{}
import math
def birthday_paradox_probability(n, m):
# n: number of files
# m: number of possible hash values (2^64 for a 64-bit hash)
probability = 1 - math.exp(-n * (n - 1) / (2 * m))
return probability
# Number of files
n = 1_000_000
# Number of possible hash values for a 64-bit hash
m = 2**64
# Calculate the probability
probability = birthday_paradox_probability(n, m)
print(f"The probability that at least two of {n} files have the same 64-bit-hash, is: {probability:.12f}")