OpenAI research collection · 1 manuscript · Source checked 2026-10-19
Could the primes be made by adding every member of one set of nonnegative integers to every member of another? The paper claims this is impossible when both sets contain at least two numbers, even after changing finitely many primes.
This is the inverse Goldbach conjecture, which is different from the famous question about writing even numbers as sums of two primes.
Proves that no finite modification of the primes can be written as A+B with A,B⊆\mathbb Z_{\ge0} each containing at least two elements. This resolves Ostmann's inverse Goldbach conjecture on additive indecomposability.
Short excerpts below come from OpenAI's abstracts. The full abstract and original PDF preserve the paper's precise scope.
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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