A Fibonacci prime is a Fibonacci number prime
number . Every prime must have a prime
index prime
The first few (possibly probable ) prime Fibonacci numbers A005478 ),
corresponding to indices A001605 ).
(Note that Gardner's statement that prime , which it must be for
term index digits discoverer status 24 5387 1126 https://t5k.org/primes/page.php?id=51129 25 9311 1946 https://t5k.org/primes/page.php?id=37470 26 9677 2023 https://t5k.org/primes/page.php?id=35537 27 14431 3016 https://t5k.org/primes/page.php?id=29537 28 25561 5342 https://t5k.org/primes/page.php?id=24043 29 30757 6428 https://t5k.org/primes/page.php?id=22126 30 35999 7523 https://t5k.org/primes/page.php?id=20235 31 37511 7839 https://t5k.org/primes/page.php?id=74907 32 50833 10624 https://t5k.org/primes/page.php?id=75849 33 81839 17103 https://t5k.org/primes/page.php?id=11084 34 104911 21925 B. de Water, Apr. 2001 https://t5k.org/primes/page.php?id=120463 35 130021 27173 D. Fox, Dec. 2001 https://t5k.org/primes/page.php?id=132290 36 148091 30949 T. D. Noe, Feb. 12, 2003 https://t5k.org/primes/page.php?id=132721 37 201107 42029 H. Lifchitz, Feb. 2003 https://t5k.org/primes/page.php?id=136445 38 397379 83047 H. Lifchitz, Aug. 2003 39 433781 90655 H. Lifchitz, Sep. 2003 40 590041 123311 H. Lifchitz, Jan. 2005 41 593689 124074 H. Lifchitz, Jan. 2005 42 604711 126377 H. Lifchitz, Feb. 2005 43 931517 194676 H. Lifchitz, Sep. 2008 44 1049897 219416 H. Lifchitz, Oct. 2008 45 1285607 268676 H. Lifchitz, Nov. 2008 46 1636007 341905 H. Lifchitz, Mar. 2009 47 1803059 376817 H. Lifchitz, Jun. 2009 48 1968721 411439 H. Lifchitz, Nov. 2009 49 2904353 606974 H. Lifchitz, Jul. 2014 50 3244369 678033 H. Lifchitz, Sep. 2017
Crandall and Pomerance (2005, p. 189) describe the proof that
It is not known if there are an infinite number of Fibonacci
primes.
See also Fibonacci Number ,
Integer Sequence Primes ,
Lucas Prime ,
Prime
Number ,
Probable Prime
Explore with Wolfram|Alpha
References Brillhart, J.; Montgomery, P. L.; and Silverman, R. D. "Tables of Fibonacci and Lucas Factorizations." Math. Comput. 50 ,
251-260, 1988. Broadhurst, D. "Fibonacci(81839) is prime."
22 Apr 2001. https://listserv.nodak.edu/cgi-bin/wa.exe?A2=ind0104&L=nmbrthry&P=R1807&D=0 . Crandall,
R. and Pomerance, C. Prime
Numbers: A Computational Perspective, 2nd ed. Dubner, H. and Keller, W. "New Fibonacci and Lucas Primes."
Math. Comput. 68 , 417-427 and S1-S12, 1999. Gardner, M.
Mathematical
Circus: More Puzzles, Games, Paradoxes and Other Mathematical Entertainments from
Scientific American. Lifchitz, H. and
Lifchitz, R. "PRP Top Records: Search for F(n)." http://www.primenumbers.net/prptop/searchform.php?form=F(n) . Noe,
T. D. and Vos Post, J. "Primes in Fibonacci n-step and Lucas n-step Sequences."
J. Integer Seq. 8 , Article 05.4.4., 2005. Pickover, C. A.
Mazes
for the Mind: Computers and the Unexpected. Pickover, C. A. A
Passion for Mathematics. PrimePages.
"PrimePage Primes: Fibonacci Number." https://t5k.org/top20/page.php?id=39 . PrimePages.
"The Prime Glossary: Fibonacci Prime." https://t5k.org/glossary/page.php?sort=FibonacciPrime . Ribenboim,
P. The
Little Book of Big Primes. Referenced
on Wolfram|Alpha Fibonacci Prime
Cite this as:
Weisstein, Eric W. "Fibonacci Prime."
From MathWorld https://mathworld.wolfram.com/FibonacciPrime.html
Subject classifications More... Less...
that is also a prime
number. Every 
that is prime must have a prime
index 
,
with the exception of 
.
However, the converse is not true (i.e., not every prime index 
gives a prime 
).
are 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, ... (OEIS A005478),
corresponding to indices 
, 4, 5, 7, 11, 13, 17, 23, 29, 43, 47, 83, 131, 137, 359,
431, 433, 449, 509, 569, 571, 2971, 4723, 5387, ... (OEIS A001605).
(Note that Gardner's statement that 
is prime (Gardner 1979, p. 161) is incorrect, especially
since 531 is not even prime, which it must be for
to be prime.) The following table
summarizes Fibonacci (possibly probable) primes with index 
.
is prime using the Coppersmith-Howgrave-Graham method.
