Erdős Problem Computational Experiments

Computational solvers and experimental results for open Erdős problems.

Author: Kenneth A. Mendoza (ORCID 0009-0000-9475-5938)

Experiments

Problem	Script	Prize	Key Finding
#86 C4-free hypercube	scripts/erdos-86/	$100	Ratio ex(Q_n,C4)/e(Q_n) trends toward 1/2
#123 d-completeness	scripts/erdos-123/	$250	All coprime triples with 2 are d-complete to N=10000
#161 Discrepancy jumps	scripts/erdos-161/	$500	F^(2)(n,α) is a step function with universal jump at α=1/3
#30 Sidon sets	scripts/erdos-30/	$1,000	Greedy Sidon, Singer construction, WalkSAT for W(k) in Rust

Results

All results in results/ as JSON with SHA-256 checksums.

Lean 4 Proofs

Formal proofs are in the companion repo: MendozaLab/erdos-lean4

Citation

@misc{mendoza2026erdos-experiments,
  author = {Mendoza, Kenneth A.},
  title = {Computational Experiments for Erdős Problems},
  year = {2026},
  url = {https://github.com/MendozaLab/erdos-experiments},
  note = {ORCID: 0009-0000-9475-5938}
}

License

Apache 2.0