"Nice" numbers.
The number 69 is "Nice"; that is a quality it has and so it is a "Nice" number. It's in decimal of course, AKA base ten, and it has other neat attributes you can see on Wikipedia if you care to look.
It is unique in that it is the "Nice" number in base 10, but there are other "Nice" numbers:
69 in base 15 is 99 in decimal 69 in base 14 is 93 in decimal 69 in base 13 is 87 in decimal 69 in base 12 is 81 in decimal 69 in base 11 is 75 in decimal
So, 99, 93, 87, 81, and 75 are all 69-related. I'll call these "TopNice Numbers"
"BottomNice Numbers" exist too.
And, if you like, the BottomNice numbers
69 in base 10: 76 in base 9 * 69 in base 10: 63 in base 11 69 in base 10: 59 in base 12 69 in base 10: 54 in base 13 69 in base 10: 49 in base 15 69 in base 10: 45 in Hexadecimal/base 16 69 in base 10: 41 in base 17 69 in base 10: 39 in base 20 69 in base 10: 36 in base 21 69 in base 10: 33 in base 22 69 in base 10: 30 in base 23 69 in base 10: 29 in base 30 69 in base 10: 27 in base 31 69 in base 10: 25 in base 32 69 in base 10: 23 in base 33 69 in base 10: 21 in base 34 69 in base 10: 18 in base 61 69 in base 10: 17 in base 62 69 in base 10: 16 in base 63
And I haven't done the calculations for anything base 65, 66, 67, or 68 so there may be a couple more BottomNice numbers..
1 is disqualified in the same way it is disqualified from being a prime number.
69 is...we'll call it "BothNice" or "TrueNice" I suppose, since we can't very well exclude it.
As with all bleeding-edge mathematical theory, the discoveries come first, and the important applications come later, but I trust there will be some great progress come from this conceptual breakthrough. I hope we're ready for what comes.