LMS Popular Lecture Series 2013
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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Akram Khan on Srinivasa Ramanujan BBC Radio 4 Great lives with Matthew Parris and Robin Wilson
“Because prime numbers didn’t let us down this year” by Evelyn Lamb, Scientific American.
“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.”