"""
Pure-Python library that provides a selection of Sophie Germain primes
that are organized by representation size.
"""
# pylint: disable=too-many-lines
from __future__ import annotations
import doctest
import base64
import zlib
_DATA: list[bytes] = [
b'eNpjAgAAAwAD',
b'eNpjBQAABgAG',
b'eNrjBgAADAAM',
b'eNoTBwAAGAAY',
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b'eNoLBgAAVABU',
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b'eNoTZXQAAACEAFc=',
b'eNqLZGxgAAACawDb',
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b'eNoLZmRgAgABVQBX',
b'eNozZGBgAQAAzAA2',
b'eNo7yMTAAQADFgDM',
b'eNpbz8AgAAAC0ADA',
b'eNrrZ2RQAAACYwCx',
b'eNpzZmBwAAABUACE',
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]
[docs]def sophiegermain(bit_length: int) -> int:
"""
Return the smallest
`Sophie Germain prime <https://en.wikipedia.org/wiki/Safe_and_Sophie_Germain_primes>`__
the representation of which requires the specified number of bits.
>>> sophiegermain(2)
2
>>> sophiegermain(8)
131
>>> sophiegermain(16)
32771
>>> sophiegermain(32)
2147483693
>>> sophiegermain(257)
115792089237316195423570985008687907853269984665640564039457584007913129658411
>>> sophiegermain(1025).bit_length()
1025
The result returned by :obj:`sophiegermain` can be represented using the
specified number of bits.
>>> all([sophiegermain(k).bit_length() == k for k in range(2, 1026)])
True
If a bit length outside the supported range is supplied, an
exception is raised.
>>> sophiegermain(-1)
Traceback (most recent call last):
...
ValueError: all Sophie Germain primes have bit lengths of at least 2
>>> sophiegermain(1)
Traceback (most recent call last):
...
ValueError: all Sophie Germain primes have bit lengths of at least 2
>>> sophiegermain(1026)
Traceback (most recent call last):
...
ValueError: bit lengths greater than 1025 are not supported
The supplied bit length must be an integer.
>>> sophiegermain('abc')
Traceback (most recent call last):
...
TypeError: bit length must be an integer
"""
if not isinstance(bit_length, int):
raise TypeError('bit length must be an integer')
if bit_length < 2:
raise ValueError(
'all Sophie Germain primes have bit lengths of at least 2'
)
if bit_length > len(_DATA) + 1:
raise ValueError(
'bit lengths greater than ' + str(len(_DATA) + 1) + ' are not supported'
)
return int.from_bytes(
zlib.decompress(base64.standard_b64decode(_DATA[bit_length - 2])),
'little'
)
if __name__ == '__main__':
doctest.testmod() # pragma: no cover