mathematics

Number Theory & Prime Numbers

The study of integers and their properties — prime sieves, Goldbach's conjecture, modular arithmetic, continued fractions, and the distribution of primes across the number line.

number theoryprime numbersmodular arithmeticGoldbach conjecturecontinued fractionsprime distributionSieve of Eratosthenes

Number theory, often called the 'queen of mathematics,' investigates the fundamental properties of integers. Prime numbers — the indivisible building blocks of arithmetic — have fascinated mathematicians for millennia, from Euclid's proof of their infinitude to the Riemann Hypothesis that governs their distribution. These ideas underpin modern cryptography, coding theory, and computational mathematics.

These simulations let you run prime sieves in real time, test Goldbach's conjecture on even numbers, explore modular arithmetic and congruence systems, expand numbers into continued fractions, and visualize how primes thin out along the number line following the Prime Number Theorem.

5 interactive simulations

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Continued Fractions Explorer

Expand any real number into its continued fraction representation — visualize convergents approaching the target and discover best rational approximations

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Goldbach's Conjecture Verifier

Test Goldbach's conjecture interactively — decompose any even number into pairs of primes and visualize the number of representations

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Modular Arithmetic & Clock Math

Explore modular arithmetic visually — compute modular exponentiation, visualize residue classes on a clock dial, and see congruence patterns

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Prime Distribution & Number Theorem

Visualize how primes thin out along the number line — compare π(x) against N/ln(N) and the logarithmic integral Li(x) in real time

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Sieve of Eratosthenes

Visualize the Sieve of Eratosthenes in real time — watch composite numbers get eliminated as primes are discovered up to any limit