Boolean Pythagorean triples problem: Difference between revisions

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Revision as of 11:22, 10 July 2019

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{{math theorem| The set {1, . . . , 7824} can be partitioned into two parts, such that no part contains a Pythagorean triple, while this is impossible for {1, . . . , 7825}.<ref name="arXiv"/>}}

There are {{nowrap|2⁷⁸²⁵ ≈ 3.63×10²³⁵⁵}} colorings for the numbers up to [[7825 (number)|7825]]. These possible colorings were logically and algorithmically narrowed down to around a trillion (still highly complex) cases, and those were examined using a [[Boolean satisfiability]] solver. Creating the proof took about 4 CPU-years of CPU timecomputation over a period of two days on the Stampede supercomputer at the [[Texas Advanced Computing Center]] and generated a 200 terabyte propositional proof, which was compressed to 68 gigabytes.

The paper describing the proof was published on [[arXiv]] on 3 May 2016,<ref name="arXiv">{{Cite journal|last=Heule|first=Marijn J. H.|last2=Kullmann|first2=Oliver|last3=Marek|first3=Victor W.|date=2016-05-03|title=Solving and Verifying the Boolean Pythagorean Triples problem via Cube-and-Conquer |arxiv=1605.00723|doi=10.1007/978-3-319-40970-2_15|journal=Lecture Notes in Computer Science|pages=228–245}}</ref> and has been accepted for the SAT 2016 conference, where it won the best paper award.<ref>[http://sat2016.labri.fr/ SAT 2016]</ref>