06-314 Imre Mikoss

The Prime Numbers Hidden Symmetric Structure and its Relation to the Twin Prime Infinitude and an Improved Prime Number Theorem. (468K, pdf) Nov 3, 06

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Abstract. Due to the sieving process represented by a Secondary Sieving Map; during the generation of the prime numbers, geometric structures with definite symmetries are formed which become evident through their geometrical representations. The study of these structures allows the development of a constructive prime generating formula. This defines a mean prime density yielding a second order recursive and discrete prime producing formula and a second order differential equation whose solutions produce an improved Prime Number Theorem. Applying these results to twin prime pairs is possible to generate a Twin Prime Number Theorem and important conclusions about the infinitude of the twin primes.

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