What is the largest known Fibonacci number?

Answer 1

Unlike some other types of numbers like prime numbers, calculating large Fibonacci numbers can be done quite easily with even a standard household computer. The process involves only repeated addition (rather than the intense division processes involved with large prime numbers). Beyond that, large Fibonacci numbers do not serve as much purpose as other large numbers (like primes). Because of this, these large numbers are generally left for quick calculation by machine if ever necessary.

An example of a computer program that could calculate the nth Fibonacci number (n greater than 1 and counting the first 1 in the sequence as the second term) is given below in pseudo-code:

Function Fibonacci(n)

a = 0

b = 1

k = 2

While n > k

(

a + b = c

a = b

b = c

k = k + 1

)

Print b

A very large Fibonacci number is the 250th in the sequence which has a value of:

12776523572924732586037033894655031898659556447352249.

The 1000th term in the sequence is:

4346655768693745643568852767504062580256466051737178040248172908953655

5417949051890403879840079255169295922593080322634775209689623239873322

471161642996440906533187938298969649928516003704476137795166849228875.

Much, much larger values (even beyond the 10,000,000th term) can be calculated quite quickly with a simple, well-written program. See related links for a site which can quickly calculate large Fibonacci numbers (using the form Fibonacci n).

Answer 2

The largest known Fibonacci number is F(1500000), which has 312679 digits.