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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"The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. " G H Hardy, A Mathematician's Apology (London 1941).

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