Prime Inventor

Mathematical Principles & Theorems

Studies the distribution of prime numbers in the integers. The Sieve of Eratosthenes finds all primes up to \(N\) in \(\mathcal{O}(N \log \log N)\) time by systematically striking composite multiples of each prime \(p \le \sqrt{N}\). Goldbach's Conjecture (1742) asserts that every even integer \(2n > 2\) can be written as the sum of two primes: \(2n = p_1 + p_2\). Twin Prime Conjecture explores infinitely many prime pairs with gap \(p_{k+1} - p_k = 2\).

Operating Instructions

• Set the upper integer bound \(N\) in the numeric value box.
• Click Run Sieve to observe animated prime sieving across the number grid.
• Enter any even integer to compute and verify Goldbach prime pairs \(p_1 + p_2 = 2n\).
• Inspect prime counting statistics \(\pi(N)\) and prime gap frequency charts.