With a SHA1 encoding the probability of a hash collision becomes, at various k (number of twts):
>>> import math
>>>
>>> def collision_probability(k, bits):
... n = 2 ** bits # Total unique hash values based on the number of bits
... probability = 1 - math.exp(- (k ** 2) / (2 * n))
... return probability * 100 # Return as percentage
...
>>> # Example usage:
>>> k_values = [100000, 1000000, 10000000]
>>> bits = 44 # Number of bits for the hash
>>>
>>> for k in k_values:
... print(f"Probability of collision for {k} hashes with {bits} bits: {collision_probability(k, bits):.4f}%")
...
Probability of collision for 100000 hashes with 44 bits: 0.0284%
Probability of collision for 1000000 hashes with 44 bits: 2.8022%
Probability of collision for 10000000 hashes with 44 bits: 94.1701%
>>> bits = 48
>>> for k in k_values:
... print(f"Probability of collision for {k} hashes with {bits} bits: {collision_probability(k, bits):.4f}%")
...
Probability of collision for 100000 hashes with 48 bits: 0.0018%
Probability of collision for 1000000 hashes with 48 bits: 0.1775%
Probability of collision for 10000000 hashes with 48 bits: 16.2753%
>>> bits = 52
>>> for k in k_values:
... print(f"Probability of collision for {k} hashes with {bits} bits: {collision_probability(k, bits):.4f}%")
...
Probability of collision for 100000 hashes with 52 bits: 0.0001%
Probability of collision for 1000000 hashes with 52 bits: 0.0111%
Probability of collision for 10000000 hashes with 52 bits: 1.1041%
>>>
If we adopted this scheme, we could have to increase the no. of characters (first N) from 11
to 12
and finally 13
as we approach globally larger enough Twts across the space. I think at least full crawl/scrape it was around ~500k (maybe)? https://search.twtxt.net/ says only ~99k