Math-4207 · mathematics · Number theory

Are there infinitely many Fibonacci primes

Status Open · unsolvedmath.comLLM status Open unverified

Statement

Definitions and mathematical statement

Shared notation.

$\mathbb N=\{1,2,\ldots\}$, and $\mathbb Z,\mathbb Q,\mathbb R,\mathbb C$ denote the integers, rationals, reals and complex numbers. Any other conventions are specified locally.

Define Fibonacci numbers by $F_0=0$, $F_1=1$ and $F_{n+2}=F_{n+1}+F_n$ for $n\ge0$. A Fibonacci prime is a prime value $F_n$.

Statement recorded in the supplied source.

Are there infinitely many integers $n\ge0$ for which $F_n$ is prime? [S2]

Short English statement

Do infinitely many Fibonacci numbers take prime values?

Sources

S1 ULAM.AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 9400149 (AMR-093-0149). CC BY 4.0. https://huggingface.co/datasets/ulamai/UnsolvedMath.
S2 Wikipedia contributors, List of unsolved problems in mathematics, revision 1366636767 (2026) Number theory, Are there infinitely many Fibonacci primes. https://en.wikipedia.org/w/index.php?title=List_of_unsolved_problems_in_mathematics&oldid=1366636767#Number_theory.
S3 OEIS Foundation and contributors, The On-Line Encyclopedia of Integer Sequences, A000045: Fibonacci numbers: F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1., official data snapshot 693b5499c9d2 (2026) Name, definition and comments. https://raw.githubusercontent.com/oeis/oeisdata/693b5499c9d248f570dd2d979e8bd1d7eecf689b/seq/A000/A000045.seq.
S4 OEIS Foundation and contributors, The On-Line Encyclopedia of Integer Sequences, A001605: Indices of prime Fibonacci numbers., official data snapshot 693b5499c9d2 (2026) Name, definition and comments. https://raw.githubusercontent.com/oeis/oeisdata/693b5499c9d248f570dd2d979e8bd1d7eecf689b/seq/A001/A001605.seq.

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Record details

Subjects: Number theory
Collection: Top Open Problems
Mathematics rank: 4207
UnsolvedMath: Catalogue entry