6, definitely, argues moustache Sam
Let’s get one thing right off the bat: 6 is just perfect. No, seriously, it is literally a perfect number! We say a number is perfect if its proper divisors add up to that number. The divisors of 6 are 1, 2 and 3… and, sure enough, $6=1+2+3$. Perfect!
Since 6 is perfect, that means it has an associated Mersenne prime; those of the form $2^p-1$. If you take any perfect number and extract all of its powers of 2, you will always get yourself a Mersenne prime. In the case of 6, $6=2^1\times3=2^1(2^2-1)$.
On the topic of primes… a pair of consecutive primes that are a distance of 6 away like {23, 29} or {6961, 6967} are called sexy primes, named aptly for their stunning appearance in the naturals and definitely not because the Latin for six is sex.
6 is a highly composite number, having more divisors than any number that precedes it. It’s also $3!$, which can be interpreted as the number of ways to arrange three distinct objects in a row. Knowing that $3!=6$ is really useful for the next time your friend asks you how many ways you can arrange three distinct objects in a row.
The final thing to say is that 6ft is an excellent height. You would definitely not want to be 7ft. And 6 is even.
Lucky #7, argues circus Sam
Not only is everyone’s lucky number a prime number, it’s a Mersenne prime: $7=2^3-1$. This means it has an associated perfect number; if you take any Mersenne prime $2^p-1$ and multiply it by $p-1$ twos, you get a perfect number. In the case of 7, $2^2(2^3-1)=28$. Perfect!
7 also appears just about everywhere. Consider the easy-to-remember rhyme I made to help you remember many occurrences of 7 in the world:
7 for the dwarfs in Snow White’s tale,
7 for the days in the week’s trail.
7 for the sins, deadly and vile,
7 for Samurai, who smites you with a smile.
7 for the wonders, both ancient and new,
7 for… red, orange, yellow, green, indigo, violet and blue.
Division by 7 is also extremely easy to do because the recurrence $0.\overline{142857}$ repeats. Just don’t ask me to test whether you can do it whole.
In chemistry, 7 remains the neutral, nay, nonchalant, constant of pH. I’m pretty sure a glass of pH 6 water would not taste good.
All jokes aside, 7 is obviously the more dominant number. It just shows strength. Why else would 6 be afraid? And 7 is seven.
