Explores the connection between incircles, excircles, and Pythagorean triangles, proving that radii are integers.
Explores Pythagorean triples with consecutive sides, including recurrence relations and formulas for primitive triples.
R function to generate Ulam Prime Spiral, a visualization of prime numbers in a spiral grid.
Explores the equivalence between Markov's equation and Zagier's approximating equation using hyperbolic identities.
Explores the relationship between pentagonal and triangular numbers through visual and algebraic proofs.
A technical guide implementing Wagon's algorithm in Python to solve x² + y² = p for large primes, using quadratic residues and a modified Euclidean algorithm.
Explains how to compute a square root of -1 modulo a prime p, using number theory and Python code examples.
Explains an algorithm for finding a non-square modulo a prime, with Python code and examples from cryptography.
Explores Fermat's theorem on expressing primes as sums of two squares, comparing Gauss's formula with a more efficient computational algorithm.
Explores prime gaps, their mathematical merit, and their use as proof-of-work in the Gapcoin cryptocurrency.
Explores prime clusters, their mathematical definition, and their use as proof-of-work in the Riecoin cryptocurrency.
Explores a method for testing Cunningham prime chains efficiently, with applications in cryptocurrency proof-of-work systems.
Explores bi-twin prime chains, a mathematical pattern where sequences of twin primes follow a doubling rule, with examples and Python verification code.
Explores prime number chains like Cunningham chains and their application in the Primecoin cryptocurrency's proof-of-work system.
A new record for the largest known 'compositorial prime' has been set, a prime number with over 3.7 million digits.
Celebrates Pi Day with two math tricks: a party trick using the 'Rule of 37' and a computer implementation of Ramanujan's formula for calculating Pi.
