GoldbachX Engine

Operator-grade verification engine for Goldbach’s Conjecture — even-number decomposition, prime-sum analysis, and counterexample searching across extremely large ranges.

Test Decompositions View Benchmarks Research Data

Findings — RiemannX

Representative outputs and diagnostics from RiemannX engine.

Finding 1

Zeros of the zeta function show symmetric distribution along the critical line.

Fig. 1 — Riemann zeta zeros visualization.

Core Engine Capabilities

Verification Tests

Tests even numbers for prime decomposition and identifies patterns across large ranges.

Even number prime decomposition
Verification of known bounds
Pattern analysis for prime sums
Distribution uniformity checks
Algorithmic counterexample search

Performance Metrics

Optimized for high-speed, memory-efficient, and distributed computation.

200M+ numbers analyzed per second
Maximum tested range: 10^18+
Memory-efficient prime storage
Parallel decomposition computation
Distributed verification architecture

Research Applications

Supports exploration of prime sums, gaps, and conjecture variants.

Prime sum frequency analysis
Gap and density studies
Conjecture variant exploration
Educational number theory visualizations
Cross-conjecture correlation studies