Primenumdiso

A professional tool application focused on the distribution of prime numbers and the verification of number theory conjectures, aimed at helping mathematics enthusiasts, students, and researchers intuitively explore the deep laws of prime numbers. The application is based on Hardy Littlewood k tuple conjecture, Dirichlet number theorem, twin prime number rule, Chebyshev function and theta function and other classical number theory fields. Each module provides real-time calculation, visual charts and theoretical explanations. The Prime Constellations module presents k-tuple prime number patterns through visualized constellation diagrams; The Arithmetic Progression module analyzes the distribution density of prime numbers under specified moduli and residues; The Prime Gap module tracks the spacing pattern between adjacent prime numbers; The Cram é r model and Riemann Zeta function module delve into the core issues of error analysis and prime number theorem. The Riemann Hypothesis analysis module uses interactive charts to compare the approximation accuracy of π (x), Li (x), and x/log x. Users can adjust the confidence interval and choose whether to calculate the upper bound of the error based on the Riemann hypothesis.