dirichlet's theorem

if you take two numbers a,q which are relatively prime (have no common factors), then the arithmetic series a, a+q, a+2q,... contains infinitely many primes.
Probably the most beautiful thing I have learned, at least since the proof of uncountability of real numbers. Or maybe since the infinity of the primes in general. (Euclid's proof)
Induces the frustrating feeling of being partly able to imagine the prime numbers tailing off infinitely to the right, and thus getting a grip on how incomprehensible and hard to picture they actually are.

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