The description of the other market noted that it's really unlikely that there's a factor below 10^50. I left a script running overnight to sample prefactored integers within 10% of Fib(1801) with no factor above 10^50. Here are my results:

{0: 0, 1: 14, 2: 23, 3: 11, 4: 2, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0}

https://r-knott.surrey.ac.uk/Fibonacci/fibtable.html almost all of them have more than 3

The first 300 Fibonacci numbers, factored

The first 300 Fibonacci numbers fully factorized. Further pages have all the numbes up to the 500-th Fibonacci number with puzzles and investigations for schools and teachers or just for recreation!

@nanob0nus (probably even the mathematical meaning of "almost all")

@nanob0nus Indeed, the prime number theorem tells us that the density of primes goes like 1/log(n), and knth fibonacci number is divisible by the nth, so for any x, almost all Fibonacci numbers will have at least x factors.

Bit more complicated here, though, since there is the bias of this being the smallest Fibonacci number that our efforts haven't factored.