Open computational mathematics. AI-audited, not peer-reviewed. All code and data open for independent verification.
bigcompute.science
Experimental results from heavy computation.
Open computational results from GPU-accelerated mathematical experiments.
Human-readable. Agent-consumable. Literature-audited.
Experiments
Erdos-Straus Conjecture: Solution Counting to 10^8 on B200
Count solutions f(p) to 4/p = 1/x + 1/y + 1/z for all primes p up to 10^8. Conjecture verified to 10^14 (Swett/Elsholtz-Tao), but solution counts f(p) and their distribution are un...
Prime Convergents: GPU Verification of the Erdos-Mahler Bound
GPU verification of the Erdos-Mahler bound on greatest prime factors of CF convergents. 10M random CFs verified: bound holds 100%, worst-case ratio 4.87, constant 50 is very conser...
Zaremba Density: Exception Sets and Phase Transitions on 8x B200
65 GPU density computations across digit sets and ranges to 10^12. Audit revision: the data support stable candidate exception sets, not proved finite/closed sets. Completed 10^11 ...
Class Numbers of Real Quadratic Fields: Extending Tables to 10^13 on 8× B200
Class numbers h(d) for 30 billion real quadratic fields across [10^9, 10^11]. h=1 rate falls monotonically: 42% → 17% → 15.4%. Goes to 0, not 75% (genus theory). Odd-part convergen...
Kronecker Coefficients: S20, S30, S40 on 8× B200
Complete Kronecker coefficient tables for S_20 (32.7M nonzero, 3.7s) and S_30 (26.4B nonzero, 7.4 min) on NVIDIA B200. Complete S_40 character table (37,338 partitions, 1.394B entr...
Ramanujan Machine: GPU-Accelerated Discovery of Continued Fraction Formulas
586 billion equal-degree polynomial CFs evaluated through degree 8 — zero new transcendental formulas. 7,030 double-precision false positives all disproven at 100-digit precision. ...
Ramsey R(5,5): Exhaustive Extension Search on 8x B200
Strongest computational evidence that R(5,5) = 43. All 656 known K42 colorings UNSAT. Structural attack toward R(5,5) <= 45 in progress.
Flint Hills Series: Partial Sums to 10^{10} with Spike Decomposition
Partial sums of the Flint Hills series computed to 10 billion terms with quad-double precision. Spike decomposition reveals 91% of the sum comes from 19 convergent spikes.
Hausdorff Dimension Spectrum: All Subsets of {1,...,20}
Hausdorff dimension computed for every non-empty subset of {1,...,20} — 1,048,575 subsets in 4,343 seconds on RTX 5090. Validated against Jenkinson-Pollicott.
Lyapunov Exponent Spectrum: All Subsets of {1,...,20}
Lyapunov exponents for all 1,048,575 non-empty subsets of {1,...,20}, computed in 305 seconds on RTX 5090. Twin dataset with the Hausdorff dimension spectrum.
Minkowski ?(x) Singularity Spectrum
Multifractal singularity spectrum f(alpha) of the Minkowski question-mark function, computed via weighted transfer operator in 4.9 seconds on RTX 5090.
Zaremba's Conjecture: 210 Billion Verified in 116 Minutes on 8× NVIDIA B200
GPU verification of Zaremba's Conjecture for all d up to 210 billion (zero failures), plus spectral gap analysis, transitivity proof, and LLM theorem proving in Lean 4.
Transfer Operator for Zaremba's Conjecture: Hausdorff Dimension to 15 Digits
Hausdorff dimension of E_5 computed to 15 digits (0.836829443681208). Spectral gaps for 1,214 square-free moduli, all positive. Property (tau) computationally supported (not proven...
Start Exploring
Every experiment on this site has CUDA source code, reproduction commands, and open datasets. Connect an AI agent to explore the data, or dive in yourself.
MCP Server
Connect Claude, Cursor, or any MCP client to query experiments, datasets, and CUDA kernels directly.
mcp.bigcompute.science/mcp Claude Code
claude mcp add bigcompute \ --transport sse \ https://mcp.bigcompute.science/mcp
Cursor / VS Code
{"mcpServers": {"bigcompute": {"url": "https://mcp.bigcompute.science/mcp"}}} Claude Desktop
// Add to claude_desktop_config.json
{"mcpServers": {"bigcompute": {"url": "https://mcp.bigcompute.science/mcp"}}} Browse the Data
All datasets are on Hugging Face — free to download, no account needed.
Hugging Face DatasetsRun the Code
Clone the repo. Every experiment has a CUDA kernel, compile command, and test case.
GitHub RepositoryNo B200 required — most kernels run on any CUDA GPU.
Contribute
Run computations on your hardware. Upload to your own HF repo. Submit a PR.
AGENTS.mdOpen problems that need GPU time listed inside.
Research Companion Model
Convergent-7B
A QLoRA fine-tuned research companion for computational number theory. Trained on 5,729 examples from this project's experiments, CUDA kernels, and synthetic mathematical reasoning. Built on Qwen2.5-7B-Instruct, trained on an RTX 5090.
- Number theory reasoning — Zaremba, Ramsey, Kronecker, Cohen-Lenstra, Hausdorff dimensions
- CUDA kernel generation and optimization (sm_86 → sm_120)
- Agentic tool calling via the bigcompute.science MCP server
git clone https://github.com/cahlen/convergent && cd convergent
pip install -r requirements.txt
./convergent agent -q "What are the Zaremba exceptions for 3?"What is this?
GPU-accelerated exploration of open conjectures — Zaremba, Ramsey R(5,5), Cohen-Lenstra, Kronecker coefficients, and more. A Guerrilla Mathematics™ project. Human-AI collaborative. Not peer-reviewed. All data open.
Every experiment includes exact hardware specs, method, raw data, and commands to reproduce. Content is designed for both human readers and AI agents — see /llms.txt.