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It is shown that prime sequences of arbitrary length, of which the prime pairs, (p, p+2), the prime triplet conjecture, (p, p+2, p+6) are simple examples, are true and that prime sequences of arbitrary length can be found and shown to repeat indefinitely. Asymptotic formulae comparable to the prime number theorem are derived for arbitrary length sequences. An elementary proof is also derived for the prime number theorem and Dirichlet’s Theorem on the arithmetic progression of primes.
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Cite this paper
Garvie, C. L. (2016). Asymptotic formulae for the number of repeating prime sequences less than N. Notes on Number Theory and Discrete Mathematics, 22(4), 29-40.