Prime Inventor

Find primes in any BigInt range using Miller-Rabin test.

Range Parameters

Start Number

End Number

Note: For extremely large numbers, the primality test is probabilistic. For very wide ranges, calculations can be slow.

Results

Calculating...

Prime Number Explorer & Sieve Handbook

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.