Is the set $S:=\{\ln p \mid p\ \text{is prime}\}$ is algebraically independent over $\Bbb Q$? i.e. if $t_1 \lt t_2 \lt \cdots \lt t_n \in S$, then $f(t_1,t_2,\cdots ,t_n) \neq 0$ for all nonzero polynomials $f \in \Bbb Q [X_1,X_2, \cdots,X_n]$ ?
2026-03-28 17:42:05.1774719725
$\ln p$ are algebraically independent over $\Bbb Q$?
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