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

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

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

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

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

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

- The guy who posted Giving the Sieve a Few More Teeth seems to have the right idea. I think we’re looking at a season of furious sieve work. 29 more words

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

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

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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