How big is 2⁶⁴, and where does it show up?

18446744073709551616 — about 1.8 × 10¹⁹, the range of a 64-bit integer and the modern address/counter ceiling.

2⁶⁴ ≈ 18.4 quintillion is the number of values a 64-bit register holds — enough addresses that 64-bit computing won't run out the way IPv4 did. The classic illustration: the wheat-on-a-chessboard legend ends with 2⁶⁴−1 grains on the last square, more wheat than humanity has ever grown. You don't peg all 20 digits — you remember the magnitude (~1.8 × 10¹⁹).

But for fun, here's the whole 20-digit number as a four-panel picture-book story, proving the peg method scales to anything. Chunk 18446744073709551616 into pairs → 18 44 · 67 44 · 07 37 · 09 55 · 16 16 → dove · rower · chick · rower · sky · mug · soap · lily · DJ · DJ, and read the tale of the wheat on the chessboard:

Tip: 2⁶⁴ is exactly (2³²)², so it's "4.3 billion squared".