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Claim. Theorem 1.1 of A. J. Irving, The largest prime factor of $X^3+2$, states: let $\varpi=10^{-52}$ and let $X$ be sufficiently large; then for at least a positive proportion of the integers $n\in(X,2X]$, $n^3+2$ has a prime factor exceeding $X^{1+\varpi}$. For $f(t)=t^3+2$ this gives $F_f(n)\geq(n/2)^{1+\varpi}$ for all large $n$, in the notation of Problem 976. It improves the exponent of Heath-Brown's 2001 theorem.

Covers. The first question for $f(t)=t^3+2$. It does not give $F_f(n)\gg n^3$.

Depends on. No page of this wiki.

Acceptance. Refereed: Acta Arithmetica 171 (2015), no. 1, 67--80. The site labels the problem OPEN.