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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