Related Erdős problems
Where this work sits among the numbered problems it is near. Statuses are as listed on the individual problem pages (68, 249, 257, 1041, 1049, 69, 250, 258) in July 2026; none of the external results is re-proved in this repository.
Bounded status route
The external catalogue status and the local release status are separate facts. Use the exact local packets before interpreting an analogy:
- #249 target:
python3 scripts/query_corpus.py --open remaining_open.erdos_249_irrationality - #257 target:
python3 scripts/query_corpus.py --open remaining_open.universal_257_all_infinite_supports - #69 neighbour:
python3 scripts/query_corpus.py --claim prime_support_irrationality - #250 neighbour:
python3 scripts/query_corpus.py --claim sigma_transcendence
The first two packets are open; the latter two are
cited only. A solved neighbour, shared transform, or
formalised special case does not advance an open target unless
docs/claims.json::machine_readable_paper.argument_graph
records an advances_open_target edge.
Problem map
| Problem | Catalogue status | Local relation class |
|---|---|---|
#68 ∑_{n≥2} 1/(n!−1) |
open | problem-owned checked reductions and finite evidence |
#249 ∑ φ(n)/2ⁿ |
open | open target |
#257 ∑_{n∈A} 1/(2ⁿ−1) |
open | open target with formalised special cases |
| #1041 short curves in polynomial lemniscates | open | problem-owned dynamical reductions and proof audit |
#1049 ∑ 1/(tⁿ−1), rational
t>1 |
open (rational t) |
integer-base theorem plus problem-owned rational-base obstructions |
#69 ∑ ω(n)/2ⁿ |
solved (Tao–Teräväinen) | cited-only solved neighbour plus formalised identity bridge |
#250 ∑ σ(n)/2ⁿ |
solved (Nesterenko 1996) | cited-only solved neighbour |
#258 ∑ τ(n)/(a₁···aₙ) |
solved | untouched analogy |
Relation in this repository
- #68 — exact factorial-successor and carry frontiers, structural consumers, and a finite denominator exclusion; no irrationality proof.
- #249 — an unconditional denominator exclusion and conditional reductions, no solution.
- #257 — named infinite-support cases and full
support (
A = ℕ), not the universal statement. - #1041 — Newton-flow ray separation and perturbation lemmas are checked; the global topology and metric gluing are open.
- #1049 — the integer-base case
b ≥ 2isirrational_erdosSum_full_support; at rational noninteger bases the public modules check clearing, height-region, and Padé obstructions but no irrationality theorem. - #69 — the prime-support case of #257; only the
identity bridge to
∑_p 1/(2ᵖ−1)is formalised, not the irrationality. - #250 — the ladder neighbour
L(Id); cited, not re-proved. - #258 — not addressed here; the monotone φ/σ sequel is the sibling territory of #249.
The one-line summary: formalised settled special cases, exact structural reductions and scoped no-go theorems across eight indexed open problems, and finite certificates whose quantifiers are stated explicitly. None of the eight open problems is solved here.