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Ostmann’s inverse Goldbach conjecture

A decomposition into two nontrivial summand sets would describe the eventual prime set additively.

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Understanding the problem

Read the background

A decomposition into two nontrivial summand sets would describe the eventual prime set additively. The inverse Goldbach question asks whether such a decomposition can exist.

The statement permits only finitely many changes to the prime set. It is distinct from the usual Goldbach conjecture about expressing even integers as sums of primes.

Why it matters

If correct, resolves the stated asymptotic additive-indecomposability question for the primes.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • The statement permits only finitely many changes to the prime set. It is distinct from the usual Goldbach conjecture about expressing even integers as sums of primes.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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