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src/test/java/de/tilman_neumann/jml/primes/RiemannRobinHypothesisAnalyzer.java
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| /* | ||
| * java-math-library is a Java library focused on number theory, but not necessarily limited to it. It is based on the PSIQS 4.0 factoring project. | ||
| * Copyright (C) 2018-2024 Tilman Neumann - tilman.neumann@web.de | ||
| * | ||
| * This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License | ||
| * as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version. | ||
| * | ||
| * This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied | ||
| * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. | ||
| * | ||
| * You should have received a copy of the GNU General Public License along with this program; | ||
| * if not, see <http://www.gnu.org/licenses/>. | ||
| */ | ||
| package de.tilman_neumann.jml.primes; | ||
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| import java.math.BigDecimal; | ||
| import java.math.BigInteger; | ||
| import java.util.ArrayList; | ||
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| import org.apache.logging.log4j.Logger; | ||
| import org.apache.logging.log4j.LogManager; | ||
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| import de.tilman_neumann.jml.Divisors; | ||
| import de.tilman_neumann.jml.base.BigDecimalMath; | ||
| import de.tilman_neumann.jml.precision.Magnitude; | ||
| import de.tilman_neumann.jml.precision.Scale; | ||
| import de.tilman_neumann.jml.smooth.CANEntry; | ||
| import de.tilman_neumann.jml.smooth.CANIterator; | ||
| import de.tilman_neumann.jml.transcendental.EulerConstant; | ||
| import de.tilman_neumann.jml.transcendental.Exp; | ||
| import de.tilman_neumann.jml.transcendental.Ln; | ||
| import de.tilman_neumann.util.ConfigUtil; | ||
| import de.tilman_neumann.util.SortedMultiset; | ||
| import de.tilman_neumann.util.SortedMultiset_BottomUp; | ||
| import de.tilman_neumann.util.Timer; | ||
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| import static de.tilman_neumann.jml.base.BigDecimalConstants.F_0; | ||
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| /** | ||
| * Tests Robin's Riemann hypothesis tests on colossally abundant numbers (CANs). | ||
| * | ||
| * From page 4 of http://www.math.lsa.umich.edu/~lagarias/doc/elementaryrh.pdf: | ||
| * "Robin showed that, if the Riemann hypothesis is false, then there will necessarily exist a counterexample | ||
| * to the inequality (1.2) that is a colossally abundant number; the same property can be established for inequality (1.1)" | ||
| * | ||
| * Inequality (1.1) (Lagarias): sigma(n) <= Hn + exp(Hn)*ln(Hn) | ||
| * | ||
| * Inequality (1.2) (Robin): sigma(n) <= exp(gamma) n ln(ln(n)) for each n >=5041 | ||
| */ | ||
| public class RiemannRobinHypothesisAnalyzer { | ||
| private static final Logger LOG = LogManager.getLogger(RiemannRobinHypothesisAnalyzer.class); | ||
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| private static final boolean DEBUG = false; | ||
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| private static final Timer timer = new Timer(); | ||
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| /** | ||
| * Test inequality (1.2) with CANs. | ||
| * | ||
| * >24k CANs checked. Typical timings: | ||
| * Tested CAN(24003) with 118278 digits... t0=2297, t1=16, t2=0, t3=0, t4=16, t5=281 | ||
| * Tested CAN(24004) with 118284 digits... t0=0, t1=26, t2=0, t3=0, t4=0, t5=297 | ||
| * Tested CAN(24005) with 118289 digits... t0=1735, t1=15, t2=0, t3=0, t4=16, t5=281 | ||
| * Tested CAN(24006) with 118295 digits... t0=0, t1=18, t2=0, t3=0, t4=0, t5=313 | ||
| * Tested CAN(24007) with 118300 digits... t0=1187, t1=31, t2=0, t3=0, t4=0, t5=282 | ||
| * Tested CAN(24008) with 118306 digits... t0=0, t1=18, t2=0, t3=0, t4=0, t5=297 | ||
| * Tested CAN(24009) with 118311 digits... t0=1703, t1=32, t2=0, t3=0, t4=0, t5=296 | ||
| * Tested CAN(24010) with 118314 digits... t0=0, t1=30, t2=0, t3=0, t4=0, t5=297 | ||
| * Tested CAN(24011) with 118319 digits... t0=609, t1=16, t2=0, t3=0, t4=15, t5=282 | ||
| * Tested CAN(24012) with 118325 digits... t0=0, t1=24, t2=0, t3=0, t4=0, t5=297 | ||
| */ | ||
| private static void runRobinsRHTest() { | ||
| long t0, t1, t2, t3, t4; | ||
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| Scale scale = Scale.valueOf(30); // precision in after-floating point decimal digits | ||
| BigDecimal expGamma = Exp.exp(EulerConstant.gamma(scale), scale); | ||
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| CANIterator canIter = new CANIterator(); | ||
| for (int m=1; ; m++) { | ||
| timer.capture(); | ||
| CANEntry canEntry = canIter.next(); | ||
| BigInteger n = canEntry.getCAN(); | ||
| t0 = timer.capture(); | ||
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| BigDecimal n_flt = new BigDecimal(n, 0); | ||
| BigDecimal lnln_n = Ln.ln(Ln.ln(n_flt, scale), scale); | ||
| t1 = timer.capture(); | ||
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| BigDecimal robin = expGamma.multiply(n_flt).multiply(lnln_n); | ||
| t2 = timer.capture(); | ||
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| // Fast sumOfDivisors computation with known prime factorization | ||
| SortedMultiset<BigInteger> factors = toSortedMultiset(canEntry.getPrimes(), canEntry.getExponents()); | ||
| t3 = timer.capture(); | ||
| if (DEBUG) LOG.debug("factors(n)=" + factors); | ||
| BigInteger sigma = Divisors.sumOfDivisors(factors); | ||
| BigDecimal diff = BigDecimalMath.subtract(robin, sigma); | ||
| t4 = timer.capture(); | ||
| if (DEBUG) LOG.debug("sigma(n)=" + sigma + ", robin=" + robin + ", diff=" + diff); | ||
| if (diff.compareTo(F_0) < 0) { | ||
| LOG.info("Found RH counterexample candidate!"); | ||
| LOG.info(" m=" + m + ": n has " + Magnitude.of(n) + " digits"); | ||
| LOG.info(" n=" + n); | ||
| } else { | ||
| LOG.info("Tested CAN(" + m + ") with " + Magnitude.of(n) + " digits... t0=" + t0 + ", t1=" + t1 + ", t2=" + t2 + ", t3=" + t3 + ", t4=" + t4); | ||
| } | ||
| } | ||
| } | ||
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| private static SortedMultiset<BigInteger> toSortedMultiset(ArrayList<BigInteger> primes, ArrayList<Integer> exponents) { | ||
| SortedMultiset<BigInteger> factors = new SortedMultiset_BottomUp<>(); | ||
| for (int i=0; i<primes.size(); i++) { | ||
| factors.add(primes.get(i), exponents.get(i)); | ||
| } | ||
| return factors; | ||
| } | ||
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| public static void main(String[] argv) { | ||
| ConfigUtil.initProject(); | ||
| runRobinsRHTest(); | ||
| } | ||
| } |