erdos-straus-solver 2.0.0

GPU-accelerated Erdos-Straus conjecture solver with multi-device distributed computing

Erdos-Straus Conjecture Solver

Guinea Pig Trench LLC

Verifies the Erdos-Straus conjecture for all integers n = 2..20,000,000 by finding positive integer decompositions:

4/n = 1/x + 1/y + 1/z    where x <= y <= z

Live Dashboard

Results

1,666,666 hard-residue targets (n mod 24 in {1, 17}) fully solved across n=2..20,000,000. All other residue classes have known parametric families and are trivially solvable.

• Stage 1 (hunter): 1,491,274/1,666,666 solved with 500K step cap (89.5%)
• Stage 2 (leviathan): remaining 175,392 solved with 50M step cap (100%)
• 97.5% of solved nodes have z > 10^14
• Max z found: 22 digits (at n=999,985 in the 1M dataset)
• Total pipeline runtime: ~3.2 hours for 20M range

Scaling behavior

Range	Hard targets	Hunter rate	Leviathan count	Time
n=2..50K	4,166	86.4%	565	24s
n=2..1M	83,332	88.7%	9,381	9.4 min
n=2..20M	1,666,666	89.5%	175,392	3.2h

Architecture

Two-stage pipeline

1. Hunter (Stage 1) — Scans the target range, filtering to only the hard residue classes (n mod 24 in {1, 17}). Uses a 500K global step cap with multiprocessing.

2. Leviathan Autopsy (Stage 2) — Retries unsolved nodes from Stage 1 with a 50M step cap.

Key solver insight

The naive approach iterates over all (x, y) pairs with a single global step budget. For hard cases, the solver would exhaust millions of steps on the y-range of a single x value (typically x = ceil(n/4)) without finding a valid z.

The fix: a per-x y-iteration cap (y_cap_per_x, default 1M). This lets the solver skip to the next x offset when a given x's y-range is unproductive. Solutions are almost always found at x = ceil(n/4) + 1 with very few y-iterations.

Across all leviathans, 86.8% solve at offset 1 (x = ceil(n/4) + 1), with a mean offset of 1.24. This pattern holds from n=2 through n=20,000,000.

Checkpoint system

Results are saved atomically via tempfile.mkstemp() + os.replace(), so checkpoint files are never left in a half-written state. The pipeline resumes cleanly from existing checkpoints.

CSV safety

Integer values exceeding 15 digits are wrapped in ="" format to prevent Excel/Sheets truncation. A pre-tool-use hook enforces this at write time. This is critical — 97.5% of solutions have z values exceeding 10^14.

Files

File	Description
erdos_straus.py	Solver module with pipeline stages
tests/test_solver.py	Test suite (23 tests)
erdos_dashboard.html	Interactive results dashboard
hunter_20M_checkpoint.csv	Stage 1 results for n=2..20M (1,666,666 rows)
leviathan_20M_checkpoint.csv	Stage 2 results for n=2..20M (175,392 rows)
hunter_1M_checkpoint.csv	Stage 1 results for n=2..1M (83,332 rows)
leviathan_1M_checkpoint.csv	Stage 2 results for n=2..1M (9,381 rows)
hunter_checkpoint.csv	Stage 1 results for n=2..50K (4,166 rows)
leviathan_checkpoint.csv	Stage 2 results for n=2..50K (565 rows)
pyproject.toml	pytest configuration

Usage

# Run the full pipeline
python erdos_straus.py

# Run tests
pytest tests/

# Use the solver programmatically
from erdos_straus import solve_single
sol, steps = solve_single(n=1009, step_cap=500_000)

Requirements

• Python 3.10+
• No external dependencies (stdlib only)
• Optional: black (code formatting), pytest (testing)