Have numbers of this form forced small factors?

Question

Let $F_n$ be the $n$ th Fibonacci-number and define $$f(n):=F_{n^2}-F_n+1$$

For most integers $n>1$ , $f(n)$ has a small prime factor :

2  3
3  3
4  5
5  3
6  5
7  11
8  227
9  3727
10  3
11  3
12  5
13  3
14  2099
15  307
16  7445729
17  11
18  3
19  3
20  197921
21  3
22  137
23  11
24  5
25  103681
26  3
27  3
28  81209593
29  3
30  547
31  17
32  5
33  11
34  3
35  3
36  701
37  3
38  5
39  647
40  353
41  17
42  3
43  3
44  5
45  3
46  5
47  11
48  40759
49  79
50  3
51  3
52  5
53  3
54  ?

The smallest prime factor of $f(54)$ has probably more than $25$ digits.

Can it be proven that $f(n)$ is composite for every integer $n>2$ by finding a forced factor ? $f(n)$ is prime for $n=2$ and no other integer $n\le 700$ ?

Update :

• $P33 = 107407032520007517281843885218879$ divides $F(54)$
• $P28 = 1731761941976002747853061853$ divides $F(94)$

factordb

Any ideas ?