Math-4215 · mathematics · Number theory

Are there infinitely many prime quadruplets

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.

A prime quadruplet is a tuple $(p,p+2,p+6,p+8)$ whose four entries are prime.

Statement recorded in the supplied source.

Are there infinitely many primes $p$ for which all four entries of this tuple are prime? [S2]

Short English statement

Do infinitely many primes start the four-prime pattern with offsets zero, two, six and eight?

Sources

S1 ULAM.AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 9400158 (AMR-093-0158). 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 prime quadruplets. 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, A007530: Prime quadruples: numbers k such that k, k+2, k+6, k+8 are all prime., official data snapshot 693b5499c9d2 (2026) Name, definition and comments. https://raw.githubusercontent.com/oeis/oeisdata/693b5499c9d248f570dd2d979e8bd1d7eecf689b/seq/A007/A007530.seq.

Catalogue entry

Statement licence: CC-BY-4.0 · Source file

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Record details

Subjects: Number theory
Collection: Top Open Problems
Mathematics rank: 4215
UnsolvedMath: Catalogue entry