def prime_gen():
"""A generator function that yields prime numbers using the `Sieve of
Eratosthenes <http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes>`_
algorithm.
.. note::
This function is based on the erat2a function which can be found
`here <http://stackoverflow.com/a/3796442>`_. Variable names were
changed and comments added for clarity.
"""
yield 2
comp_dict = {}
for num in it_islice(it_count(3), 0, None, 2):
p = comp_dict.pop(num, None)
if p is not None:
# num is a composite. Get the next composite that is not already
# in the dictionary and that has p as prime factor. Add it to
# the dictionary. The composite number is thus "sieved" out.
# By taking a 2*p step, we avoid checking if test is even.
test = num + 2 * p
while test in comp_dict:
test = test + 2 * p
comp_dict[test] = p
else:
# num is a prime.
# Add the first composite number that has 'num' as the
# only prime factor to the composite numbers dictionary
comp_dict[num * num] = num
# return num
yield num
def prime_gen():
"""A generator function that yields prime numbers using the `Sieve of
Eratosthenes <http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes>`_
algorithm.
.. note::
This function is based on the erat2a function which can be found
`here <http://stackoverflow.com/a/3796442>`_. Variable names were
changed and comments added for clarity.
"""
yield 2
comp_dict = {}
for num in it_islice(it_count(3), 0, None, 2):
p = comp_dict.pop(num, None)
if p is not None:
# num is a composite. Get the next composite that is not already
# in the dictionary and that has p as prime factor. Add it to
# the dictionary. The composite number is thus "sieved" out.
# By taking a 2*p step, we avoid checking if test is even.
test = num + 2 * p
while test in comp_dict:
test = test + 2 * p
comp_dict[test] = p
else:
# num is a prime.
# Add the first composite number that has 'num' as the
# only prime factor to the composite numbers dictionary
comp_dict[num * num] = num
# return num
yield num
def prime_wheel_fact_gen():
"""A generator function that yields prime numbers using the `wheel
factorized <http://en.wikipedia.org/wiki/Wheel_factorization>`_ `Sieve of
Eratosthenes`_.
.. note::
This function is based on the erat3 function which can be found
`here <http://stackoverflow.com/a/3796442>`_. Variable names were
changed and comments added for clarity.
"""
yield 2
yield 3
yield 5
# The mask is used with itertools.compress method to generate prime
# candidates after eliminating numbers using the wheel. The mask
# contains a 1 when the corresponding number has 2,3 or 5 as a factor
# only odd numbers are considered so the mask has only 15 values instead
# of 30.
wheel_mask = [
0 if x % 3 == 0 or x % 5 == 0 else 1 for x in range(7, 37, 2)
]
modulos = frozenset(
[x % 30 for x in range(31, 61, 2) if x % 3 != 0 and x % 5 != 0])
comp_dict = {}
for num in it_compress(it_islice(it_count(7), 0, None, 2),
it_cycle(wheel_mask)):
p = comp_dict.pop(num, None)
if p is not None:
# num is a composite. Get the next composite that is not already
# in the dictionary, that meets the wheel criteria and that has p
# as prime factor. Add it to the dictionary. The composite number
# is thus "sieved" out.
# By taking a 2*p step, we avoid checking if test is even.
test = num + 2 * p
while test in comp_dict or test % 30 not in modulos:
test = test + 2 * p
comp_dict[test] = p
# delete 'num' from comp_dict to free memory.
else:
# num is a prime.
# Add the first composite number that has 'num' as the
# only prime factor to the composite numbers dictionary
comp_dict[num * num] = num
# return num
yield num
def prime_wheel_fact_gen():
"""A generator function that yields prime numbers using the `wheel
factorized <http://en.wikipedia.org/wiki/Wheel_factorization>`_ `Sieve of
Eratosthenes`_.
.. note::
This function is based on the erat3 function which can be found
`here <http://stackoverflow.com/a/3796442>`_. Variable names were
changed and comments added for clarity.
"""
yield 2
yield 3
yield 5
# The mask is used with itertools.compress method to generate prime
# candidates after eliminating numbers using the wheel. The mask
# contains a 1 when the corresponding number has 2,3 or 5 as a factor
# only odd numbers are considered so the mask has only 15 values instead
# of 30.
wheel_mask = [0 if x % 3 == 0 or x % 5 == 0 else 1 for x in range(7, 37, 2)]
modulos = frozenset([x % 30 for x in range(31, 61, 2) if x % 3 != 0 and x % 5 != 0])
comp_dict = {}
for num in it_compress(it_islice(it_count(7), 0, None, 2), it_cycle(wheel_mask)):
p = comp_dict.pop(num, None)
if p is not None:
# num is a composite. Get the next composite that is not already
# in the dictionary, that meets the wheel criteria and that has p
# as prime factor. Add it to the dictionary. The composite number
# is thus "sieved" out.
# By taking a 2*p step, we avoid checking if test is even.
test = num + 2 * p
while test in comp_dict or test % 30 not in modulos:
test = test + 2 * p
comp_dict[test] = p
# delete 'num' from comp_dict to free memory.
else:
# num is a prime.
# Add the first composite number that has 'num' as the
# only prime factor to the composite numbers dictionary
comp_dict[num * num] = num
# return num
yield num