def q37():
from My_functions import primes_up_to_n_using_sieve
from My_functions import truncatable_possibilities
from My_functions import is_prime
x = filter(
lambda x: int(str(x)[::-1]) % 2 != 0,
primes_up_to_n_using_sieve(1000000)) + primes_up_to_n_using_sieve(100)
x = sorted(list(set(x)))[4:]
ans = []
for i in x:
if all(is_prime(j) for j in truncatable_possibilities(i)):
ans.append(i)
return sum(ans), ans
def cycle_of(n):
if is_terminating(n):
return "1/" + str(n) + " is not a recurring decimal"
else:
if n in primes_up_to_n_using_sieve(n + 1):
return prime_cycle(n)
else:
pass
def q41():
from My_functions import is_pandigital_from_digits
from sieve import primes_up_to_n_using_sieve
n = primes_up_to_n_using_sieve(8000000)
ns = []
for i in n:
if is_pandigital_from_digits(i):
ns.append(i)
return max(ns)
def recurring(n):
if n < 8:
return 7
for d in primes_up_to_n_using_sieve(n)[::-1]:
period = 1
while __builtin__.pow(10, period, d) != 1:
period += 1
if d - 1 == period:
break
return d
def q35():
from sieve import primes_up_to_n_using_sieve
from My_functions import rotations
n = set(primes_up_to_n_using_sieve(1000000))
ans = set()
for i in n:
j = rotations(str(i))
if j.issubset(n):
ans.update(j)
n.discard(j)
return len(ans)
def q51():
from sieve import primes_up_to_n_using_sieve
from My_functions import eight_prime_family
sieve = primes_up_to_n_using_sieve(1000000)
for prime in sieve:
if prime > 100000:
s = str(prime)
lastDigit = s[5:6]
if (s.count('0') == 3 and eight_prime_family(s, '0') \
or s.count('1') == 3 and eight_prime_family(s, '1') \
or s.count('2') == 3 and eight_prime_family(s, '2')):
answer = s
return answer
def q50():
from sieve import primes_up_to_n_using_sieve
from My_functions import is_prime
prime_sieve = primes_up_to_n_using_sieve(1000000)
list_of_primes = []
number = 0
while True:
for i in prime_sieve[3:]:
number += i
if is_prime(number):
list_of_primes.append(number)
if number > 1000000:
break
break
return list_of_primes[-1]
def q49():
from itertools import permutations
from sieve import primes_up_to_n_using_sieve
def create(b):
for i in xrange(len(b)):
for j in xrange(i + 1, len(b)):
difference = b[j] - b[i]
if b[j] + difference in b:
return str(b[i]) + str(b[j]) + str(b[j] + difference)
return False
primes = primes_up_to_n_using_sieve(10000)
primes = [x for x in primes if x > 1487]
for i in primes:
p = permutations(str(i))
a = [int(''.join(x)) for x in p]
a = list(set([x for x in a if x in primes]))
a.sort()
if len(a) >= 3:
if create(a):
return create(a)
def sum_of_primes():
prime_list = primes_up_to_n_using_sieve(2000000)
result = 0
for i in prime_list:
result += i
return result
def q7():
primes = primes_up_to_n_using_sieve(1000000)
return primes[10000]
