Prime permutations.py

from math import sqrt
from functools import reduce

'''
Problem 49
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?
'''

def getSieve():

    sieve = {i: False for i in range(1009, 10000) if i % 2 != 0}
    for key in sieve.keys():
        for i in range(3, int(sqrt(key)) + 1, 2):
            if key % i == 0:
                sieve[key] = True
                break

    primeNumbers = list(map(str, filter(lambda x: sieve[x] == False, sieve.keys())))
    primeNumbers.remove("1487")
    return primeNumbers

if __name__ == '__main__':

    primeNumbers = getSieve()
    length = len(primeNumbers)
    firstNum = 0
    secondNum = 0
    thirdNum = 0
    for i in range(0, length):

        firstDigitList = list(primeNumbers[i])
        tempFirstDigitList = list(primeNumbers[i])
        tempFirstDigitList.sort()
        c = 0
        for j in range(i + 1, length):
            thirdDigitList = list(primeNumbers[j])
            tempThirdDigitList = list(primeNumbers[j])
            tempThirdDigitList.sort()

            if tempThirdDigitList == tempFirstDigitList:
                firstNum = reduce(lambda x, y: int(x)*10 + int(y), firstDigitList)
                thirdNum = reduce(lambda x, y: int(x)*10 + int(y), thirdDigitList)
                secondNum = (firstNum + thirdNum)//2

                if str(secondNum) in primeNumbers:

                    secondDigitList = list(str(secondNum))
                    secondDigitList.sort()
                    if secondDigitList == tempFirstDigitList:
                        print(firstNum)
                        print(secondNum)
                        print(thirdNum)
                        c = 1
                        break
        if c == 1:
            break


    print(str(firstNum) + str(secondNum) + str(thirdNum))