# It can be seen that the number, 125874, and its double, 251748, contain exactly the same digits,
# but in a different order.
#
# Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits.
from tools import is_permutation
for i in range(1, 10000000):
if is_permutation(str(i), str(i*2)):
if is_permutation(str(i), str(i*3)):
if is_permutation(str(i), str(i*4)):
if is_permutation(str(i), str(i*5)):
if is_permutation(str(i), str(i*6)):
print i
break
from tools import get_primes
from tools import is_permutation
import datetime
a = []
n = 9999
ts = datetime.datetime.now()
list_of_primes = [prime for prime in get_primes(n) if prime > 999]
set_of_primes = set(p for p in list_of_primes)
#print "\n".join(str(p) for p in list_of_primes)
print datetime.datetime.now() - ts
ts = datetime.datetime.now()
for p1p in range(len(list_of_primes)):
p1 = list_of_primes[p1p]
for p2p in range(p1p+1, len(list_of_primes)):
p2 = list_of_primes[p2p]
p3 = (p2+(p2-p1))
if p3 in set_of_primes:
#print "p1 " + str(p1) + " p2 " + str(p2) + " (p2+(p2-p1)) " + str(p2+(p2-p1))
if is_permutation(str(p1), str(p2)) and is_permutation(str(p2), str(p3)):
print str(p1) +" "+ str(p2) +" "+ str(p3)
print datetime.datetime.now() - ts
