Tupleconject

A professional level analytical tool that deeply focuses on the distribution patterns of prime numbers and verifies classical number theory conjectures. The applications cover core areas such as Chebyshev θ (x) and ψ (x) functions, Hardy Littlewood k-tuple conjecture, prime interval distribution, twin prime law, Riemann Zeta function zero point error analysis, and Cram é r prime model. Each analysis module integrates input validation, visual charts, and theoretical documentation, and supports real-time numerical calculations within the range of 1000 to 10000000. Users can observe the degree of approximation between θ (x) and x · log x through histograms, visually identify prime number patterns through k-tuple constellation diagrams, compare the accuracy decay of prime number theorems through π (x)/Li (x) curves, adjust confidence intervals using the Riemann Hypothesis module, and dynamically choose whether to derive error bounds based on Riemann hypothesis.