MPMP15: Prime Pairs Naive Solution

output.txt

(1, 2, 3, 4, 7, 6, 5, 8, 9): [3, 5, 7, 11, 13, 11, 13, 17]
(1, 2, 3, 4, 9, 8, 5, 6, 7): [3, 5, 7, 13, 17, 13, 11, 13]
(1, 2, 3, 8, 5, 6, 7, 4, 9): [3, 5, 11, 13, 11, 13, 11, 13]
(1, 2, 3, 8, 9, 4, 7, 6, 5): [3, 5, 11, 17, 13, 11, 13, 11]
(1, 2, 5, 6, 7, 4, 3, 8, 9): [3, 7, 11, 13, 11, 7, 11, 17]
(1, 2, 5, 6, 7, 4, 9, 8, 3): [3, 7, 11, 13, 11, 13, 17, 11]
(1, 2, 9, 4, 3, 8, 5, 6, 7): [3, 11, 13, 7, 11, 13, 11, 13]
(1, 2, 9, 4, 7, 6, 5, 8, 3): [3, 11, 13, 11, 13, 11, 13, 11]
(1, 2, 9, 8, 3, 4, 7, 6, 5): [3, 11, 17, 11, 7, 11, 13, 11]
(1, 2, 9, 8, 5, 6, 7, 4, 3): [3, 11, 17, 13, 11, 13, 11, 7]
(1, 4, 3, 2, 9, 8, 5, 6, 7): [5, 7, 5, 11, 17, 13, 11, 13]
(1, 4, 3, 8, 9, 2, 5, 6, 7): [5, 7, 11, 17, 11, 7, 11, 13]
(1, 4, 7, 6, 5, 2, 3, 8, 9): [5, 11, 13, 11, 7, 5, 11, 17]
(1, 4, 7, 6, 5, 2, 9, 8, 3): [5, 11, 13, 11, 7, 11, 17, 11]
(1, 4, 7, 6, 5, 8, 3, 2, 9): [5, 11, 13, 11, 13, 11, 5, 11]
(1, 4, 7, 6, 5, 8, 9, 2, 3): [5, 11, 13, 11, 13, 17, 11, 5]
(1, 4, 9, 2, 3, 8, 5, 6, 7): [5, 13, 11, 5, 11, 13, 11, 13]
(1, 4, 9, 8, 3, 2, 5, 6, 7): [5, 13, 17, 11, 5, 7, 11, 13]
(1, 6, 5, 2, 3, 8, 9, 4, 7): [7, 11, 7, 5, 11, 17, 13, 11]
(1, 6, 5, 2, 9, 8, 3, 4, 7): [7, 11, 7, 11, 17, 11, 7, 11]
(1, 6, 5, 8, 3, 2, 9, 4, 7): [7, 11, 13, 11, 5, 11, 13, 11]
(1, 6, 5, 8, 9, 2, 3, 4, 7): [7, 11, 13, 17, 11, 5, 7, 11]
(1, 6, 7, 4, 3, 2, 5, 8, 9): [7, 13, 11, 7, 5, 7, 13, 17]
(1, 6, 7, 4, 3, 2, 9, 8, 5): [7, 13, 11, 7, 5, 11, 17, 13]
(1, 6, 7, 4, 3, 8, 5, 2, 9): [7, 13, 11, 7, 11, 13, 7, 11]
(1, 6, 7, 4, 3, 8, 9, 2, 5): [7, 13, 11, 7, 11, 17, 11, 7]
(1, 6, 7, 4, 9, 2, 3, 8, 5): [7, 13, 11, 13, 11, 5, 11, 13]
(1, 6, 7, 4, 9, 2, 5, 8, 3): [7, 13, 11, 13, 11, 7, 13, 11]
(1, 6, 7, 4, 9, 8, 3, 2, 5): [7, 13, 11, 13, 17, 11, 5, 7]
(1, 6, 7, 4, 9, 8, 5, 2, 3): [7, 13, 11, 13, 17, 13, 7, 5]
(3, 2, 1, 4, 7, 6, 5, 8, 9): [5, 3, 5, 11, 13, 11, 13, 17]
(3, 2, 1, 4, 9, 8, 5, 6, 7): [5, 3, 5, 13, 17, 13, 11, 13]
(3, 2, 1, 6, 5, 8, 9, 4, 7): [5, 3, 7, 11, 13, 17, 13, 11]
(3, 2, 1, 6, 7, 4, 9, 8, 5): [5, 3, 7, 13, 11, 13, 17, 13]
(3, 2, 5, 8, 9, 4, 1, 6, 7): [5, 7, 13, 17, 13, 5, 7, 13]
(3, 2, 9, 8, 5, 6, 1, 4, 7): [5, 11, 17, 13, 11, 7, 5, 11]
(3, 4, 1, 2, 9, 8, 5, 6, 7): [7, 5, 3, 11, 17, 13, 11, 13]
(3, 4, 7, 6, 1, 2, 5, 8, 9): [7, 11, 13, 7, 3, 7, 13, 17]
(3, 4, 7, 6, 1, 2, 9, 8, 5): [7, 11, 13, 7, 3, 11, 17, 13]
(3, 4, 9, 8, 5, 2, 1, 6, 7): [7, 13, 17, 13, 7, 3, 7, 13]
