def eul25():
"""What is the index of the first term in the Fibonacci sequence to contain 1000 digits?"""
index, a, b = 1, 0, 1
while eul.num_len(b) < 1000:
a, b = b, a + b
index += 1
return index
def eul57():
"""In the first one-thousand expansions,
how many fractions contain a numerator with more digits than denominator?"""
count = 0
for i in range(1, 1001):
num = 1
den = 2
for j in range(i-1, 0, -1):
num += 2 * den
tmp = den
den = num
num = tmp
num += den
if eul.num_len(num) > eul.num_len(den):
count += 1
return count