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import FormalConjecturesUtil
namespace Erdos952
Is there an infinite sequence of distinct Gaussian primes $x_1,x_2,\ldots$ such that $\lvert x_{n+1}-x_n\rvert \ll 1$?
@[category research open, AMS 11]
theorem erdos_952 :
∃ (x : ℕ → GaussianInt) (C : ℤ),
Function.Injective x ∧
∀ n, Prime (x n) ∧ (x (n + 1) - x n).norm < C := ⊢ ∃ x C, Function.Injective x ∧ ∀ (n : ℕ), Prime (x n) ∧ Zsqrtd.norm (x (n + 1) - x n) < C
All goals completed! 🐙
end Erdos952