Numerical Fulcrums: Providing Leverage for Work with Primes

What might be a numerical fulcrum? Consider the sequence of consecutive positive integers 1, 2, 3, 4, 5, 6, 7, 8. Which, if any, integer could serve as a fulcrum for the sequence? One way to create a meaning in this context is to ask if there exists a number that separates the list into two sub-lists with equal sums. A little inspection reveals that 6 is a numerical fulcrum for this list because 1 + 2 + 3 + 4 + 5 = 7 + 8. Students might ask, or you can prompt them to ponder the question, where did this definition come from?