Timeline for answer to The most outrageous (or ridiculous) conjectures in mathematics by Gerry Myerson
Current License: CC BY-SA 4.0
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16 events
| when toggle format | what | by | license | comment | |
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| Aug 24, 2024 at 7:31 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
added 49 characters in body
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| Mar 25, 2021 at 18:11 | comment | added | Yaakov Baruch | Assuming k-tuples, is the Hensley and Richards' proof effective in disproving convexity? If so with what bound? | |
| Jan 25, 2020 at 14:25 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
added eudml link
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| Jan 24, 2017 at 21:54 | comment | added | Gerry Myerson | @nigel, if 2nd Hardy-Littlewood is false, then there is a counterexample, so it's not unproveable. | |
| Jan 24, 2017 at 11:57 | comment | added | nigel222 | Godel proved there must be unproveable true statements. One mark of such might be that A and B are both plausible, neither leads to anything outright ridiculous, but that it is proven that A implies not-B, and vice versa. | |
| Jan 21, 2017 at 23:05 | comment | added | gnasher729 | And I think this conjecture being called "the second Hardy-Littlewood conjecture" - which means that if the first Hardy-Littlewood conjecture is true, the second one is false :-) | |
| Jan 21, 2017 at 23:03 | comment | added | gnasher729 | opertech.com/primes/k-tuples.html shows some numerical details. There might be a counter example to the conjecture before 10^1197 - trying to find it with current methods is quite hopeless. @MarkS Quite possible they found both conjectures plausible at the same time; a k-tuple contradicting it is quite hard to find. | |
| Jan 19, 2017 at 1:55 | comment | added | Gerry Myerson | @Mark, it's not even entirely clear where or whether Hardy & Littlewood made the conjectures. See mathoverflow.net/questions/54223/whence-the-k-tuple-conjecture and mathoverflow.net/questions/30827/… and math.stackexchange.com/questions/1072194/… for some discussions. | |
| Jan 19, 2017 at 0:53 | comment | added | Mark S | Is it the case that Hardy-Littlewood really considered both the k-tuples conjecture and the convexity conjecture to be plausible? Makes me wonder what mutually implausible conjectures are also held to be believed nowadays (2017). | |
| Jan 18, 2017 at 13:46 | comment | added | Wojowu | This is nowadays known as the second Hardy-Littlewood conjecture. | |
| Jan 18, 2017 at 5:36 | comment | added | Gerry Myerson | @orlp, there are heuristic arguments that not only do prime $k$-tuples exist but there are asymptotic formulas for how many of them there are up to any given bound, and these asymptotic formulas are always in close agreement with the numerical evidence. I don't think there are any such arguments for convexity, so it's gotta go. | |
| Jan 18, 2017 at 4:08 | comment | added | orlp | What makes the consensus favor prime $k$-tuples over the Hardy-Littlewood convexity conjecture? Intuitively the former seems much less plausible than the latter. | |
| Jan 17, 2017 at 23:14 | comment | added | Gerry Myerson | I've seen it referred to as "the Hardy-Littlewood convexity conjecture". See Section 1.2.4 of the Crandall and Pomerance book, Prime Numbers: A Computational Perspective. | |
| Jan 17, 2017 at 23:04 | comment | added | Brevan Ellefsen | Does this conjecture have a name? | |
| S Jan 17, 2017 at 22:14 | history | answered | Gerry Myerson | CC BY-SA 3.0 | |
| S Jan 17, 2017 at 22:14 | history | made wiki | Post Made Community Wiki by Gerry Myerson |