def run():
maximum_index = 0
maximum = 0
num_list = []
P = [i for i in xrange(2, 1000000) if is_probable_prime(i)]
for p in P:
num_list.append(0)
for i in xrange(len(num_list)):
num_list[i] += p
if num_list[i] in P and num_list[i] < 1000000:
if maximum_index < len(num_list) - i:
maximum_index = len(num_list) - i
maximum = num_list[i]
if num_list[-1] >= 1000000 or p > 4000:
return maximum
if num_list[0] > 1000000:
del num_list[0]
from itertools import product
from eulertools import is_probable_prime
for n in set([i[0]*i[1] for i in product(range(3, 1000, 2), repeat=2)]):
i = 0
detect = True
while True:
i += 1
if 2 * pow(i, 2) > n: break
remainder = n - (2 * pow(i, 2))
if remainder >= 2 and is_probable_prime(remainder):
detect = False
if detect:
print n
break
#!/usr/bin/python
# Euler Project Problem 41
"""Benchmark
Intel Core2 Duo CPU P8400 @ 2.26GHz
real 0m0.028s
user 0m0.028s
sys 0m0.000s
"""
from eulertools import is_probable_prime
from itertools import permutations
for p in reversed([int(''.join(n)) for n in permutations('1234567')]):
if is_probable_prime(p):
ans = p
break
print 'Answer to problem 41:', ans