  ABSTRACT. In this article we present a point of view that highlights the
importance of finding the upper bounds for prime gaps, in order to solve the
twin primes conjecture and the Goldbach conjecture. For this purpose, we
present a procedure for the determination of the upper bounds for prime gaps
different from the most famous and known approaches. The proposed method
analyzes the distribution of prime numbers using the set of relative numbers.
Using negative numbers too, it becomes intuitive to understand that that the
arrangement of 2P+1 consecutive numbers that goes -P to P, is the only
arrangement that minimizes the distance between two powers having the same
absolute value of the base D, with |D|<=P. This arrangement is considered
important because by increasing the number of powers of the prime numbers
within a range of consecutive numbers, it is presumed to decrease the overlap
between the prime numbers considered. Consequently, by reducing these overlaps,
we suppose to obtain an arrangement, in which the prime numbers less than and
equal to P and their multiples occupy the greatest possible number of positions
within a range of 2P+1 consecutive numbers. If this result could be
demonstrated, would imply not only the resolution of the Legendre conjecture,
but also a step forward in the resolution of the twin primes conjecture and the
Goldbach conjecture.
