Erdős Problems

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The Mathematical Bounty Board

Erdős Prize Problems

"A mathematician is a device for turning coffee into theorems." Unsolved problems with cash rewards, awaiting bold minds.

All Open Prize Erdős Problems

59 open problems • $37,670 total • Ready for AI
Prize # Problem
Problem Comments
Solver
Gemini-3-Pro-Preview Gemini-3-Pro Deepthink GPT-5.2 Pro Extended thinking
Evolver
Synth Data
Formalizer
Lean
Evaluator
Eval of G3P by itself Eval of Deepthink by GPT-5.2 Eval of GPT-5.2 by Deepthink Human Eval
$10,000 142 Asymptotic formula for r_k(N) - arithmetic progression-free sets NANANANANANANANANA
$5,000 3 Arithmetic progressions in sets with divergent reciprocal sum NANANANANANANANANA
$1,00020 Sunflower Conjecture - k-sunflowers in uniform set families NANANANANANANANANA
$1,00030 Sidon Sets - maximum size h(N) bounds NANANANANANANANANA
$1,00064 Power-of-two cycles in graphs with min degree ≥3 NANANANANANANANANA
$1,000592 Partition ordinals - Ramsey properties of countable ordinals NANANANANANANANANA
$1,000625 Cochromatic number - χ(G) - ζ(G) growth for random graphs NANANANANANANANANA
$1,000687 Jacobsthal function Y(x) bounds NANANANANANANANANA
$5001 Subset sums distinctness - N ≫ 2^n conjecture NANANANANANANANANA
$50028 Sumset density - if A+A cofinite then limsup 1_A∗1_A(n)=∞ NANANANANANANANANA
$50039 Infinite Sidon set growth rate N^{1/2-ε} NANANANANANANANANA
$50040 Generalized sumset density with growth function g(N) NANANANANANANANANA
$50041 Triple sum distinctness - liminf |A∩{1,...,N}|/N^{1/3}=0? NANANANANANANANANA
$50066 Convolution limit - does lim 1_A∗1_A(n)/log n exist and ≠0? NANANANANANANANANA
$50074 Infinite chromatic graphs with locally bipartite subgraphs NANANANANANANANANA
$50089Distinct distances - ≫ n/√(log n) distances? AI EVOLVINGViewNANANANANANANANANA
$50090Unit distance problem - max pairs at distance 1 AI EVOLVINGViewNANANANANANANANANA
$50092 Equidistant points - is f(n) ≤ n^{o(1)}? NANANANANANANANANA
$500107 Happy ending problem - f(n)=2^{n-2}+1 for convex polygons? NANANANANANANANANA
$500138 van der Waerden numbers - prove W(k)^{1/k}→∞ NANANANANANANANANA
$500143 Sparse sets with |kx-y|≥1 constraint NANANANANANANANANA
$500146 Bipartite r-degenerate Turán exponent 2-1/r NANANANANANANANANA
$500161 Ramsey discontinuity in hypergraph colorings NANANANANANANANANA
$500500 3-uniform hypergraph Turán number ex_3(n,K_4^3) NANANANANANANANANA
$500564 3-uniform hypergraph Ramsey R_3(n) ≥ 2^{2^{cn}}? NANANANANANANANANA
$500593 High chromatic 3-uniform hypergraph characterization NANANANANANANANANA
$500601 Ordinal Ramsey - infinite paths or independent sets NANANANANANANANANA
$500604 Pinned distance problem - ≫ n^{1-o(1)} distances? NANANANANANANANANA
$500712 Hypergraph Turán density ex_r(n,K_k^r)/C(n,r) NANANANANANANANANA
$500713 Bipartite Turán exponent rationality NANANANANANANANANA
$5001135 Collatz Conjecture - f^{(k)}(m)=1 for all m? NANANANANANANANANA
$25018 Practical numbers and divisor sums h(m) bounds NANANANANANANANANA
$25050 Density of integers where φ(n)<cn is purely singular NANANANANANANANANA
$25052 Sum-product problem - max(|A+A|, |AA|) bounds NANANANANANANANANA
$25077 Find lim R(k)^{1/k} for Ramsey numbers NANANANANANANANANA
$250114 Polynomial with max curve length when p(z)=z^n-1 NANANANANANANANANA
$250123 d-completeness of {a^k b^l c^m} for coprime a,b,c NANANANANANANANANA
$250126 Distinct prime factors in products of pairwise sums NANANANANANANANANA
$250128 Dense induced subgraphs must contain triangles NANANANANANANANANA
$250165 Asymptotic formula for R(3,k) NANANANANANANANANA
$250183 Multicolor Ramsey limit R(3;k)^{1/k} NANANANANANANANANA
$250595 Infinite K₄-free graph not union of countable triangle-free NANANANANANANANANA
$250671 Lagrange interpolation convergence despite unbounded constants NANANANANANANANANA
$10043 Two Sidon sets with disjoint difference sets NANANANANANANANANA
$10078 Constructive proof that R(k) > C^k NANANANANANANANANA
$10086 C₄-free subgraphs of hypercube Q_n NANANANANANANANANA
$10097 Convex polygon vertex equidistance property NANANANANANANANANA
$10099 Unit distance sets containing equilateral triangles NANANANANANANANANA
$100101 Lines through exactly four points among n points NANANANANANANANANA
$100104 Unit circles through three or more points NANANANANANANANANA
$100119 Polynomial maximum on unit circle NANANANANANANANANA
$100120 Measure avoiding scaled copies of infinite sets NANANANANANANANANA
$100132 Multiple distances in point configurations NANANANANANANANANA
$100241 Maximum sets with distinct triple sums NANANANANANANANANA
$100552 Ramsey number R(C₄, S_n) bounds NANANANANANANANANA
$100588 Lines through k points in point configurations NANANANANANANANANA
$100708 Products and divisibility in integer intervals NANANANANANANANANA
$1001029 Ramsey number growth rate R(k)/(k·2^{k/2}) NANANANANANANANANA
$78710 Minimal f(n) for divisibility k|a_k in interval NANANANANANANANANA
$78711 Related divisibility function f(n,m) NANANANANANANANANA
$5032 Additive complement to primes with minimal size NANANANANANANANANA
$50661 Distinct distances between two sets minimization NANANANANANANANANA
$44647 Robin's inequality type - τ(n) divisor count NANANANANANANANANA
$257 Distinct odd covering system existence NANANANANANANANANA
$25633 Triangles into square number of congruent pieces NANANANANANANANANA
$25634 Find all n for triangle into n congruent triangles NANANANANANANANANA
$25825 Abundancy index bounds for weird numbers NANANANANANANANANA
$10470 Existence of odd weird numbers NANANANANANANANANA
$101052 Finiteness of unitary perfect numbers NANANANANANANANANA
$101071 Maximal disjoint unit line segments in unit square NANANANANANANANANA

