I came up with the idea when I was observing the Gilbreath's conjecture. (I am unsure, if the thing that I have thought upon already exists as a conjecture or not.) The proposed Conjecture (let me not say) states that: For any consecutive even numbers in a series, if the number has a divisor two, upon addition of the divisor and quotient, a new series is introduced in the form of x, x+1, x+2, .......... Alternatively, for any consecutive even numbers (>2) in a series, if the number is divided by two, upon addition of all factors (excluding itself) forms a new series in the form of x, x+1, x+2, ..........