Math-4205 · mathematics · Number theory

Are there infinitely many Cullen 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.

For $n\ge1$ put $C_n=n2^n+1$. A Cullen prime is a prime value among these integers.

Statement recorded in the supplied source.

Is $C_n$ prime for infinitely many $n\ge1$? [S2]

Short English statement

Are infinitely many Cullen numbers prime?

Sources

S1 ULAM.AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 9400147 (AMR-093-0147). 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 Cullen 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, A050920: Cullen primes: primes of the form n*2^n+1., official data snapshot 693b5499c9d2 (2026) Name, definition and comments. https://raw.githubusercontent.com/oeis/oeisdata/693b5499c9d248f570dd2d979e8bd1d7eecf689b/seq/A050/A050920.seq.

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Statement licence: CC-BY-4.0 · Source file

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Record details

Subjects: Number theory
Collection: Top Open Problems
Mathematics rank: 4205
UnsolvedMath: Catalogue entry