Formal target: Corpus.Erdos891.erdos_891.variants.weisenberg
Weisenberg has observed that Dickson's conjecture implies the answer is no if we replace $p_1\cdots p_k$ with $p_1\cdots p_k-1$.
Exact formal statement
∀ (k : Nat),
GE.ge.{0} k 2 →
Filter.Frequently.{0}
(fun n =>
∀ (m : Nat),
Membership.mem.{0, 0}
(Finset.Ico.{0} n
(HSub.hSub.{0, 0, 0}
(HAdd.hAdd.{0, 0, 0} n (Finset.prod.{0, 0} (Finset.range k) fun i => Nat.nth Nat.Prime i)) 1))
m →
LE.le.{0} (DFunLike.coe.{1, 1, 1} ArithmeticFunction.cardDistinctFactors m) k)
Filter.atTop.{0}This target is a formal statement, not a proof of the problem.
Environment availability: available.