A friend of mine wrote up an article On the Interesting Properties of the Number 37. I think his article is great. However, it must be said that 37 is not just some random number, but 37 is related in a very special way to the number 73. And so I have written this article as a sort of supplement.
To state the obvious, 73 is 37 written backwards. Both also are prime numbers, and both have a digital root of 1.
Looking a little deeper, we see that 37 is equal to (1×36) + 1, just as 73 is equal to (2×36) + 1. Already there is what looks to be a pattern. I wonder if 109 may also be related? (The number 109 has its own special properties too, which will blow your mind. And this is why 109 is one of my all-time favourite numbers. It also represents the relative distances between the sun, earth, and moon. Perhaps I will write up an article on that one next.)
All repeating eight-digit “octuplets” are divisible by 73. Not only that, but these quotients are each equal to 137 times the corresponding four-digit “quadruplet”.
00000000÷73 = 0 = 137×0000
11111111÷73 = 152207 = 137×1111
22222222÷73 = 304414 = 137×2222
33333333÷73 = 456621 = 137×3333
44444444÷73 = 608828 = 137×4444
55555555÷73 = 761035 = 137×5555
66666666÷73 = 913242 = 137×6666
77777777÷73 = 1065449 = 137×7777
88888888÷73 = 1217656 = 137×8888
99999999÷73 = 1369863 = 137×9999
I also find it interesting that the number 137 shows up, as this 137 contains within itself the 37, along with a perfect 100.
Also, without having thoroughly tested this, I think the digital root of the “octuplet” is always going to be equal to the digital root of the corresponding quotient. For example, 11111111÷73 = 152207, so 1+1+1+1+1+1+1+1 = 8, and 1+5+2+2+0+7 = 17 where 1+7 = 8.
(This section is in need of further research.)
73×5 = 365, and there are 365 days in the year.
The 73rd triangular number is 2701, which is the sum of all the letters in the first verse of the Hebrew bible.
Also, 73 multiped by 37 is equal to the same 2701.
There are exactly 73 books in the Catholic bible if you count Jeremiah and Lamentations as two separate books. (I prefer to group them together though, such that there are 72 books.)