AI progress

18+ AI solutions • 30+ partial • 4 under evolution • 40+ formalizations

Full Solutions by AI

SOLVED ERD-205

Problem 205

Complete Lean formalization achieved.

Aristotle
ChatGPT 5.2
📅 Jan 10, 2026
SOLVED ERD-281

Problem 281

Complete via locating Davenport & Erdős (1936) + Rogers theorem.

GPT 5.2 Pro
📅 Jan 17, 2026
SOLVED ERD-333

Problem 333

Full Lean proof matching Erdős & Newman (1977).

ChatGPT 5.2
Claude Opus 4.5
📅 Dec 25, 2025
SOLVED ERD-347

Problem 347

Human-AI collaboration with Terence Tao, van Doorn, Naskrecki.

GPT Codex
Aristotle
📅 Oct 2025–Jan 2026
SOLVED ERD-397

Problem 397

Complete Lean formalization; related to Elkies (2013).

Aristotle
ChatGPT 5.2
📅 Jan 10, 2026
SOLVED ERD-401

Problem 401

Collaboration: Alexeev, Barreto, Leeham, Sothanaphan.

Aristotle
ChatGPT 5.2
📅 Jan 10-11, 2026
SOLVED ERD-652

Problem 652

Complete by applying existing theorem.

GPT 5.2 Pro
📅 Jan 17, 2026
SOLVED ERD-659

Problem 659

Full Lean solution by Benjamin Grayzel.

Gemini 3.0
📅 Jan 13, 2026
SOLVED ERD-728

Problem 728

Complete proof; surpassed Pomerance (2014) partial.

Aristotle
ChatGPT 5.2
📅 Jan 6, 2026
SOLVED ERD-729

Problem 729

Full Lean solution building on problem 728.

Aristotle
ChatGPT 5.2
📅 Jan 8-10, 2026
SOLVED ERD-848

Problem 848

By Mehtaab Sawhney & Mark Sellke.

GPT-5
📅 Oct-Nov 2025
SOLVED ERD-871

Problem 871

Upgraded Erdős & Nathanson (1989) to complete Lean proof.

Claude Opus 4.5
Gemini 3 Pro
📅 Jan 5, 2026
SOLVED ERD-897

Problem 897

Full Lean proof matching Wirsing (1981).

Aristotle
Archivara
📅 Dec 26, 2025
SOLVED ERD-958

Problem 958

New Lean proof; matched Clemen, Dumitrescu, Liu (2025).

Aristotle
📅 Dec 27, 2025
SOLVED ERD-1007

Problem 1007

Complete Lean proof; related to House (2013).

Aristotle
📅 Jan 19, 2026
SOLVED ERD-1026

Problem 1026

Collaboration: Alexeev, Cambie, Tao, Wu. Matched Tidor, Wang, Yang (2016).

ChatGPT
Aristotle
AlphaEvolve
📅 Dec 8, 2025
SOLVED ERD-1043

Problem 1043

Complete Lean proof; matched Pommerenke (1961).

Aristotle
📅 Dec 28, 2025
SOLVED ERD-1047

Problem 1047

New Lean proof of Goodman (1966) result.

Aristotle
📅 Jan 21, 2026