Ostmann's inverse Goldbach conjecture at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Ostmann's inverse Goldbach conjecture

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	primes, fractions, patience	Levels:	1
Category:	Number theory	Lean version:	YES! ✔
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Ostmann’s inverse Goldbach conjecture. Proves that no finite modification of the primes can be written as $A+B$ with $A,B\subseteq\mathbb Z_{\ge0}$ each containing at least two elements. This resolves Ostmann's inverse Goldbach conjecture on additive indecomposability.

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LEVEL 1 The additive indecomposability of the primes

released 2026-09-24 | 2 theorems · 8 lemmas · 11 proofs · 34,977 words | PLAY LEVEL 1 » (pdf)

We prove Ostmann's inverse Goldbach conjecture: no set differing from the primes by finitely many elements can be written as $A+B$, where A and B are sets of nonnegative integers with at least two elements each.

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