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Thursday, January 13, 2022

How Big is 2**256 ( 2 to the power of 256)

Excerpt from the book Programming Bitcoin by Jimmy Song

How Big is 2**256?

2**256 doesn’t seem that big because we can express it succinctly, but in reality, it is an enormous number. To give you an idea, here are some relative scales:
2**256 ~ 10**77

  • Number of atoms in and on Earth ~ 10**50
  • Number of atoms in the solar system ~ 10**57
  • Number of atoms in the Milky Way ~ 10**68
  • Number of atoms in the universe ~ 10**80

  • A trillion (10**12) computers doing a trillion computations every trillionth (10 **–12) of a second for a trillion years is still less than 10**56 computations. Think of finding a private key this way: there are as many possible private keys in Bitcoin as there are atoms in a billion galaxies.

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