"""
We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once.
For example, 2143 is a 4-digit pandigital and is also prime.
What is the largest n-digit pandigital prime that exists?
"""
from math import sqrt
import primes
import permutations
primesToCheck = primes.create_primes(sqrt(987654321))
primeFound = False
def is_prime(number):
limit = sqrt(number)
for p in primesToCheck:
if p > limit:
return True
elif number % p == 0:
return False
return True
for x in xrange(10, 1, -1):
allPermutations = permutations.permutations(range(1, x))
for perm in sorted([permutations.combine_numbers(y) for y in allPermutations], reverse=True):
"""
The number 3797 has an interesting property. Being prime itself,
it is possible to continuously remove digits from left to right,
and remain prime at each stage: 3797, 797, 97, and 7.
Similarly we can work from right to left: 3797, 379, 37, and 3.
Find the sum of the only eleven primes that are both truncatable from left to right and right to left.
NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
"""
import primes
allPrimes = primes.create_primes(1000*1000)
def is_left_truncatable(prime):
for i in xrange(1, len(str(prime))):
if (prime % (10 ** i)) not in allPrimes:
return False
return True
def is_right_truncatable(prime):
for i in xrange(1, len(str(prime))):
if (prime / (10 ** i)) not in allPrimes:
return False
return True
sumOfTruncatablePrimes = 0
"""
The prime factors of 13195 are 5, 7, 13 and 29.
What is the largest prime factor of the number 600851475143 ?
"""
import math
import primes
highestNumber = 600851475143
highestPrime = int(math.sqrt(highestNumber))
relevantPrimes = reversed(primes.create_primes(highestPrime))
for p in relevantPrimes:
if highestNumber % p == 0:
print str(p)
break
""" The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. """ import primes print str(sum(primes.create_primes(2 * 1000 * 1000)))
"""
2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
"""
import primes
primeNumbers = primes.create_primes(20)
primeFactors = {}
def get_prime_factors(number):
prime_factors = {}
original_number = number
for p in primeNumbers:
number = original_number
factor = 0
while number % p == 0:
number /= p
factor += 1
prime_factors[p] = factor
return prime_factors
def merge_prime_factors(new_prime_factors):
for p in new_prime_factors:
