Number Theory Lab

N: 100Mod: 12Even: 100

Number Theory Explorer – Primes, Modular Arithmetic

Number theory is the study of the integers and the deep, often surprising properties that govern divisibility, primality, and congruence. This explorer brings abstract results to life: you can sieve prime numbers up to any bound, watch the Euclidean algorithm compute GCDs step by step, and perform modular arithmetic to verify Fermat's little theorem and Euler's theorem with concrete numbers. These are the exact techniques that underpin RSA cryptography, hash functions, and pseudorandom number generators.

What you can do in this simulation

Run the Sieve of Eratosthenes and see prime numbers highlighted up to any bound you set
Trace the Euclidean algorithm computing GCD(a, b) step by step with remainder tables
Perform modular exponentiation and verify Fermat's little theorem for prime moduli
Factor integers and display prime factorizations with an animated factor tree
Explore the distribution of primes with a prime-counting function graph

Concepts covered

number theory · prime numbers · modular arithmetic · Euclidean algorithm · Fermat's theorem · prime factorization

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