PyPE solution to PE problem 49

    ProjectEuler.net 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?

    Solution
    --------

    We know we are looking for prime numbers, so we pre-compute a list of all
    prime numbers up to 10,000 (since the largest number of interest will be
    9,999), and store a boolean for primality in an array (for fast indexing).
    We then loop over all 4-digit primes (the first one being index 168 in the
    list of primes). For each starting prime in the sequence, we loop through
    all the possible arithmentic increases. For each one, we compute the second
    number in the sequence; if the second number is prime, we compute the third
    number in the sequence; if the third number is prime, we continue our more
    extensive -- and more expensive -- tests.

    The next test is to see if the digits of y (the second number in the
    sequence) are some permutation of the digits of x. If so, then we also
    check the digits of z. The problem statement tells us that there are only
    two 4-digit sequences, and so we skip the one we are already aware of, and
    return an answer the next time we find something.

    Note that when looping over differences, in order for all numbers to be
    prime, the difference must be even -- otherwise one of the numbers in the
    sequence (specifically, the middle one) will end up being even, and thus
    definitely not prime.

    Answer
    ------

    296962999629