 156)

7: 22812704758392002353 ... 84405125167217413149 (digits: 218)

8: 28347687473208792918 ... 45794572911130248059 (digits: 318)

9: 78440559440644426017 ... 30422337523878698419 (digits: 520)

10: 22706893975121925531 ... 02173859396183964989 (digits: 649)

11: 27310394808585898968 ... 86311385662644388271 (digits: 935)

12: 13001072736642048751 ... 08635832246554146071 (digits: 984)

13: 15086863305391456002 ... 05367804007944918693 (digits: 1202)

14: 23541935187269979100 ... 02324742766220468879 (digits: 1518)

15: 40306783143871607599 ... 58901192511859288941 (digits: 1539)

</pre>