def prob_027():
b_list = primes.primes_list(1000)
max_primes, ans = 0, 0
for a in range(-999, 1000):
for b in b_list:
number_primes = first_non_prime(a, b)
if number_primes > max_primes:
max_primes, ans = number_primes, a*b
return ans
def prob_027():
b_list = primes.primes_list(1000)
max_primes, ans = 0, 0
for a in range(-999, 1000):
for b in b_list:
number_primes = first_non_prime(a, b)
if number_primes > max_primes:
max_primes, ans = number_primes, a * b
return ans
def find():
primes = primes_list(10**4)
for length in xrange(1000, 0, -1):
first = 0
while True:
summ = sum(primes[first:first+length])
# print summ
if summ >= 10**6: break
if prime(summ): return summ
first += 1
from primes import primes_list, primes_dict
PRIMES_LIST = primes_list(999999)
PRIMES_DICT = primes_dict(999999)
print("Primes list and dict built")
def shift_one(num):
str_num = str(num)
cycled_num_str = str_num[1:len(str_num)] + str_num[0]
return int(cycled_num_str)
def is_cyclic_prime(prime):
shifted = prime
if '0' in str(prime):
return False
for _ in range(len(str(prime))+2):
shifted = shift_one(shifted)
if shifted not in PRIMES_DICT:
return False
return True
def check_all_primes(n, print_circular=False):
cyclic_count = 0
for prime in PRIMES_LIST:
if prime > n:
break
if is_cyclic_prime(prime):
if print_circular:
print(prime)
cyclic_count += 1
return cyclic_count
#!/usr/bin/env python2 # coding=utf-8 """ Summation of primes Problem 10 The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. """ from primes import primes_list from functools import reduce print(reduce(lambda x, y: x + y, primes_list(2000000)))
from performance import make_timed
from primes import primes_list, primes_dict
from math import sqrt, floor
PL = primes_list(1000000)
PD = primes_dict(1000000)
def is_pandigital(number):
str_num = str(number)
for i in range(1,len(str_num)+1):
if not str(i) in str_num:
return False
return True
def is_prime(n):
if n < 1000000:
if n in PD:
return True
else:
return False
else:
for i in PL:
if n % i == 0:
return False
for i in range(1000001, int(sqrt(n)), 2):
if n % i == 0:
return False
return True
def run():
largest = 0
from performance import make_timed
from primes import primes_list, primes_dict
from math import sqrt, floor
PL = primes_list(1000000)
PD = primes_dict(1000000)
def is_pandigital(number):
str_num = str(number)
for i in range(1, len(str_num) + 1):
if not str(i) in str_num:
return False
return True
def is_prime(n):
if n < 1000000:
if n in PD:
return True
else:
return False
else:
for i in PL:
if n % i == 0:
return False
for i in range(1000001, int(sqrt(n)), 2):
if n % i == 0:
return False
return True
from primes import primes_list, primes_dict
PRIMES_LIST = primes_list(1000000)
PRIMES_DICT = primes_dict(1000000)
def truncate_right(n):
return int(str(n)[0:-1])
def truncate_left(n):
return int(str(n)[1:])
def is_prime(n):
return n in PRIMES_DICT
def is_truncatable(n):
if '0' in str(n):
return False
if len(str(n)) < 2:
return False
return True
def is_truncatable_prime(n):
if not is_truncatable(n):
return False
if not is_prime(n):
return False
from primes import primes_list, primes_dict
P_LIST = primes_list(100000)
P_DICT = primes_dict(100000)
S_LIST = [2*(n**2) for n in range(1,100000)]
S_DICT = {}
for i in range(len(S_LIST)):
S_DICT[S_LIST[i]] = None
def test(n):
for prime in P_LIST:
if prime > n:
break
for sq in S_LIST:
if prime + sq > n:
break
if prime + sq == n:
return True
return False
for i in range(33, 1000000, 2):
if i in P_DICT:
continue
if not test(i):
print(i)
break
def prob_010():
return sum(primes.primes_list(2000000))
from primes import primes_list, primes_dict
PRIMES_LIST = primes_list(1000000)
PRIMES_DICT = primes_dict(1000000)
def truncate_right(n):
return int(str(n)[0:-1])
def truncate_left(n):
return int(str(n)[1:])
def is_prime(n):
return n in PRIMES_DICT
def is_truncatable(n):
if '0' in str(n):
return False
if len(str(n)) < 2:
return False
return True
def is_truncatable_prime(n):
if not is_truncatable(n):
return False
if not is_prime(n):
return False
left = truncate_left(n)
right = truncate_right(n)
while(is_truncatable(left)):
if (not is_prime(left)) or (not is_prime(right)):
return False
from performance import make_timed, memoize
from primes import primes_list, primes_dict
MAX_NUM = 28123
P_LIST = primes_list(MAX_NUM)
P_DICT = primes_dict(MAX_NUM)
def sum_prop_divs(n):
return sum(proper_divisors(n))
def proper_divisors(n):
p_factors = prime_factors(n)
divisors = {}
width = len(p_factors)
for i in range(2**width-1):
divisor = choose_factors(p_factors, binary_str(i, width))
divisors[divisor] = None
return list(divisors.keys())
def choose_factors(factors, bit_str):
product = 1
for i in range(len(factors)):
if bit_str[i] == '1':
product *= factors[i]
return product
def binary_str(value, length):
return str(bin(value))[2:].zfill(length)
def prime_factors(n, primes_list=P_LIST, primes_dict=P_DICT):
factors = []
if n == 1 or n == 0:
#!/usr/bin/env python2
import primes
def is_prime(n):
if n < 2: return False
for i in xrange(3, int(n**0.5) + 1, 2):
if not n % i: return False
return True
result = len((2,5))
for number in primes.primes_list(10**6):
snum = str(number)
if filter(lambda d: d in '024568', snum): continue
rotations = {int(snum[i:] + snum[:i]) for i in xrange(len(snum))}
result += len(rotations) == len(filter(is_prime, rotations))
print 'result: %s' % result
