The Number 37
2024-12-05 | tags : number
The number \(37\) has always been near and dear to my heart. Here I am listing an astonishing list of facts that make this number really stand out of the crowd (of natural numbers). I am not claiming that there is anything special about this number.... it's just that I fell in love with it!
- The number 37 is a prime number, and it is palindromic - meaning that if we flip around the digits you get another prime number (\(73\)).
- \(37\) is composed of digits that are primes themselves (\(3\) and \(7\)).
- If we take the sum of its digits we get the number \(10\) - that is the binary representation of the first prime number (i.e. \(2\)).
- Things get interesting if we look at the indexes of \(37\) and \(73\) on the list of primes: \(37\) and \(73\) occur at positions \(12\) and \(21\), respectively - another palindromic number!
- Adding \(37\) to \(73\) returns \(110\) that is equivalent to \(6\) in binary base. And guess what?! The peaks in the distribution of gap numbers occur at multiples of \(6\) (see here and my previous post)
Now, another interesting fact about the number \(37\):
$$\frac{111}{1+1+1}=37 $$
Similarly,
$$\frac{222}{2+2+2}=37 $$
and so on, until we get to
$$\frac{1x+10x+100x}{x+x+x}=37 $$
Finally we conclude with few permutations of the digits of \(37\) that lead to prime numbers: \(337\), \(373\), \(3373\), \(3733\), \(7333\), \(33377\), \(77773\).