Erdős problem 1106

Let $p(n)$ be the partition number of $n$ and $F(n)$ be the number of distinct prime factors of $∏_{i= 1} ^ {n} p(n)$ , then $F(n)$ tends to infinity when $n$ tends to infinity.

Sources

The source's own material, retained exactly.

2 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

1106.lean

Retained formal statement2 of 2

Let $p(n)$ be the partition number of $n$ and $F(n)$ be the number of distinct prime factors of $∏_{i= 1} ^ {n} p(n)$ , $F(n)>n$ for sufficiently large $n$ .

FormalConjectures/ErdosProblems/1106.leanErdos1106.erdos_1106.parts.ii1 lineExact file

1True ↔ ∀ᶠ (n : ℕ) in Filter.atTop, (∏ i ∈ Finset.Icc 1 n, Erdos1106.p i).primeFactors.card > n

OpenStatement only, no proof