Contents
Prologue - Page ix
1. Primes Factorial Intervals - Page 001
1. Eratosthenes’s Sieve - A Geometrical Approach - Page 003
2. Periodic Behaviour – First Observation - Page 005
3. Symmetry – Second Observation - Page 008
2. Gaps Sequences - Generating Primes - Page 015
1. Gap Functions of First Degree - Page 017
2. Properties of Gap Functions of First Degree - Page 022
3. Fractal like Behaviour of Gap Functions - Page 025
4. Recursive Method for Generating Gap Functions – Case Study - Page 026
5. Recursive Method for Generating Prime Numbers - Page 028
6. A New Life to Euclid’s Prime Test - Page 040
7. The numbers of Primes between n and n2 - Page 046
8. The number of Primes between n and 2n - Page 048
3. More than Statistics - Page 053
1. Histograms of Gap Functions - Page 055
2. Couple Functions - Page 057
3. Gap Pairs Sum Functions - Page 062
4. Gap Functions and Riemann’s Zeta Function for s = 1 - Page 067
5. Gap Functions and Step Functions - Page 069
6. Other Results from Gap Sequences - Page 076
7. Patterns in the Distribution of the Number of Factors - Page 077
8. The Histogram of Gap Functions and the Blackbody Radiation - Page 083
4. Big Gaps between Primes - Page 087
1. Chinese Reminder Theorem – Where are the big gaps? - Page 089
5. Gap Functions of Higher Degrees - Page 097
1. Gap Functions of Second Degree - Page 099
2. Properties of Gap Functions of Second Degree - Page 102
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