sophiegermain module

Pure-Python library that provides a selection of Sophie Germain primes that are organized by representation size.

sophiegermain.sophiegermain.sophiegermain(bit_length: int) → int

Return the smallest Sophie Germain prime 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 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