Tag - Number Theory

Modular Arithmetic Mon, May 11, 2020 02:00 CEST

Positional notation. An arbitrary precision integer on a computer is represented as a list of digits (limbs). They are just bigger. Today’s computers can hold 64 bits per limb. Modular arithmetic consists in applying addition and multiplication to integers modulo a certain number \(n\). Given an implementation of addition, multiplication, and division over the integers, we can emulate addition or multiplication modulo \(n\) by performing the corresponding operation on integers then taking the result modulo \(n\).

Ulam's Spiral
Infinite Number of Primes Sat, Jul 22, 2017 02:00 CEST

The erroneous proof I hear most often is: Suppose \(P\) is a finite set that contains all the primes, then \(p^* = 1 + \prod_{p \in P} p\) is prime. Indeed, the flaw is that \(p^*\) is not necessarily prime but rather must be a multiple of some prime not in \(P\).