Dubner's conjecture

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 $p$ is a twin member if at least one of $p-2$ and $p+2$ is prime. The two chosen summands need not come from the same twin pair and need not be distinct.

Statement recorded in the supplied source.

For every even integer $N>4208$, do there exist primes $p,q$ with $N=p+q$ such that each of $p$ and $q$ is a twin member? [S2]

Short English statement

Can every even integer above four thousand two hundred eight be expressed as a sum of two primes, each belonging to some twin-prime pair?

Sources

• S1 ULAM.AI and the UnsolvedMath Contributors, UnsolvedMath: A Curated Collection of Open Mathematics Problems, record 9400120 (AMR-093-0120). CC BY 4.0. https://huggingface.co/datasets/ulamai/UnsolvedMath.
• S2 Tushar Pandey, An intermediate conjecture between Goldbach and Dubner: every even number is the sum of a prime and a twin prime, arXiv:2608.02381v2 (2026) Introduction, p. 1, definition of twin members and Dubner conjecture. https://arxiv.org/pdf/2608.02381.
• S3 Wikipedia contributors, List of unsolved problems in mathematics, revision 1366636767 (2026) Number theory, Dubner's conjecture. https://en.wikipedia.org/w/index.php?title=List_of_unsolved_problems_in_mathematics&oldid=1366636767#Number_theory.