Timeline for Does this prime-gaps pattern occur infinitely often?
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Feb 6, 2014 at 11:40 | vote | accept | Joseph O'Rourke | ||
| Feb 6, 2014 at 0:38 | comment | added | Joseph O'Rourke | Sharp eyes, Gerry! Corrected---Thanks! | |
| Feb 6, 2014 at 0:38 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Correction as per Gerry Myerson.
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| Feb 6, 2014 at 0:00 | comment | added | Gerry Myerson | In the illustration for $k=1$, 47 should be 43 (I'd fix it myself, but pretty displays are beyond my TeXnical level). | |
| Feb 5, 2014 at 20:58 | answer | added | Jan-Christoph Schlage-Puchta | timeline score: 15 | |
| Feb 5, 2014 at 17:26 | comment | added | Joseph O'Rourke | @quid: I removed the claim that the $k=0$ pattern---three consecutive primes in arithmetic progression---is resolved by recent results. Thanks for the correction! | |
| Feb 5, 2014 at 17:25 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Removed claim re k=0.
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| Feb 5, 2014 at 17:09 | comment | added | user9072 | @TheMaskedAvenger the work of Green and Tao is not for consecutive primes; it is not even known if there are 3-AP of consecutive primes (wheras 3-AP of primes is "ancient"). For k-tuples conjecture, yes, I think it is also conjetured for consecutive, but I was under the impression it is more common not to insist on this in that conjecture too. | |
| Feb 5, 2014 at 17:03 | comment | added | The Masked Avenger | I guess I need to review the literature, as I had the impression that the progressions were of consecutive primes. Perhaps I am confusing Tao and Green's work with work on 3-tuples occurring infinitely often. If so, I apologize for the chatter. | |
| Feb 5, 2014 at 16:59 | comment | added | The Masked Avenger | @quid, its quite possible that I am confusing my idea with what is actually in the literature. My recall is that if an admissible pattern of prime gaps occur, then that pattern occurs infinitely often WITH no extra primes "inside" the pattern. What might be in the literature instead would have the constellation occur as a proper subconstellation, allowing extra primes. | |
| Feb 5, 2014 at 16:52 | comment | added | user9072 | @TheMaskedAvenger as far as I can see it does not follow from results on progressions in primes (since nothing guarantees the primes to be consecutive, which is also the point of my first comment) | |
| Feb 5, 2014 at 16:52 | comment | added | The Masked Avenger | In fact, you might tweak your write up to say that the case k=0 follows from the work on arithmetic progressions on primes, which is less recent than what many might think. | |
| Feb 5, 2014 at 16:50 | comment | added | user9072 | @TheMaskedAvenger how exactly would you use k-tuples conjecture? | |
| Feb 5, 2014 at 16:48 | comment | added | The Masked Avenger | Terry Tao might weigh in on whether one could "Maynardize" (sorry!) his and Ben Green's work on primes in arithmetic progressions to produce a more regular pattern. That's one chance I see of this being answered positively before k tuples conjecture. | |
| Feb 5, 2014 at 16:39 | comment | added | The Masked Avenger | Likely yes. No proof yet. Stay tuned. Also, this would follow from the k-primes conjecture, which seems more likely to be answered before your question. | |
| Feb 5, 2014 at 16:04 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |