Yesterday, I started thinking about how many prime factors the average number contains along different sections of the number line. For example, between 5 and 10: 396 more words

## Tags » Primes

#### Diophantine Equation & Primes

I stumbled upon following statement on some webpage (don’t have link):

There exist infinitely many integers such that divides .

I tried proving it, though not able to prove it but here are my insights:

459 more words#### Ulam spiral

The Ulam spiral or prime spiral is an interesting way to visualize prime numbers using a simple manner of construction. I’ve included my own script using HTML5 that generates in a 250×250 grid. 64 more words

#### Number theory, RH, physics, and more

Matthew R. Watkins presents an excellent and accessible resource for mathematicians of any level. Answers many questions you might have or never thought to have on several important topics.

#### Expmath2 - Strictly non-palindromic numbers

https://en.wikipedia.org/wiki/Strictly_non-palindromic_number

Denote the number of strictly non-palindromic numbers up to x.

I suspect that where and is the prime counting function.

In a familiar form : … 95 more words

#### Linnik's Theorem for Sato-Tate Laws on CM Elliptic Curves

Here I talk about my first project at the Emory REU. Prerequisites for this post: some familiarity with number fields.