Number of digits in Fibonacci term (Project Euler problem 25)

Q: The question from the problem 25  is to find the first term in the Fibonacci sequence to contain 1000 digits. 


A: The answer comes from wiki: 


Since F_n is asymptotic to , the number of digits in  is asymptotic to . As a consequence, for every integer d > 1 there are either 4 or 5 Fibonacci numbers with d decimal digits.


So, 1000/0.2090 is approximately  4784, and the first Fibonacci term with 1000 digits is the 4782th term.