Finding 1
Zeros of the zeta function show symmetric distribution along the critical line.
RiemannX Engine
Operator-grade verification engine for the Riemann Hypothesis — zero testing, prime-counting validation, and functional symmetry analysis across massive computational ranges.
Findings — RiemannX
Representative outputs and diagnostics from RiemannX engine.
Core Engine Capabilities
Verification Tests
Ensures non-trivial zeros lie on the critical line and analyzes spacing patterns.
- Non-trivial zero identification
- Critical line validation
- Zero spacing statistics
- Dirichlet L-function testing
- High-precision floating-point validation
Performance Metrics
Optimized for high-speed, memory-efficient, distributed zero computations.
- 50M+ zeros computed per second
- Maximum tested imaginary parts: 10^12+
- Parallelized zero detection
- Memory-efficient caching
- Distributed computation supported
Research Applications
Supports exploration of prime-counting functions and zero distributions in analytic number theory.
- Prime-counting approximation verification
- Zero spacing statistical analysis
- Analytic number theory support
- Educational visualizations
- Cross-conjecture correlation studies