def main():
primes = make_primes(10000)
primes.remove(2)
all_five_primes = combinations(primes, 5)
for p in all_five_primes:
if a_set_of_five_primes(p):
print sum(p)
return
#!/usr/bin/python
# coding: UTF-8
"""
@author: CaiKnife
Prime permutations
Problem 49
The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.
There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.
What 12-digit number do you form by concatenating the three terms in this sequence?
"""
from itertools import permutations
from euler import make_primes, is_prime, get_digits
def to_tuple(n):
return tuple(str(n))
primes = [p for p in make_primes(10000) if len(str(p)) == 4]
primes = [p for p in primes if
is_prime(p + 3330) and len(str(p + 3330)) == 4 and is_prime(p + 6660) and len(
str(p + 6660)) == 4]
for p in primes:
per = permutations(to_tuple(p))
if to_tuple(p + 3330) in per and to_tuple(p + 6660) in per:
print p, p + 3330, p + 6660
9 = 7 + 212
15 = 7 + 222
21 = 3 + 232
25 = 7 + 232
27 = 19 + 222
33 = 31 + 212
It turns out that the conjecture was false.
What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
"""
from euler import is_prime, make_primes
from itertools import product
PRIMES = make_primes(10000)
def is_conjecture(n):
if is_prime(n):
return False
if not n % 2:
return False
c = product(PRIMES, [2 * i ** 2 for i in range(1, 100)])
for p in c:
if n == p[0] + p[1]:
return True
return False
for i in range(9, 10000):