number theory - OpenGenus IQ: Computing Expertise & Legacy

Lagrange’s Four Squares Theorem

In this article, we will discus Lagrange’s four square theorem in detail with examples and an algorithm to verify it.

Mersenne prime numbers

When 2^n -1 is prime, it is said to be a Mersenne prime. In this article, we have explored this concept of Mersenne prime numbers in depth along with algorithms + implementations to find Mersenne prime numbers.

List of Mathematical Algorithms

Cramer's conjecture

In this article, we have explored Cramer's conjecture which is an important conjecture for prime numbers. We have developed a code to verify this conjecture.

List of Mathematical Algorithms

Zeckendorf's theorem

The Zeckendorf's theorem states that every positive integer can be represented uniquely as a sum of one or more distinct non-neighboring or non-consecutive Fibonacci numbers.

Algorithms

Find primes using Sieve of Eratosthenes

Sieve of Eratosthenes is a simple and ancient algorithm (over 2200 years old) used to find the prime numbers up to any given limit. It is one of the most efficient ways to find small prime numbers. Implementations in C, C++, C Sharp, Java, Go, Haskell, JavaScript, PHP and Python.