15 interactive notebooks ready to launch.
Generate primes efficiently using the classic sieve algorithm.
Explore the distribution of primes and asymptotic prime counting.
Visualize primes in the Ulam spiral and search for patterns.
Compute large powers mod n efficiently with repeated squaring.
Compute Euler’s totient function and study its number-theoretic properties.
Use Fermat’s theorem for primality tests and modular simplifications.
Solve congruences and compute modular inverses with the extended Euclidean algorithm.
Combine congruences using the Chinese remainder theorem.
Explore the hardness of discrete logarithms in modular arithmetic.
Test primality probabilistically with Carmichael and Miller-Rabin checks.
Factor integers using Pollard’s Rho randomized algorithm.
Study the quadratic sieve approach to large integer factorization.
Simulate Diffie-Hellman key exchange and shared secret generation.
Build RSA encryption and decryption routines from first principles.
Explore elliptic curve point addition as a basis for modern cryptography.