Erdős–Woods number

An Erdős–Woods number is a specific type of integer related to the study of sets of consecutive integers and their relationships to prime numbers. More formally, an integer \( n \) has an Erdős–Woods number if there exists a positive integer \( k \) such that the set of integers: \[ \{ n, n+1, n+2, \ldots, n+k \} \] contains \( k \) or more prime numbers.