I was wondering about how can one find the nth term of fibonacci sequence for a very large value of n say, 1000000. Using the grade-school recurrence equation fib(n)=fib(n-1)+fib(n-2), it takes 2-3 min to find the 50th term!
After googling, I came to know about Binet's formula but it is not appropriate for values of n>79 as it is said here
Is there an algorithm to do so just like we have for finding prime numbers?
You can use the matrix exponentiation method (linear recurrence method). You can find detailed explanation and procedure in this or this blog. Run time is O(log n).
I don't think there is a better way of doing this.