The Distribution of Primes in a Short Interval
Jan Feliksiak *
Language School in Krakow, Poland.
*Author to whom correspondence should be addressed.
Abstract
This research paper begins the presentation, with the topic of the distribution of primes in a short interval. The lower and upper limits for the number of primes within the interval are defined unambiguously. This provides us with a solid foundation, to resolve conclusively the Second Hardy - Littlewood \(\pi\)k \(\ge\) \(\pi\)(n+k) - \(\pi\)n conjecture. The paper concludes with the Merit of a Prime Gap and the Second Harald Cramer's Conjecture.
Keywords: Density of primes in short interval, distribution of primes, Erdos P. conjecture for primes in short intervals, logarithmic integral, maximal prime gaps lower bound, maximal prime gaps Supremum, Prime Gap Merit, prime number theorem, second Cramer's conjecture, second hardy and Littlewood's conjecture, supremum for primes in short intervals, tailored logarithmic integral, the primorial