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Oct 6, 2016 at 4:38 comment added Fedor Petrov strictly speaking, this is not $\leqslant (n-1)/k$, but $\leqslant (n-1)/k+1$, since our small positive idempotent is either $f_j-f_i$ or $1-(f_j-f_i)$.
Jun 21, 2016 at 16:18 vote accept Xiaosheng Mu
Jun 21, 2016 at 16:18
Jun 20, 2016 at 21:58 comment added Fedor Petrov Nice! This looks to be essentially sharp, and even strong conjectures like twin primes are not necessary, see update to my answer.
Jun 20, 2016 at 19:46 history answered David E Speyer CC BY-SA 3.0