2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129934We study the gaps between consecutive prime numbers directly through Eratosthenes sieve. Using elementary methods, we identify a recursive relation for these gaps and for specific sequences of consecutive gaps, known as constellations. Using this recursion we can estimate the numbers of a gap or of a constellation that occur between a prime and its square. This recursion also has explicit implications for open questions about gaps between prime numbers, including three questions posed by Erdös and Turán.21 pages, LaTeX, 2 pdf figuresNumber Theory11N05; 11A41; 11A07text