"Why is it that two people can't generate the same #bitcoin private key?"
"How can a wallet generate a private key offline, and be sure that nobody else has picked that private key before?"
"How do I know that nobody else is using the same seed as me?"
"How do I know that nobody else can figure out or guess which private keys I'm using?"
- A #bitcoin private key is a 256-bit number, or 2^256
that's the number 2 multiplied by two 256 times
- Exponents are hard for humans to wrap their brains around them; half of 2^256 is 2^255, not 2^128
- 2^256 expressed as a decimal number is 10^77
- That's the number 1 and seventy-seven 0's after it;
10X10, 77 times
How big is 10^77?
- There are between 10^16 and 10^20 grains of sand (in all of the deserts and all of the beaches and on all of the ocean floor) on Earth
- There are 10^20 molecules of silica in a single grain of sand
- Multiplying the number of molecules in one grain of sand (10^20) by the number of grains of sand on Earth (10^20) is 10^40
- If you assume there's ten planets in the solar system, and assume they're all made of sand; 10^40 molecules of silica on all the grains of sand multiplied by ten is 10^41
- There are a hundred billion stars in the milky way galaxy, or 10^11
- 10^11 stars in the milky way multiplied by all of the molecules of silica in all the beaches on all of the planets in all of the milky way is 10^52
- There are perhaps a hundred billion *galaxies* in the observable universe, or 10^11
- 10^11 galaxies multiplied by all of the molecules of silica in all the beaches/oceans in all of the planets across the solar system in all of the stars in all of the galaxies is...10^63
- In astrophysics, the "Eddington number" (or NEdd) is the number of atoms in the "observable universe"
- The observable universe is just the part of the universe that has light that will ever reach us, or the matter that is all within the observation cone of space time that we occupy as humans; 13.8 billion light years across
- *ALL* matter - every atom of hydrogen in the entire observable universe - is approximately 10^77
- Current estimates put the NEdd at 10^80
- 10^77 happens to be the center of the range of estimates of the NEdd, and is the maximum number of possible #bitcoin private keys
That means that every atom of matter, in the entire observable universe of over a hundred billion galaxies, could have its own #bitcoin private key
tl;dr:
Pick an atom; any atom
See if someone else picks the same one
