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Abstract

The present work aims to be a compendium of the main results and open problems generated by certain numbers that have interesting properties. The interesting numbers selected for this work were friendly numbers, twin prime numbers and perfect numbers. Tocarry out thiscompendium, we studied the contents of numbers theory that served as a basis for the development of the results. Hence, we go on to study the search for pairs of friendly numbers, from formulas that generate only one pair, to those that generate several. We continue to study the twin prime numbers and the openconjecture that permeates them as well as the results associated with such a conjecture. We ended up studying the perfect numbers and the theorems that use the idea of such numbers in their statements. For all of the aforementioned interesting numbers, theorems or conjectures were presented that require the demonstration of the respective interesting numbers in order to be demonstrated or, still, problems arising from the study of such numbers.