alt Hacker News`9↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑9` seems like a reasonable guess (barring encoding cheats/trickery like @masfuerte commented!)
Edit: I've misread the above comment and my number is is 64 bytes (significantly more than 64 bits. The largest 64 bit number through my approach would be `9↑↑↑↑↑↑9`, which is significantly smaller.
I can do you one better and specify that the normal base-2 integer represented by the bits is the number of up-arrows. But as /u/tromp has already pointed out, that is not very interesting.