Arbitrarily long strings of consecutive primes in special sets
Let $F(x)$ be a function of the form $ \sum_{i=1}^r d_i x^{ρ_i}$ where $d_1,\ldots,d_r\in\mathbb{R}$, $0 \leq ρ_1 < \ldots < ρ_r,$ $ρ_r \not\in \mathbb{Z},ρ_i \in \mathbb{R}$ for $ 1 \leq i \leq r$ and $d_r\not=0$. We prove that sets of the form $\{ n \in \mathbb{N}: \{ F(n) \} \in U \}$ for any non-empty open set $U \subset [0,1)$ contain arbitrarily long strings of consecutive primes.
math.NT↗