The topologist J. H. C. Whitehead (not to be confused with his famous uncle) said it is naive to think a theorem is trivial merely because its proof is trivial. Hence I'm wondering if a certain trivial proposition appears in the literature somewhere. Maybe the best way to state it is this: If $p$ is the smallest prime factor of $n$ and $p^3>n$, then $n/p$ is prime.
Suppose I'm trying to factor $5497$ by hand. I've ruled out divisibility by all primes through $19$, and I do long division by $23$ and get $239$ as the quotient. Since all prime factors of $5497$ must be at least $23$, and $23^3$ is clearly too big to be $5497$, there's room for only one more prime factor, so I have to conclude that the quotient, $239$, is prime.
A standard step in standard algorithms appearing in all textbooks? Or somewhere else in published sources?
I suppose you could say I've tacitly ruled out divisibility of $239$ by all primes less than $\sqrt{239}$, and of course every (?) book mentions that, but I wasn't thinking of $239$ at the time, and I couldn't have reached my conclusion without going beyond the square root of $239$ and including $17$ and $19$ in my search.