The number 12 is very flexible. You can write it as 2 x 6 or as 3 x 4. Or, even better, as 2 x 2 x 3. Which brings us to those very special numbers called the primes: those numbers that are not divisible by any other number apart from 1 and themselves. Every number can be decomposed into a product of primes, for example 12 = 2 x 2 x 3. The primes are the atoms of number theory, they are also connected to one of the hardest open problems in maths, and even to the weird world of quantum physics.

If you love the primes, or at least feel curious about them, then try Marcus du Sautoy's book The music of the primes: why an unsolved problem in mathematics matters. It's a gentle introduction to the primes, their importance in the modern world, and all the mathematicians they have taunted over the centuries. To get a feel for the subject, read du Sautoy's Plus articles The prime numb lottery and The music of the primes, or watch his lecture below.

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