Let $x_i=i+1, 1\le i \le n$, $y_i = +1,$ if $x_i$ is prime, $-1$ otherwise.
Conjecture: Then (?) there exists $b,c_i \in \mathbb{R}, 1 \le i \le n$ such that for all $j=1,\ldots,n$:
$$y_j = \text{ sgn }\left(\left[\sum_{i=1}^n c_iy_i\gcd( x_i, x_j)\right] - b\right)$$
Motivation for asking this question: https://mathoverflow.net/questions/349589/are-primes-linearly-separable
Thanks for your help!
this question has been answered at mo.