Twin Prime Conjecture – with James Maynard on Numberphile


You can’t hide from the primes

The Intrepid Mathematician

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.

Image result for ulam spiral 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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Feynman on Fermat’s Last Theorem by Luis Batalha

Feynman on Fermat’s Last Theorem by Luis Batalha

“While reading more about Feynman’s derivation of the Schrödinger equation in Schweber’s book QED and the Men who made it I ended up finding a mention to an undated two-page manuscript written by Feynman about Fermat’s Last Theorem. The manuscript doesn’t appear in the book but Schweber casts some light on Feynman’s approach which I will try to explain here in more detail.”