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. In this article we present a point of view that highlights theimportance of finding the upper bounds for prime gaps, in order to solve thetwin primes conjecture and the Goldbach conjecture. For this purpose, wepresent a procedure for the determination of the upper bounds for prime gapsdifferent from the most famous and known approaches. The proposed methodanalyzes the distribution of prime numbers using the set of relative numbers.Using negative numbers too, it becomes intuitive to understand that that thearrangement of 2P+1 consecutive numbers that goes -P to P, is the onlyarrangement that minimizes the distance between two powers having the sameabsolute value of the base D, with |D|<=P. This arrangement is consideredimportant because by increasing the number of powers of the prime numberswithin a range of consecutive numbers, it is presumed to decrease the overlapbetween the prime numbers considered. Consequently, by reducing these overlaps,we suppose to obtain an arrangement, in which the prime numbers less than andequal to P and their multiples occupy the greatest possible number of positionswithin a range of 2P+1 consecutive numbers. If this result could bedemonstrated, would imply not only the resolution of the Legendre conjecture,but also a step forward in the resolution of the twin primes conjecture and theGoldbach conjecture.

The importance of finding the upper bounds for prime gaps in order to solve the twin primes conjecture and the Goldbach conjecture