(3, 8, 5, 2, 1, 6, 7, 4, 9): [11, 13, 7, 3, 7, 13, 11, 13]
(3, 8, 5, 2, 9, 4, 1, 6, 7): [11, 13, 7, 11, 13, 5, 7, 13]
(3, 8, 5, 6, 1, 2, 9, 4, 7): [11, 13, 11, 7, 3, 11, 13, 11]
(3, 8, 5, 6, 7, 4, 1, 2, 9): [11, 13, 11, 13, 11, 5, 3, 11]
(3, 8, 9, 2, 1, 4, 7, 6, 5): [11, 17, 11, 3, 5, 11, 13, 11]
(3, 8, 9, 2, 5, 6, 1, 4, 7): [11, 17, 11, 7, 11, 7, 5, 11]
(3, 8, 9, 4, 1, 2, 5, 6, 7): [11, 17, 13, 5, 3, 7, 11, 13]
(3, 8, 9, 4, 7, 6, 1, 2, 5): [11, 17, 13, 11, 13, 7, 3, 7]
(5, 2, 1, 6, 7, 4, 3, 8, 9): [7, 3, 7, 13, 11, 7, 11, 17]
(5, 2, 3, 8, 9, 4, 1, 6, 7): [7, 5, 11, 17, 13, 5, 7, 13]
(5, 2, 9, 8, 3, 4, 1, 6, 7): [7, 11, 17, 11, 7, 5, 7, 13]
(5, 6, 1, 2, 3, 8, 9, 4, 7): [11, 7, 3, 5, 11, 17, 13, 11]
(5, 6, 1, 2, 9, 8, 3, 4, 7): [11, 7, 3, 11, 17, 11, 7, 11]
(5, 6, 7, 4, 1, 2, 3, 8, 9): [11, 13, 11, 5, 3, 5, 11, 17]
(5, 8, 3, 2, 1, 6, 7, 4, 9): [13, 11, 5, 3, 7, 13, 11, 13]
(5, 8, 3, 2, 9, 4, 1, 6, 7): [13, 11, 5, 11, 13, 5, 7, 13]
(5, 8, 3, 4, 7, 6, 1, 2, 9): [13, 11, 7, 11, 13, 7, 3, 11]
(5, 8, 3, 4, 9, 2, 1, 6, 7): [13, 11, 7, 13, 11, 3, 7, 13]
(5, 8, 9, 2, 3, 4, 1, 6, 7): [13, 17, 11, 5, 7, 5, 7, 13]
(5, 8, 9, 4, 3, 2, 1, 6, 7): [13, 17, 13, 7, 5, 3, 7, 13]
(7, 4, 1, 6, 5, 2, 3, 8, 9): [11, 5, 7, 11, 7, 5, 11, 17]
(7, 4, 1, 6, 5, 8, 3, 2, 9): [11, 5, 7, 11, 13, 11, 5, 11]
(7, 4, 3, 2, 1, 6, 5, 8, 9): [11, 7, 5, 3, 7, 11, 13, 17]
(7, 4, 3, 8, 5, 6, 1, 2, 9): [11, 7, 11, 13, 11, 7, 3, 11]
(7, 6, 1, 2, 5, 8, 3, 4, 9): [13, 7, 3, 7, 13, 11, 7, 13]
(7, 6, 1, 4, 3, 2, 5, 8, 9): [13, 7, 5, 7, 5, 7, 13, 17]
(7, 6, 1, 4, 3, 8, 5, 2, 9): [13, 7, 5, 7, 11, 13, 7, 11]
(7, 6, 5, 2, 1, 4, 3, 8, 9): [13, 11, 7, 3, 5, 7, 11, 17]
(7, 6, 5, 8, 3, 2, 1, 4, 9): [13, 11, 13, 11, 5, 3, 5, 13]
(7, 6, 5, 8, 3, 4, 1, 2, 9): [13, 11, 13, 11, 7, 5, 3, 11]
there are 70 solutions not including mirrored permutations

prime_pairs_naive.py

from itertools import permutations

primes = set([2, 3, 5, 7, 11, 13, 17])

def pair_sums(permutation):
    sums = []
    for i in range(len(permutation) - 1):
        sums.append(sum(permutation[i:i+2]))
    return sums

count = 0

for permutation in permutations(range(1,10)):
    if permutation[0] > permutation[-1]:
        continue
    sums = pair_sums(permutation)
    if set(sums).issubset(primes):
        print(f'{permutation}: {sums}')
        count += 1
        
print(f'there are {count} solutions not including mirrored permutations')