def substring_divisible(x):
"""
Determine if number is substring divisible
check that each 3 digit part is divisible by all the primes up to 18
:param x:
:return:
"""
# iterate through successive three digits and check if they
# can be divided by successively larger primes
for i, j in zip(sieve_of_eratosthenes(18), range(1, 8)):
if int(x[j:j + 3]) % i == 0:
continue
else:
return False
return True
from problem07 import sieve_of_eratosthenes
if __name__ == "__main__":
"""
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?
https://radiusofcircle.blogspot.com/2016/06/problem-49-project-euler-solution-with-python.html
"""
# 4 digit primes
primes = [
prime for prime in sieve_of_eratosthenes(10000)
if len(list(str(prime))) == 4 and prime > 1487
]
for key, prime in enumerate(primes):
# get list of permutations, and convert to ints (permutations() returns list of strings)
permutation_numbers = [
int(''.join(x)) for x in itertools.permutations(str(prime))
if int(''.join(x)) in primes
]
# get rid of non prime permutations
permutation_numbers = list(
set([number for number in permutation_numbers
if number in primes]))
# check that they all of the same difference?
for i in range(len(permutation_numbers)):
def primes_below(n):
return sieve_of_eratosthenes(n)
import time
from problem07 import sieve_of_eratosthenes
from problem32 import is_pandigital
if __name__ == "__main__":
start_time = time.time()
primes = sieve_of_eratosthenes(7654321)
pandigital_primes = []
for prime in primes:
if is_pandigital(prime, len(str(prime))):
pandigital_primes.append(prime)
print(max(pandigital_primes), time.time() - start_time)
import time
from problem07 import sieve_of_eratosthenes
if __name__ == "__main__":
"""
The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.
How many circular primes are there below one million?
https://radiusofcircle.blogspot.com/2016/05/problem-35-project-euler-solution-with-python.html
"""
start_time = time.time()
primes = sieve_of_eratosthenes(1000000)
count = 0
for prime in primes:
# assuming that there are no non-prime digits (2, 4, 6, 8, 5, 0)
all_prime_digits = True
# start with tens digit
number = prime // 10
# looping through digits
while number:
if (number % 10) % 2 == 0 or (number % 10) % 5 == 0:
all_prime_digits = False
break
number //= 10
if not all_prime_digits:
continue
length = len(str(prime))
number = prime