What is the biggest Fibonacci prime number?

George M · 2018-01-02, 07:49

The biggest Fibonacci prime I know is the 9311st Fibonacci number. Are there bigger ones? According to bigprimes.net, their biggest Fibonacci number (not particularly prime) is the 70333rd. That seems pretty big, but I’m asking for the biggest known Fibonacci prime. Does anyone have bigger ones than the 9311st??

Just curious :)

gophne · 2018-01-02, 07:59

Quote:

Originally Posted by George M

The biggest Fibonacci prime I know is the 9311st Fibonacci number. Are there bigger ones? According to bigprimes.net, their biggest Fibonacci number (not particularly prime) is the 70333rd. That seems pretty big, but I’m asking for the biggest Fibonacci prime. Does anyone have bigger ones than the 9311st??

Just curious :)

Hi George M

F130021 with 27173 digits....source https://en.wikipedia.org/wiki/Fibonacci_prime

Batalov · 2018-01-02, 08:03

There is no 'biggest Fibonacci prime number', as far as we know. Almost certainly, there is an infinite number of them.

As for the largest currently known, see here and here.
Other sources, even https://oeis.org/A001605, are not updated regularly.

George M · 2018-01-02, 08:05

Quote:

Originally Posted by Batalov

There is no 'biggest Fibonacci prime number', as far as we know. Almost certainly, there is an infinite number of them.

As for the largest currently known, see here and here.
Other sources, even https://oeis.org/A001605, are not updated regularly.

Yes, true that. I guess, more precisely, what is the biggest KNOWN fibonnaci prime to date. I think I should rephrase the question to that, so thanks for the pickup :)

George M · 2018-01-02, 08:08

Quote:

Originally Posted by gophne

Hi George M

F130021 with 27173 digits....source https://en.wikipedia.org/wiki/Fibonacci_prime

I also found another link from the one you showed me. Apparently, F(3244369) is likely to be the biggest known Fibonacci number with 678033 digits, pursuant to the link below:

http://www.primenumbers.net/prptop/s...&action=Search

ET_ · 2018-01-02, 08:13

Quote:

Originally Posted by George M

I also found another link from the one you showed me. Apparently, F(3244369) is likely to be the biggest known Fibonacci number with 678033 digits, pursuant to the link below:

http://www.primenumbers.net/prptop/s...&action=Search

They are PRP, not (yet) primes.

George M · 2018-01-02, 08:15

Quote:

Originally Posted by ET_

They are PRP, not (yet) primes.

I know. They are probable primes, however for them to make it to the list, they must be likely to be prime.

Batalov · 2018-01-02, 08:24

It is also obvious that Wiki was never restored from ignorant vandalism and is incorrect Re: F(130021). It is easily verified by checking the reference [4] which leads to F(104911), 21925 digits long, which was indeed proven by Stein and Water in 2015. Not the F(130021).

But then again, everyone knows (or should know) that Wiki is not a source for serious data. It is merely a starting point. Another case of vandalism about M50 is an easy illustration.

George M · 2018-01-02, 08:47

Quote:

Originally Posted by Batalov

It is also obvious that Wiki was never restored from ignorant vandalism and is incorrect Re: F(130021). It is easily verified by checking the reference [4] which leads to F(104911), 21925 digits long, which was indeed proven by Stein and Water in 2015. Not the F(130021).

But then again, everyone knows (or should know) that Wiki is not a source for serious data. It is merely a starting point. Another case of vandalism about M50 is an easy illustration.

And perhaps the Prime Gap Equation...

axn · 2018-01-02, 09:29

Quote:

Originally Posted by Batalov

It is also obvious that Wiki was never restored from ignorant vandalism and is incorrect Re: F(130021). It is easily verified by checking the reference [4] which leads to F(104911), 21925 digits long, which was indeed proven by Stein and Water in 2015. Not the F(130021).

Fixed it. FWIW, this was not the result of vandalism, but human error.

Batalov · 2018-01-02, 09:44

Yeah, there is a strange evolution of edits. There was someone in July trying to restore the correct known value, but his edits were reverted.

"4" also gets deleted and then added back again, and again, and again.

In one word, ... Wikipedia! Where everyone is an expert.

2018-01-02, 07:49	#1
George M Dec 2017 110010₂ Posts	What is the biggest Fibonacci prime number? The biggest Fibonacci prime I know is the 9311st Fibonacci number. Are there bigger ones? According to bigprimes.net, their biggest Fibonacci number (not particularly prime) is the 70333rd. That seems pretty big, but I’m asking for the biggest known Fibonacci prime. Does anyone have bigger ones than the 9311st?? Just curious :) Last fiddled with by George M on 2018-01-02 at 08:10

2018-01-02, 08:03	#3
Batalov "Serge" Mar 2008 San Diego, Calif. 3²×7×163 Posts	Get a habit of saying 'biggest known' There is no 'biggest Fibonacci prime number', as far as we know. Almost certainly, there is an infinite number of them. As for the largest currently known, see here and here. Other sources, even https://oeis.org/A001605, are not updated regularly.

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2018-01-02, 08:24	#8
Batalov "Serge" Mar 2008 San Diego, Calif. 3²·7·163 Posts	It is also obvious that Wiki was never restored from ignorant vandalism and is incorrect Re: F(130021). It is easily verified by checking the reference [4] which leads to F(104911), 21925 digits long, which was indeed proven by Stein and Water in 2015. Not the F(130021). But then again, everyone knows (or should know) that Wiki is not a source for serious data. It is merely a starting point. Another case of vandalism about M50 is an easy illustration.

2018-01-02, 09:44	#11
Batalov "Serge" Mar 2008 San Diego, Calif. 281D₁₆ Posts	Yeah, there is a strange evolution of edits. There was someone in July trying to restore the correct known value, but his edits were reverted. "4" also gets deleted and then added back again, and again, and again. In one word, ... Wikipedia! Where everyone is an expert.