Please try this activity:
Tell me if I have made mistakes or omissions, or any ideas for improvement.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
There is only a single spelling error. Almost half way down the page "Amd."
To really investigate those stars would require a good sketcher type program. I quickly made a big mess with pen and paper.
What is the reason why for difference between the 6 and 7? Is it because they composite and prime?
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.