def get_prime(n):
# Для x >= 17 доказано следующее неравенство касательно функции распределения простых чисел - Pi(x):
# x / ln(x) < Pi(x) < 1.25506 * x / ln(x), воспользуемся этим и сформируем диапозон чисел
# для просеивания в решете Эратосфена достаточной длины, но в то же время без избыточности
# (для получения более оптимального алгоритма).
# Нам нужно решать обратную задачу: по известной Pi(x) найти супремум для x,
# для него известна и доказана следующая верхняя грань (для n >= 6): x < n * ln(n) + n * ln(ln(n))
# Таким образом, на выходе мы получим простые числа в количестве, гарантированно превышающем изначально заданное
if n >= 6:
primes = eratosthenes(get_numbers_supremum(n))
else:
# На 17 чисел приходится 6 простых, поэтому в решето пойдут лишь они
primes = eratosthenes(17)
return primes[n - 1]
def __init__(self, debug):
self.ignore = Ignore(modules = [], dirs = [os.path.dirname(__file__),
os.path.abspath(os.path.join(os.path.dirname(__file__), "../../common_modules")),
"/usr/lib/python2.6",
"/usr/lib/python2.7"])
self.SI = None
self.trace_func = self._Tracer
self.no_symbolic = debug
self.unique_op_map = {}
self.execution_context = None
self.known_code_blocks = {}
self.parser = ByteCodeParser(self)
self.prime_generator = eratosthenes()
self.arguments = {}
self.inside_tracing_code = True
self.function_to_be_traced = None
def __init__(self, debug):
# this line is very important; if the ignore directories are not correctly set
# (especially PYTHONHOME), the whole thing silently fails to work. Should make
# more robust in future
self.ignore = Ignore(modules = [], dirs = [os.path.dirname(__file__), os.environ["PYTHONHOME"]])
self.SI = None
self.trace_func = self._Tracer
self.no_symbolic = debug
self.unique_op_map = {}
self.execution_context = None
self.known_code_blocks = {}
self.parser = ByteCodeParser()
self.prime_generator = eratosthenes()
self.arguments = {}
self.inside_tracing_code = True
self.function_to_be_traced = None
def factor(N):
"""Factor a integer number N.
>>> factor(1)
defaultdict(<class 'int'>, {1: 1})
>>> factor(2)
defaultdict(<class 'int'>, {2: 1})
>>> factor(4)
defaultdict(<class 'int'>, {2: 2})
>>> factor(41)
defaultdict(<class 'int'>, {41: 1})
>>> factor(38556)
defaultdict(<class 'int'>, {17: 1, 2: 2, 3: 4, 7: 1})
>>> factor(1307674368000)
defaultdict(<class 'int'>, {17: 1, 2: 2, 3: 4, 7: 1})
"""
sqrt_n = int(math.sqrt(N))
factors = defaultdict(int)
if N == 1:
factors[1] = 1
return factors
# Find the primes that can be factors
primes = eratosthenes(N)
canstop = False
for p in primes:
while N % p == 0:
factors[p] += 1
N /= p
if p > sqrt_n:
canstop = True
if canstop:
break
return factors
def main(local_argv):
"""
local_argv is the argument list, progrom name is first arugment
this function prints the fibonacci list calcuated by the command line argument n
"""
if len(local_argv) != 2:
print("must add one and only one command argument, , exit ")
return
argument_n = int(
local_argv[1]) #remember, this is the 2nd argument in command line
if argument_n <= 0:
print("please input an pistive interger number, exit")
return
retList = eratosthenes.eratosthenes(argument_n)
return retList
def __init__(self, debug):
self.ignore = Ignore(modules=[],
dirs=[
os.path.dirname(__file__),
os.path.abspath(
os.path.join(os.path.dirname(__file__),
"../../common_modules")),
"/usr/lib/python2.6", "/usr/lib/python2.7"
])
self.SI = None
self.trace_func = self._Tracer
self.no_symbolic = debug
self.unique_op_map = {}
self.execution_context = None
self.known_code_blocks = {}
self.parser = ByteCodeParser(self)
self.prime_generator = eratosthenes()
self.arguments = {}
self.inside_tracing_code = True
self.function_to_be_traced = None
def generateTestData(max):
inp = [i for i in range(2, max)]
inpbitlist = [transBitList(x, max) for x in inp]
primelist = eratosthenes.eratosthenes(inp)
ans = [transBool(i in primelist) for i in inp]
return [inp, inpbitlist, ans]
return [N]
for c in n_str:
if c in "024568":
return None
res = []
cur = n_str
for i in range(len(n_str)):
res.append(int(cur))
cur = cur[-1] + cur[:-1]
return res
N = 1000000
primes = eratosthenes(N)
print(len(primes))
assert N > 1
circ_primes = []
for p in primes:
circulars = gen_circular(p)
if circulars is None:
continue
print(p)
print(circulars)
prime_test = list(map(lambda x: x in primes, circulars))
print(prime_test)
if all(prime_test):
circ_primes.append(p)
