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    Eight-page prime-gap paper is claimed to achieve a double-log factor over the Erdős–Rankin bound

    A post calls it the first such result in almost a century, versus triple-log factors in prior human work.

    Jared Duker LichtmanJD
    1 Source, 8h ago, first seen 8h ago

    TLDR

    A post says “Improved long gaps between primes” obtained the first double-log factor over the Erdős–Rankin bound in almost a century. It describes prior human results as breakthroughs but says they reached only triple-log factors, which the author calls an order of magnitude weaker.

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    1 Source, first seen 8h ago

    Combined views

    9K

    1 Source, first seen 8h ago

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    Featured Source
    JDJared Duker Lichtman@jdlichtman4:18 AM · Oct 8, 2026

    At only 8 pages, "Improved long gaps between primes" obtained the first double-log factor over the Erdos-Rankin bound in almost a century. All other results (themselves rightly recognized as breakthroughs in the field, Erdos offered $10,000) by humans only obtained triple-log…

    openai.comcdn.openai.com/pdf/51126fac-1b68-4128-9666-c908bcc16033/long_gaps.pdf
    DO
    doomslide@doomslide

    @jconorgrogan I am willing to predict no LLM (say in the next 5 years though might as well be indefinite) will *prove* (rather than disprove) a major open conjecture using an argument that's more than 10-20 pages long when written properly.

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    1 Source

    Jared Duker Lichtman@jdlichtmanAt only 8 pages, "Improved long gaps between primes" obtained the first double-log factor over the Erdos-Rankin bound in almost a century. All other results (themselves rightly recognized as breakthroughs in the field, Erdos offered $10,000) by humans only obtained triple-log factors, an order of magnitude weaker. https://cdn.openai.com/pdf/51126fac-1b68-4128-9666-c908bcc16033/long_gaps.pdf8h