def solve():
result = 0 #@UnusedVariable
start = time.clock()
i = 0
primes = {}
truncatable_primes = []
for i in range(0, 7):
border = ['37']
if i == 0:
border = ['2357']
digit_sets = border + i*['1379'] + border
for digits in produce(digit_sets):
number = "".join(digits)
nums = sorted(set([int(n) for n in generate_left_truncated_string(number)] + [int(n) for n in generate_right_truncated_string(number)]))
all_are_primes = True
for n in nums:
if n < 10:
continue
try:
is_p = primes[n]
except KeyError, e:
is_p = miller_rabin(n, 20)
primes[n] = is_p
if not is_p:
all_are_primes = False
if all_are_primes:
truncatable_primes.append(int(number))
def solve(n):
# It is 999.999 > 9^5 + 9^5 + 9^5 + 9^5 + 9^5
i=0
m = range(10)
numbers = []
for i in range(1,7):
for digits in produce([m]*i):
sum_of_fifth_powers = sum([d**n for d in digits])
number = int("".join([str(d) for d in digits]))
if number > 1 and number == sum_of_fifth_powers:
numbers.append(number)
result = sum(set(numbers))
print("The sum of all the numbers that can be written as the sum of fifth powers of their digits is %(result)d" % vars())
def solve(N):
primes = find_product_primes_below(N)
factors_set = [[n for n in powers_below(p, N, 1)] for p in primes]
max_frac = 0.0
max_number = 0
for factors in produce(factors_set):
n = product_of(factors)
if n > N:
continue
phi = product_of([num - num/p for (num,p) in zip(factors, primes)])
frac = float(n)/phi
if frac > max_frac:
print(n, frac, factors)
max_frac = frac
max_number = n
return max_number