def euler():
middle = math.ceil(math.sqrt(HIGHEST_N))
for p in range(middle, 0, -1):
if prime.is_prime(p):
for q in range(middle + 1, math.ceil((10 ** 7) / p)):
if prime.is_prime(q):
n = p * q
t = discreet.totient(n)
if sequence.is_permutation(str(n), str(t)):
return n
def euler():
for n in range(346, 6000):
# number of cubes that are permutations of n^3
cube_permutations = 0
digits = str(n * n * n)
maximum = maximum_for(digits)
# for each number from n to maximum (see maximum_for()), check if its
# cube is a permutation of n
for m in range(n, maximum):
cube = m * m * m
if is_permutation(str(cube), digits):
cube_permutations += 1
# return it if it has the right number of permutations
if cube_permutations == 5:
return n ** 3
def is_int_permutation(x, y):
"""Return True iff two integers are permutations of eachother's digits."""
return sequence.is_permutation(list(str(x)), list(str(y)))