"""
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 eulertools import prime_gen_dict
from itertools import permutations, combinations
prime_dict = prime_gen_dict(10000)
#Remove the sequence in the example
for num in (1487, 4817, 8147):
prime_dict.pop(num)
found = False
prime_lst = [p for p in sorted(prime_dict.keys()) if p > 1000 and p < 10000]
for prime in prime_lst:
seq = []
for perm in permutations(str(prime), 4):
if not perm[0] == '0':
num = int(''.join(perm))
if num not in seq and prime_dict.has_key(num):
seq.append(num)
if len(set(seq)) >= 3:
for c in combinations(sorted(seq), 3):
if c[2] - c[1] == c[1] - c[0]:
"""
The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.
Find the sum of the only eleven primes that are both truncatable from left to right and right to left.
NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
"""
from eulertools import prime_gen_dict
primes = prime_gen_dict(1000000)
def is_truncatable(p):
if p < 20:
return False
s = str(p)
length = len(s)
#If the prime begins or ends with 1 or 9 return False
if s[0] in ('1', '9') or s[length-1] in ('1', '9'):
return False
#If the prime contains 2 or 5, return False
if '2' in s[1:] or '5' in s[1:]:
return False
if any(not primes.has_key(int(s[i:])) for i in xrange(1, length)):
return False
if any(not primes.has_key(int(s[:j])) for j in xrange(1, length)):
return False
return True
print sum(p for p in primes if is_truncatable(p))
