Project Euler Problem 049


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?


It's a brute-force approach with some performance improvements.

from CommonFunctions import find_primes_less_than
from itertools import dropwhile
is_anagram = lambda x, y: sorted(str(x)) == sorted(str(y))
if __name__ == '__main__':
    primes = find_primes_less_than(10000)
    primes_greater_1000 = dropwhile(lambda x: x <= 1000, primes)
    primes = set(primes)
    found_one = False
    for base in primes_greater_1000:
        for increment in range(1, ((10000 - base) // 2)):
            n1 = base + increment
            n2 = base + increment * 2
            if n1 in primes and n2 in primes and is_anagram(base, n1) and is_anagram(base, n2):
                if found_one:
                    print("The result is:", str(base) + str(n1) + str(n2))
                found_one = True

The Python file is available for download here.

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