steady square numbers

"""puzzle from Labyrint van Occam
"""
def extend(number, length):
    """given a steady square number with length add extra digit"""
    f = 10 ** length
    f10 = 10 * f
    for digit in range(10):
        cand = f * digit + number
        if cand == pow(cand, 2, f10):
            return cand

def make_long(number, N):
    """N: desired length of number"""
    for i in xrange(1, N):
        number = extend(number, i)
    return number

def make_long5(N):
    """N: desired length of number
       simply square number and add digit i+1 to number (or
       calculate number**2 % 10**i+1)
    """
    number = 5
    p = 10
    for i in xrange(1, N):
        p *= 10
        number = (number * number) % p
    return number

NEXT6 = dict(zip("3710926485",[int(s) for s in "7390184625"]))
def make_long6(N):
    """N: desired length of number
    """
    number = 6
    p = 1
    for i in xrange(1, N):
        p *= 10
        n = NEXT6[str(number * number)[-i-1]]
        number += n * p
    return number


N = 100

N5 = make_long5(N)
N6 = 10 ** N + 1 - N5
print "{0:d}: {1:s}".format(5, str(N5).zfill(N))
print "{0:d}: {1:s}".format(6, str(N6).zfill(N))