Tags » Primes

Prime Polynomial Theorem

I just wanted to point towards a nice theorem, analogous to the Prime Number Theorem, which is not talked about much:

# irreducible monic polynomials with coefficients in and of degree , for a prime power .

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Prime Numbers And How To Find Them 1: Introduction

The fundamental theorem of arithmetic states that every integer greater than one is either is prime or the unique product of primes, ignoring the order. 389 more words


Claims and Proofs

It appears that many of the statements made in a recent linked post had little to no proof to back them up. Let’s try to give some extra details here… 2,099 more words


Twin Primes Conjecture Attempt


A nice article on recent progress on solving the twin prime conjecture

The twin prime conjecture (see here, here and here for more information) asserts that there are infinitely many primes that have a difference of 2. 184 more words


Positive Definite Quadratic Forms

I’m reading through Primes of the Form , by David Cox (link; it’s good!). Here are the high-level notes I took on the first chapter, which is about the theory of quadratic forms. 2,557 more words


Prime Consequences

Most of us are aware of the following consequence of Fundamental Theorem of Arithmetic:

There are infinitely many prime numbers.

The classic proof by Euclid…

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