#The maximum number of prime factors is the largest k such that the product of the first k primes is < 10^n

lim = 5000 #get primes
sieve = [i for i in range(3,lim,2)]
primes = [2]
while sieve:
..p = sieve.pop(0)
..if p*p > lim:
....primes.extend([p] + sieve)
....break
..primes.append(p)
..sieve = [i for i in sieve if i%p]

for n in range(1,41):
..primorial = 1 #how many prime factors do we need?
..leng = 0
..for p in primes:
....if primorial * p > 10**n: break
....primorial *= p
....leng += 1

..#obtain upper bound for prime factors
..upper = (primes[leng-1] * 10**n) // primorial
..if upper >= lim:
....print("Increase lim to >", upper)
....break
..prim = [p for p in primes if p <= upper]

..nums = [1]
..for k in range(leng):
....nex = set([])
....for p in prim:
......for m in nums:
........if m*p**(leng-k) >= 10**n: break
........if not m%p: continue
........nex.add(m*p)
....nums = sorted(list(nex))
..print(n,nums[-1])