A Math Question

Post by **Surlethe** » 2005-07-12 08:39am

Is there any function governing the distribution of primes in the basic fibonacci sequence? {1, 1, 2, 4, 5, 8, 13, ...}

NPComplete · Post by **NPComplete** » 2005-07-12 10:32am

Well, (and you won't like this answer) yes, there is, only because any 1-1 (injective) relation is a function. So I could define the function fib_prime:N->N (which goes from the naturals to the naturals)

fib_prime(1) = 1
fib_prime(2) = 1
fib_prime(3) = 3
fib_prime(4) = 13

etc.

However, what you probably wanted to know is "Is there a closed form function ...", to which I suspect the answer is no.

To give an example, here is a function

fake_squared (1) = 1
fake_squared (2) = 4
fake_squared (3) = 9
fake_squared (4) = 16
etc

which is not the same as
f(x) = x^2

because fake_squared(5) might equal something other than 25, for example.

Sriad · Post by **Sriad** » 2005-07-12 03:37pm

No. If there were, math would have a way to find arbitrarily large prime numbers by digging deep into the Fibonacci sequence. That would be pretty big news.

Post by **Surlethe** » 2005-07-12 03:50pm

NPComplete wrote:However, what you probably wanted to know is "Is there a closed form function ..."

Heh. Silly me, with imprecise wording.

Yes, that is what I wanted to know.

More generally, is there a way we can figure out the distribution of primes within the fibonacci sequence?

Kuroneko · Post by **Kuroneko** » 2005-07-12 09:32pm

Surlethe wrote:More generally, is there a way we can figure out the distribution of primes within the fibonacci sequence?

There is no known way to do that. Actually, it is even worse, as it is not even known whether or not there is a finite or infinite amount of Fibonacci primes, much less how they are distributed.