Finding Primes Using Complex Numbers

With complex numbers, I always feel as if I’m getting a glimpse of something truly awesome that lies hidden within mathematics. The first time I understood how they worked, I thought it was some form of magic.

I get the same feeling with prime numbers. Like many, I’ve looked at them from all angles – prime gaps, large primes, prime densities, prime sieves – and they continue to fascinate. A few months ago I was thumbing through Henry Warren’s programmers cookbook Hacker’s Delight (A) and discovered a whole chapter on the various formulas for (some of) them. Mind-bending stuff.

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