NishMath

This cluster focuses on open questions and conjectures in number theory, specifically related to perfect powers in Lucas and Fibonacci sequences and Diophantine equations. It explores the sparsity of such numbers and their forms. The research seeks to identify and prove conjectures related to perfect powers arising from these sequences, looking for counterexamples or modified proof techniques.

This cluster investigates number theory, focusing on primes and their distribution. It covers sieving techniques, including the Sieve of Eratosthenes, and their application to the twin prime conjecture. Ergodic principles are used to estimate the number of primes and twin primes, suggesting a connection between number theory and statistical mechanics. The research delves into the distribution of prime numbers and explores methods for understanding their behavior, offering insights into fundamental number-theoretic problems. It also touches upon the idea of primes and how it is connected to other mathematical structures.

This cluster discusses number theory related to palindromic and other special numbers. The discussion includes the generation of palindromic numbers, exploration of 2025 as a perfect square, and Kaprekar numbers. These topics are part of recreational mathematics and number theory. The cluster investigates the properties and structures of various classes of numbers, providing interesting results to the mathematical community.

This cluster focuses on recreational mathematics, specifically the properties of the number 2025. It covers the fact that it’s a square number, a Kaprekar number, and other interesting properties. It also includes links to math carnivals and websites related to math blogging.

The Great Internet Mersenne Prime Search (GIMPS) has discovered the 52nd Mersenne prime number, 2^136279841-1. This is a significant achievement in computational number theory, and extends the list of known Mersenne primes. The discovery highlights the ongoing efforts to find large prime numbers and their importance in various fields of mathematics and computer science.