def main(x):
pandigitals = number_permutations.main(x)
#gets all permutations of entered digits
pandigitals = sorted(pandigitals)
#sorts the pandigital permutations (smallest to largest)
pandigitals = pandigitals[::-1]
#reverses the order so the pandigitals are largest to smallest
prime = 0
#will store eventual answer
index = 0
#placeholder index
while prime == 0:
#continues until a prime is found
print(index)
if check_prime.main(pandigitals[index]) == 1:
#checks if number is prime
prime = pandigitals[index]
#stores prime if found
else:
#if number checked is not prime, increments index for search
index += 1
return prime
def main():
import number_permutations
permutations = number_permutations.main(123456789)
#imports function and then uses it to find a list of all 1-9 pandigital sequences
digits_list = ['1', '2', '3', '4', '5', '6', '7', '8', '9']
#stores the digits one through nine, each as a string, for use in splitting the pandigital strings later
good_trios = []
for perm in permutations:
#performs loop for each permuation
for i in digits_list:
parts_list = str(perm).partition(str(i))
#splits permutation at digit i
parts_list = [parts_list[0], (parts_list[1] + parts_list[2])]
#combines the last two entries (i and whatever was after it) into a single entry
if parts_list[0] != '' and parts_list[1] != '':
#ignores the split if either part ends up empty
for j in digits_list:
#must split at a different digit than before
if j != i:
splits = parts_list[1].partition(str(j))
#splits the second part at digit j
trio = [
parts_list[0], splits[0], (splits[1] + splits[2])
]
#combines the last two entries (j and whatever was after it) into a single entry
if trio[0] != '' and trio[1] != '' and trio[2] != '':
#ignores further actions if any part ends up empty
if int(trio[0]) * int(trio[1]) == int(trio[2]):
#stores trio if it meets the criteria
good_trios.append(trio)
#print(trio)
#TEST
return good_trios
def main(p): #finds first number with p cube permutations i = 100 # need to start search with at least 3-digit number desired_number = 0 #will hold number once found, used as check in while loop while desired_number == 0: #loop continues until suitable number found #TEST print(i) q = i ** 3 #finds cube of number cube_permutations = 0 #will be used to count number of permutations that are cubes permute_list = number_permutations.main(q) #gets the permutations of i^3 cube_list = [] #for testing purposes, stores list of cube permutations for j in permute_list: #checks if j is a cube, if it is adds one to the number of found cube permutations cube_num = is_cube(j) cube_permutations += cube_num if cube_num == 1: #for testing purposes, stores list of cube permutations cube_list.append(j) if cube_permutations == p: #defines required criteria desired_number = q else: i += 1 #increments i if desired number has not been found return [i,desired_number,cube_list]
def main():
#solves given problem
permutations = number_permutations.main(1234567890)
#finds all 0-9 pandigital numbers
num_with_prop = []
#will store all numbers with desired property
for i in permutations:
if check_property(i) == 1:
num_with_prop.append(i)
return sum(num_with_prop)
def main():
#solves defined problem by searching through pairs of primes
primes = find_primes_below.main(10**4)
#arbitrarily chosen cap for primes based on problem cap of 10^7
stored_num = [0, 0]
#will store highest totient / n as well as the number n
for i in primes:
for j in primes:
n = i * j
#since we are searching for numbers with 2 prime factors
if n < (10**7):
#requirement for max n
p_list = [i, j]
tot_div_n = totient_over_n(p_list)
#calculates totient/n using above function
totient = tot_div_n * n
#calculates the totient
if totient in number_permutations.main(n):
#i.e. if φ(n) is a permutation of n
if tot_div_n > stored_num[0]:
#i.e. if higher than last previous highest totient/n found
stored_num = [tot_div_n, n]
#stores numbers to be compared to or for answer if best
#TEST
print('i=', i, 'j=', j, 'stored_num=', stored_num)
#TEST
return stored_num
import find_primes_below
primes_list = find_primes_below.main(10000) #gets list of all primes below 10000 (4 digits or less)
import number_permutations #number_permutations.main(x) returns a list of all permutations of x
matches_criteria=[] #will hold all numbers meeting desired criteria
for i in primes_list:
#NOT NECESSASRY AND MISSES SOME## if len("".join(set(str(i)))) == 4: #checks that there are no duplicate digits in i
permutations = number_permutations.main(i) #gets permutations of i
prime_permutations = [] #starts list of permutations that are prime
for j in permutations: #loop adds any prime permutations to list
if j in primes_list:
prime_permutations.append(j)
for k in range (1,5000): #arithmetic difference between primes must be at least in this range
if (i + k) in prime_permutations and (i + (2*k)) in prime_permutations: #checks if there is a 3-tuple of primes
matches_criteria.append([i,i+k,i+2*k]) #adds them to list of tuples matching criteria