What is the biggest Fibonacci prime number?

[CRGreathouse]

Originally Posted by Batalov

Other sources, even https://oeis.org/A001605, are not updated regularly.

It's hard -- to add another term to the OEIS it's not enough to show that you have a (probable) prime, but that there are no intervening primes. If there's information on how far the search has been done and all the primes found I'd be happy to update the OEIS.

[LaurV]

Originally Posted by CRGreathouse

It's hard -- to add another term to the OEIS it's not enough to show that you have a (probable) prime, but that there are no intervening primes. If there's information on how far the search has been done and all the primes found I'd be happy to update the OEIS.

Maybe a good idea would be to use question marks in between? Like for example (fictive sequence, only to illustrate the idea): 2, 8, 18, ?, 50, ...
This will record the found terms, so they do not get lost, and not only will mark the fact that some unknown terms may lay in between, but will also tickle the reader's curiosity so they will want to investigate the gaps and who knows? maybe fill them in, or eliminate the doubt...

[science_man_88]

Originally Posted by CRGreathouse

It's hard -- to add another term to the OEIS it's not enough to show that you have a (probable) prime, but that there are no intervening primes. If there's information on how far the search has been done and all the primes found I'd be happy to update the OEIS.

Could make a comment to the effect of the next known probably prime is ...

[George M]

Originally Posted by CRGreathouse

It's hard -- to add another term to the OEIS it's not enough to show that you have a (probable) prime, but that there are no intervening primes. If there's information on how far the search has been done and all the primes found I'd be happy to update the OEIS.

Well according to this thread, it seems like the biggest known fibonnaci prime is F(104911). Essentially, I was asking to see if there were bigger fibonnaci primes than F(9311).

[CRGreathouse]

Originally Posted by science_man_88

Could make a comment to the effect of the next known probably prime is ...

That's the way it's usually handled.

[George M]

Originally Posted by George M

Well according to this thread, it seems like the biggest known fibonnaci prime is F(104911). Essentially, I was asking to see if there were bigger fibonnaci primes than F(9311).

Since 9311 is prime, perhaps another question could be, what is the biggest fibonnaci number F(n) such that F(n) is prime and n is also prime, however 104911 is also a prime number so this answers our question... for now. Doing some research, it seems like if F(n) is prime with n < 5000, then the largest value of n is 2222. Nonetheless, 2222 is definitely not a prime number.

From this, could we perhaps raise an upper bound on n? For instance, is there a way of mathematically showing the largest value of n < k such that F(n) is prime? I have made an attempt of trying to look at a pattern of the last digits of the fibonnaci numbers. Of course, if they are odd, then the fibonnaci number with that odd last digit stands a chance of being prime. Through my work, I noticed that the final digits of the fibonnaci sequence have a cycle length of 60.

For example, the first few fibonnaci numbers in the sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

So the sequence of the last digits would be in this case 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9.

But why must this sequence have a cycle length of 60? Well, 60 is the smallest number to be divisible by all the numbers from 1 to 6 (it is a weak factorial of 6) and the first 6 fibonnaci numbers represent its own last digit... hmmm... maybe that’s the reason? Any suggestions?

[Batalov]

https://en.wikipedia.org/wiki/Pisano_period

[George M]

Originally Posted by Batalov

https://en.wikipedia.org/wiki/Pisano_period

Yes, along with that, I came across this:

https://m.youtube.com/watch?v=Nu-lW-Ifyec

Thank you for showing me that link :)

[axn]

Originally Posted by George M

Since 9311 is prime, perhaps another question could be, what is the biggest fibonnaci number F(n) such that F(n) is prime and n is also prime, however 104911 is also a prime number so this answers our question... for now. Doing some research, it seems like if F(n) is prime with n < 5000, then the largest value of n is 2222. Nonetheless, 2222 is definitely not a prime number.

WTF? Did you even bother reading the wikipedia article on Fibonacci prime?

[CRGreathouse]

Originally Posted by George M

Since 9311 is prime, perhaps another question could be, what is the biggest fibonnaci number F(n) such that F(n) is prime and n is also prime, however 104911 is also a prime number so this answers our question... for now. Doing some research, it seems like if F(n) is prime with n < 5000, then the largest value of n is 2222. Nonetheless, 2222 is definitely not a prime number.

F(2222) is not prime, it has 131,072 divisors. As axn hinted, the only composite number n such that F(n) is prime is 4.