Problem 49 - Find arithmetic sequences, made of prime terms, whose four digits are permutations of each other.

링크 

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?

python

limit = 10000 isPrime = [True] * limit isPrime[0] = isPrime[1] = False for i in range(2, int(round(limit**0.5))+1): if isPrime[i]: isPrime[2*i:limit:i] = [False] * ((limit-1)/i-1) primes = [x for x in range(1001, limit) if isPrime[x]] def func(n): s = list(str(n)) s.sort() return "".join(s) for i1 in range(len(primes)): for i2 in range(i1+1, len(primes)): a = primes[i1] b = primes[i2] c = b + b - a if c < limit and isPrime[c] and func(a) == func(b) == func(c): print a, b, c