Distribution of prime numbers
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This book discusses a wide range of topics related to the distribution of prime numbers. We develop the maximal prime gaps upper bounds, based on the binomial coefficients - the sharpest to date. Implementing the theory, we discuss several related historical conjectures, eg. the Brocard, Cramer's and Legendre's Conjectures to name a few. Next it presents an enhanced bound on the Mandl's inequality, the sharpest to date. The distribution of primes in a short interval follows, culminating with the proof of the Second Hardy-Littlewood Conjecture. The book is richly illustrated to aid in visual pr...
This book discusses a wide range of topics related to the distribution of prime numbers. We develop the maximal prime gaps upper bounds, based on the binomial coefficients - the sharpest to date. Implementing the theory, we discuss several related historical conjectures, eg. the Brocard, Cramer's and Legendre's Conjectures to name a few. Next it presents an enhanced bound on the Mandl's inequality, the sharpest to date. The distribution of primes in a short interval follows, culminating with the proof of the Second Hardy-Littlewood Conjecture. The book is richly illustrated to aid in visual presentation of the pertinent concepts.
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