Abstract

Of course, better estimates can be obtained from Bertrand's Postulate, or from versions of the Prime Number Theorem having explicit constants, but the proofs of these results are also much harder. Euclid's argument yields some special cases of Dirichlet's great theorem on primes in arithmetic progressions. The preceding modification can also be adapted to this context. In what follows, we use pi to denote the ith prime of the form p = 4k + 3.

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