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But from the article: >> In fact, Larsen’s argument didn’t just allow him to show that a Carmichael number must always appear between X and 2X. And yet the Wi
by phkahler 4y ago
But from the article:
>> In fact, Larsen’s argument didn’t just allow him to show that a Carmichael number must always appear between X and 2X.
And yet the Wikipedia page says 2821 and 6601 are the 5th and 6th Carmichael numbers, which means there are not between 3000 and 6000 (X and 2X). So is his result actually that one must always exist between X and 2.5X or some other small multiple? If so, what multiple did he prove?
- bibanez 4y agoI only read the abstract and the result is in the same spirit but doesn't say exactky between X and 2X. It's between some more complicated expressions (using logs like usual in number theory)
- zeroonetwothree 4y agoThe bounds are tighter than n and 2n. So he actually proved a stronger result.
- renewiltord 4y agoAh I didn't mean to mislead that it was x and 2x. Corrected to be slightly clearer. The bound is easiest seen on the arxiv link above, in the abstract. The HN forum software doesn't do math very well.
- zeroonetwothree 4y agoIt’s true for x sufficiently large. So there will be some small counterexamples.