Appendix
Appendix B
Tables: Powers of Two and Probability
Landmark powers of two
Continuing Chapter 1's ladder (\(2^1\) through \(2^{20}\)) to the rungs this book uses:
| \(n\) | \(2^n\) | |
|---|
| 32 | 4,294,967,296 | a 32-bit space (Chapter 6's 72 minutes) |
| 64 | 18,446,744,073,709,551,616 | |
| 128 | 340,282,366,920,938,463,463,374,607,431,768,211,456 | |
| 132 | 5,444,517,870,735,015,415,413,993,718,908,291,383,296 | |
| 256 | 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936 | |
The card, counted (Chapter 1)
| Question | Exact count |
|---|
| 12 words of 2,048, repeats allowed | \(2^{132}\) (40 digits) |
| 12 distinct words, order mattering | 5,271,537,971,301,488,476,000,309,317,528,177,868,800 |
| 12 distinct words, order ignored | \(\binom{2048}{12} = 11{,}005{,}261{,}717{,}918{,}037{,}175{,}659{,}349{,}191{,}168\) |
| Alphabetizing price (12 words) | division by \(12! = 479{,}001{,}600\) (\(\approx 28.8\) bits) |
Physical and network constants used in this book
| Quantity | Value used |
|---|
| Seconds in a year | 31,557,600 |
| Age of the universe | ≈ 13.8 billion years ≈ \(4.35 \times 10^{17}\) s |
| Landauer limit per bit flip (300 K) | ≈ \(2.9 \times 10^{-21}\) joules |
| Sun's output per year | ≈ \(1.2 \times 10^{34}\) joules |
| Bitcoin network rate (mid-2020s) | ≈ \(10^{21}\) hashes/second |
| secp256k1 group order \(n\) | 115792089237316195423570985008687907852837564279074904382605163141518161494337 |
All values are the ones the chapters compute with; every one appears in a runnable specimen or an exercise's printed answer somewhere in the book.