Partitions
Counts prime pairs `(p, q)` for even inputs where `p + q = n` and `p <= q`.
GoldbachX
GoldbachX counts prime-pair decompositions for even numbers and helps rank sparse candidate families for bounded counterexample search.
Browser Decomposer
Enter an even number >= 4, capped at 100,000, to inspect prime-pair decompositions and nearby partition counts in your browser.
Prime-Pair Positions
p <= n / 2Nearby Counts
even inputsVerified Run Artifact
Metadata-complete run output for the public demo. Verified here means reproducible metadata and bounded inputs, not a theorem.
What It Computes
Deficits
Compares observed partition counts with Hardy-Littlewood-style predictions for ranking.
Families
Explores sparse residue and factor families as candidates for closer inspection.
A decomposition for one input is evidence about that input only. It is not a proof of Goldbach's conjecture.