A project euler problem

prime_ap_seq.py

"""
The arithmetic sequence 1487, 4817, 8147, in which each of the terms increase by
3330 is unusual in 2 ways. (i) each of the terms are prime (ii) there are permutations
of each other.

There is one more 4 digit sequence like this. Find the 12digit number formed by 
concatenating them.
"""
 
########################################################################################
 
"""
EDIT:
When the problem says about another 4 digit sequence like the given one, it also means
that the difference between the terms is 3330. (This actually simplifies the matter a lot).

I found this out after generating the 2nd sequence the normal way. When I saw the 2nd
sequnce, I understood that it meant the difference was to be 3330 and I could have done it
more easily. :D
"""


LIM = 9999      # The number upto which we search

def seive(n):   # Seive of Eratosthenes to find all primes till 9999
    l=[True for i in range(n+1)]
    l[0:2] = [False,False]
    primes = []
    lim = int(n**0.5)+2
    for i in range(2,lim):
        if l[i]:
            primes.append(i)
            j=i*2
            while j<=n:
                l[j]=False
                j+=i
    for i in range(lim, n+1):
        if l[i]:
            primes.append(i)
    return [l,primes]

[Seive,Primes] = seive(LIM) # Run the seive and generate the list of primes

def find_ap_seqs():         # Find all AP sequences in the generated list of primes
    res = []
    for i in range(len(Primes)-2):
        for j in Primes[i+1:-1]:
            diff = j-Primes[i]
            if j+diff <= LIM:
                if Seive[j+diff]:
                    res.append([Primes[i],j,j+diff])
    return res

def find_ap_seqs_new():
    """This new function is written to speed up the search considering the condition 
    that the difference between two terms in the sequence is 3330"""

    res = []
    for i in Primes[:-2]:
        if i+3330 <= LIM:
            if Seive[i+3330]:
                if i+6660 <= LIM:
                    if Seive[i+6660]:
                        res.append([i,i+3330,i+6660])
    return res


AP = find_ap_seqs_new()

def isPerm(a,b):            # Check if two numbers are permutations of each other
    return sorted(str(a))==sorted(str(b))

def check_permutations():   # Check the list of sequences to find the sequence which satisfies the permutation condition    
    res = []
    for seq in AP:
        if isPerm(seq[0],seq[1]) and isPerm(seq[0], seq[2]):
            res.append(seq)
    return res

Final = check_permutations()
## Final: [[1487, 4817, 8147], [2969, 6299, 9629]]

del Final[Final.index([1487,4817,8147])]
print(''.join([str(x) for x in Final[0]]))

# Output : 296962999629