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Mar 2, 2019 at 17:00 comment added Sylvain JULIEN That was my initial feeling. To me these problems are different instances of the same fundamental phenomenon.
Mar 2, 2019 at 11:46 comment added Jan-Christoph Schlage-Puchta @SylvainJULIEN: On a strictly logical level Bateman-Horn does not seem to imply Goldbach. However, the methods we know do not see any difference between these problems, so it is quite likely that if one of prime twins, Goldbach, or Sophie-Germain primes is solved, then all of them are solved within the following year.
S Mar 1, 2019 at 13:06 history edited Fedor Petrov CC BY-SA 4.0
Corrected constant.
S Mar 1, 2019 at 13:06 history suggested Zhou CC BY-SA 4.0
Corrected constant.
Mar 1, 2019 at 12:55 review Suggested edits
S Mar 1, 2019 at 13:06
Feb 28, 2019 at 21:48 comment added Fedor Petrov @SylvainJULIEN I am afraid that no. If some large even number is not a sum of two primes, there still can be very large prime tuples of any prescribed form. At least it looks so.
Feb 28, 2019 at 21:11 comment added Sylvain JULIEN Incidentally, is Bateman-Horn conjecture known to imply Goldbach's one?
Feb 28, 2019 at 19:32 comment added Fedor Petrov in general we write $1-a/p$, where $a$ is the number of residues $n$ modulo $p$ for which at least of the numbers $f_i(n)$ is divisible by $p$
Feb 28, 2019 at 19:13 comment added Sylvain JULIEN Is there a precise reason for writing $(1-1/2)$ rather than $(1/2)$ directly?
Feb 28, 2019 at 19:04 history edited Fedor Petrov CC BY-SA 4.0
added 335 characters in body
Feb 28, 2019 at 18:44 history answered Fedor Petrov CC BY-SA 4.0