def primes(n):
    array = []
    sieve = [True] * (n+1)
    for p in range(2, n+1):
        if (sieve[p]):
          array.append(p)
          for i in range(p, n+1, p):
            sieve[i] = False
    return array

primelist = primes(9999999)
sequence = [1,2,4,7,11]

def loop(j):
    new=[]

    for i in range(len(j)):
        try:
            new.append(j[i+1] - j[i])
        except IndexError:
            pass
    return new

def process(sequence):
    layer = 1
    looped = loop(sequence)

    while True:
        count = 0
        for i in looped:
            count = count+i
        if looped != []:
            if count == 0:
                return looped, layer
            else:
                layer = layer + 1
                looped = loop(looped)
        else:
            return "Impossible with dataset", None



print(process(primelist))