mersenneforum.org GIMPS and Fibonacci prime project?
 User Name Remember Me? Password
 Register FAQ Search Today's Posts Mark Forums Read

 2017-10-25, 07:42 #1 Shen   Jan 2017 5 Posts GIMPS and Fibonacci prime project? I have run prime95 for several years, as many of you, I didn't find one prime, that makes me a little disappointed. At the same time, I do some research on Fibonacci prime, it seems a little easier to find one prime or PRP. There are 15 PRP and 34 primes , 49 totally until now. Could someone set up a project for Fibonacci prime like GIMPS?
2017-10-25, 10:46   #2
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

2·5·839 Posts

Quote:
 Originally Posted by Shen I have run prime95 for several years, as many of you, I didn't find one prime, that makes me a little disappointed. At the same time, I do some research on Fibonacci prime, it seems a little easier to find one prime or PRP. There are 15 PRP and 34 primes , 49 totally until now. Could someone set up a project for Fibonacci prime like GIMPS?
you already can find they must be in specific positions, when done mod 6 the fibonacci sequence is 0,1,1,2,3,5,2,1,3,4,1,5,0,5,5,4,3,1,4,5,3,2,5,1,0,1,1,2,... repeats. So, the indexes that could be primes greater than 3 are 1,2,5,7,10,11,13,14,17,19,22,23 mod 24.

2017-10-25, 13:50   #3
Dr Sardonicus

Feb 2017
Nowhere

170616 Posts

Quote:
 Originally Posted by science_man_88 you already can find they must be in specific positions, when done mod 6 the fibonacci sequence is 0,1,1,2,3,5,2,1,3,4,1,5,0,5,5,4,3,1,4,5,3,2,5,1,0,1,1,2,... repeats. So, the indexes that could be primes greater than 3 are 1,2,5,7,10,11,13,14,17,19,22,23 mod 24.
Since

Fa | Fab,

Fa > 1 for a > 2,

F2k = Fk*Lk, and Lk > 1 for k > 1,

it is clear that Fn can be prime only if n = 4, or if n is prime.

I did find a page of Possible Fibonacci Primes listing some large Fibonacci PRP's, but it hasn't been updated in 11 years...

2017-10-25, 14:13   #4
paulunderwood

Sep 2002
Database er0rr

22×1,063 Posts

Quote:
 Originally Posted by Dr Sardonicus I did find a page of Possible Fibonacci Primes listing some large Fibonacci PRP's, but it hasn't been updated in 11 years...
This extends that list: http://www.primenumbers.net/prptop/s...&action=Search

 2017-10-25, 15:35 #5 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 11001001101102 Posts The problem is that Fibonacci numbers aren't the right shape for group-theoretic primality proofs, and nobody's seriously interested in finding large PRPs.
2017-10-25, 15:39   #6
chris2be8

Sep 2009

26·37 Posts

Quote:
 Originally Posted by Dr Sardonicus I did find a page of Possible Fibonacci Primes listing some large Fibonacci PRP's, but it hasn't been updated in 11 years...
Fibonacci (104911) is prime, see http://factordb.com/index.php?query=I%28104911%29 . The other 3 PRPs listed are still PRP in factordb.

Chris

2017-10-25, 20:59   #7
Dr Sardonicus

Feb 2017
Nowhere

2×7×421 Posts

Quote:
 Originally Posted by fivemack The problem is that Fibonacci numbers aren't the right shape for group-theoretic primality proofs, and nobody's seriously interested in finding large PRPs.
People are, however, actively working on composite factors of Fibonacci and Lucas numbers that are, perhaps barely, within the range of present factoring methods.

See, e,g, posts 2201 and 2205 to the thread NFS@Home.

 Similar Threads Thread Thread Starter Forum Replies Last Post George M Lounge 20 2018-01-03 16:04 sweety439 sweety439 17 2017-06-13 03:49 serge2k Homework Help 1 2010-03-25 02:24 robert44444uk Math 3 2007-05-19 07:15 GP2 Software 10 2003-12-09 20:41

All times are UTC. The time now is 04:47.

Thu Aug 11 04:47:18 UTC 2022 up 34 days, 23:34, 2 users, load averages: 1.29, 1.42, 1.71

Copyright ©2000 - 2022, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎𝜍 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