Sieve: Prime Number Explorer

Unlock the mysteries of number theory with Sieve, your comprehensive companion for exploring the world of prime numbers. Whether you are a student, an educator, or a math enthusiast, this app provides a powerful set of tools to visualize and analyze the building blocks of mathematics.
Key Features:
• The Sieve of Eratosthenes: Discover primes within any range up to 100,000. Our efficient implementation allows you to generate lists of primes instantly and examine their distribution density.
• Prime Factorization: Decompose any positive integer into its prime components. View results in clear multiplication strings or professional exponent notation for deep numerical analysis.
• The Ulam Spiral: Visualize the hidden patterns of mathematics. Our dynamic spiral plots primes in a coordinate system, revealing the fascinating diagonal clusters that have intrigued mathematicians for decades.
• Goldbach Conjecture: Put one of the oldest unsolved problems to the test. Input even numbers to find the prime pairs that sum together to create them.
• Prime Gap Analysis: Examine the "silence" between primes with our interactive gap histogram. Understand how the distance between prime numbers changes as they grow larger.
• Numerical Statistics: Get instant data on prime density, average gaps, and largest gaps within your chosen ranges, alongside approximations based on the Prime Number Theorem.
• Educational Knowledge Hub: Learn the history and logic behind every tool. Read curated summaries about the Fundamental Theorem of Arithmetic and the ancient algorithms that shaped number theory.
Designed for Learning: Sieve focuses on a clean, intuitive interface that puts the numbers front and center. With smooth animations, interactive charts, and the ability to copy results to your clipboard, it is the perfect tool for classroom demonstrations or personal study.
Explore the beauty of primes and deepen your understanding of number theory today with Sieve.