# Category: Number Theory

## Secret Link Uncovered Between Pure Math and Physics – Minhyong Kim with Kevin Hartnett

Secret Link Uncovered Between Pure Math and Physics

“An eminent mathematician reveals that his advances in the study of millennia-old mathematical questions owe to concepts derived from physics.”

by Kevin Hartnett, Quanta Magazine

## Mathematicians Crack the Cursed Curve – Kevin Hartnett

Mathematicians Crack the Cursed Curve

“A famously difficult mathematical problem resisted solution for over 40 years. Mathematicians have finally resolved it by following an intuition that links number theory to physics.”

by Kevin Hartnett, Quanta Magazine

## UNCRACKABLE? The Collatz Conjecture – Professor David Eisenbud on Numberphile

## Twin Prime Conjecture – with James Maynard on Numberphile

## Dr Vicky Neale “Addictive Number Theory”

LMS Popular Lecture Series 2013

## You can’t hide from the primes

### What are primes?

A *prime number* is a positive integer with exactly two different divisors. For example, 2 is prime, as 1 and 2 divide it. The same is true for 3, 5, and 7. But 6 is not prime as it has four divisors 1, 2, 3 and 6.

The Ulam spiral, where colored cells are primes. A larger version is the featured image of the blog.

On first glance, we may think that primes are not so useful. After all, we don’t use primes in daily life. Or do we? Read on!

First, we provide a few basic and not so basic facts about primes.

- A handy fact: to determine that a number n is prime, check for prime divisors at most √n. For example, we can quickly determine that 83 is prime by checking that 2, 3, 5 and 7 are not divisors.
- Every number is a product of primes. For example…

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