Cain lived a lo-o-ong time.
We are not told how long he wandered alone.
How many distant sisters and nieces could he have after two or three-hundred years?
Scripture says that Eve is the mother of all living thus we know where his wife came from.
I asked some math friends :
I am bothered not knowing how to work out exponent growth patterns. To use a simple population pattern, no twins, no deaths, let’s consider one birth a year by one person for 13 years when the oldest child also starts having children. All children start having children at 13 years old and keep having children every year. How many people are there in 125 years?
The answer :
Yeehaw. Branching processes.
Let’s do the simplest case we can first, which we can arrive at because in the case you have here, everything is deterministic and happens in 13 year increments, so you can take one generation to be 13 years and work only in terms of generations. In generation 0, there is 1 person. Each person in the previous generation produced 13 people in the next generation, plus themselves, so, notating the number of people in generation i as N_i,
N_i = 14 * N_{i-1}
with N_0 = 1, the solution to this is N_i = 14^i.
125 years is between 9 and 10 generations, so there are between 20 billion and 289 billion people in this model.
Genesis 5:3 When Adam had lived one hundred and thirty years, he became the father of a son in his own likeness, according to his image, and named him Seth.
If Cain and Abel were 125 years old when they had the first religious war, they had between 20 billion and 289 billion neighbours...not counting death by accident and remembering how long people were living in those days.