Department of Decision Sciences, School of Economics and Financial Sciences, College of Economics and Management Sciences, Université Sud-Africaine (UNISA), Pretoria, South Africa
This paper presents, in algebraic form, the set of prime numbers as obtained by the sieve of Eratosthenes and as contained in an arithmetic progression. In this way, it unifies old and recent studies on prime numbers: Euclid’s theorem, Dirichlet’s theorem, Green-Tao’s theorem, the conjecture of twin primes (generalized by Polignac) and Chebyshev’s Bias Phenomenon. It re-demonstrates the three theorems, solves Chebyshev’s Bias Phenomenon, demonstrates the twin primes conjecture and elucidates Polignac’s conjecture.
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