Timeline for What keeps asymptotic Goldbach's conjecture out of reach of current technology?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 15 at 15:24 | comment | added | David E Speyer | I'll link to an answer I wrote over at math.SE math.stackexchange.com/a/4719444/448 : with plausible assumptions, there is a set of primes $\mathcal{P}$ such that (1) for all $a$ and $b$ with $\text{GCD}(a,b)=1$, almost all primes of the form $a+kb$ lie in $\mathcal{P}$ but (2) there are infinitely many (though very sparse) $n$ for which $p+q=2n$ is not solvable for $p$, $q \in \mathcal{P}$. So you need better than first order control on primes in arithmetic progressions. | |
| Apr 1, 2014 at 20:11 | comment | added | Tom Leinster | To state the obvious, one possible reason is that it's false... | |
| Apr 1, 2014 at 18:19 | vote | accept | Sylvain JULIEN | ||
| Apr 1, 2014 at 17:51 | answer | added | Jan-Christoph Schlage-Puchta | timeline score: 22 | |
| Mar 31, 2014 at 12:00 | history | edited | Nate Eldredge |
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| Mar 31, 2014 at 11:53 | comment | added | Stanley Yao Xiao | I think one of the main obstructions is the "parity problem" in sieve theory, which all of the results above depend on to some extent. This is summarized by Terry Tao as follows: "If $A$ is a set whose elements are all products of an odd number of primes (or are all products of an even number of primes), then (without injecting additional ingredients), sieve theory is unable to provide non-trivial lower bounds on the size of $A$. Also, any upper bounds must be off from the truth by a factor of 2 or more." | |
| Mar 31, 2014 at 11:46 | history | asked | Sylvain JULIEN | CC BY-SA 3.0 |