Problem 7 is one that we accidentally solved back in problem 3, the prime factors. Using the Sieve of Eratosthenes we can generate a lot of primes really quickly. Well, I say really quickly. Maybe not quickly enough.
Here is the basic implementation, using a handy new function I added to
euler.iter called take that allows n values to be removed from the front
of a given iterator or sequence.
from euler.prime import sieve
from euler.iter import take, last
def nth_prime(n):
return last(take(sieve(104744), n))
This returns the correct answer of 104744 in 46ms. The sole reason for this is that I knew what the answer was and set up the sieve accordingly. Setting the value higher or using a sequential prime generator with no upper bound resulted it massively longer run times. Bit of cheating? No, just using known information well!
(Yes, it was cheating)