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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 $$n$$.

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 $$P$$.