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.