JP Journal of Algebra, Number Theory and Applications
Abstract: This paper examines, through new elementary methodologies, the
pairs of numbers of the type with h
integer. Infinite pairs of that type are twin primes: here one constructs the
succession of the primes of the first type, the succession of
the primes of the second type, the three successions of the twin
primes and the finite succession of the pairs of the consecutive pairs of the
type of
twin primes and their total number
It is here reported the number
obtained through the combinations and the same number
obtained through the integrals, of the primes of the
first type between two consecutive mixed productstoand as well as
the number of primes of the second type between two consecutive squares, which
confirms the Riemann Hypothesis. Here there is also the number of pairs of twin
primes between two
consecutive squares of the types and which is at
least two, as well as the number of pairs of twin primes between and which is at
least four, and their distribution in the various intervals limited by
consecutive squares. The paper also reports many tables useful for the
factorization.
Keywords and phrases: primes, twin primes, consecutive twin primes.
