## Analytic Demonstrations on the Fourfold Root Topics of Primes

**Authors:** Shaban A. Omondi Aura

This paper is concerned with formulation and demonstration of new versions of equations that can help us resolve problems concerning maximal gaps between consecutive prime numbers, the number of prime numbers at a given magnitude and the location of nth prime number. There is also a mathematical argument on why prime numbers as elementary identities on their own respect behave the way they do. Given that the equations have already been formulated, there are worked out examples on numbers that represent different cohorts. This paper has therefore attempted to formulate an equation that approximates the number of prime numbers at a given magnitude, from N=3 to N=〖10〗^25. Concerning the location of an nth prime number, the paper has devised a method that can help us locate a given prime number within specified bounds. Nonetheless, the paper has formulated an equation that can help us determine extremely bounded gaps. Lastly, using trans-algebraic number theory method, the paper has shown that unpredictable behaviors of prime numbers are due to their identity nature.

**Comments:** 30 Pages. Preferably for journals, academies and conferences

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### Submission history

[v1] 2017-05-19 01:01:55

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