def search(goal):
"""
>>> search(6)
13
>>> search(7)
56003
"""
already_searched = set()
for prime in primes():
if prime in already_searched:
continue
positions_list = list(position_combinations(prime))
for positions in positions_list:
digits = list(digits_of(prime))
family = set()
for digit in range(10):
if 0 in positions and digit == 0:
continue
for pos in positions:
digits[pos] = digit
number = from_digits(digits)
if is_prime(number):
already_searched.add(number)
family.add(number)
if len(family) >= goal:
return min(family)
def cancel_unorthodox(numerator, denominator):
"""
>>> cancel_unorthodox(49, 98)
(4, 8)
>>> cancel_unorthodox(499, 998)
(4, 8)
>>> cancel_unorthodox(11, 12)
(1, 2)
"""
n_digits = digits_of(numerator)
d_digits = digits_of(denominator)
matching_digits = [d for d in n_digits if d in d_digits]
for m in matching_digits:
if m in n_digits and m in d_digits:
n_digits.remove(m)
d_digits.remove(m)
return from_digits(n_digits), from_digits(d_digits)
def reverse_and_add(n):
"""
>>> reverse_and_add(47)
121
>>> reverse_and_add(349)
1292
>>> reverse_and_add(1292)
4213
>>> reverse_and_add(4213)
7337
"""
rev_n = from_digits(list(reversed(digits_of(n))))
return n + rev_n
def check(digits):
"""
>>> from utility import digits_of
>>> check(digits_of(1406357289))
True
>>> check(digits_of(1406357298))
False
"""
digits = digits[1:] # ignore the first number
for prime, number in zip(primes, tuplewise(3, digits)):
number = from_digits(number)
if not number % prime == 0:
return False
return True
def truncatable_primes():
seen_primes = set()
one_digit_primes = (2, 3, 5, 7)
for p in primes():
seen_primes.add(p)
digits = digits_of(p)
# One-digit primes are not considered truncatable.
if len(digits) == 1:
continue
# All digits besides the first must be odd.
if not all(d % 2 == 1 for d in digits[1:]):
continue
# First and last digit must be prime.
if digits[0] not in one_digit_primes or \
digits[-1] not in one_digit_primes:
continue
# Test whether each truncation is a prime.
truncs = sorted(list(from_digits(d) for d in truncations(digits)))
if all(t in seen_primes for t in truncs):
yield p
import itertools
from utility import from_digits, tuplewise
primes = [2, 3, 5, 7, 11, 13, 17]
def check(digits):
"""
>>> from utility import digits_of
>>> check(digits_of(1406357289))
True
>>> check(digits_of(1406357298))
False
"""
digits = digits[1:] # ignore the first number
for prime, number in zip(primes, tuplewise(3, digits)):
number = from_digits(number)
if not number % prime == 0:
return False
return True
solutions = []
for digits in itertools.permutations(range(10)):
if check(digits):
solutions.append(from_digits(digits))
print(sum(solutions))
def digit_permutations(n):
for digits in itertools.permutations(digits_of(n)):
yield from_digits(digits)