def prime_n(n):
'''Return the n'th prime.'''
if n == 0:
return 1
j = 0
count = 1
while count != n:
primes = sieve_erato(int(2**j * log(n) * n))
count = 1
for i, elem in enumerate(primes):
if elem:
count += 1
if count == n:
break
j += 1
return 2*i + 3
def segmented_sieve(L, R, B):
'''Perform a segmented Sieve of Eratosthenes.'''
# Typechecking
if (R - L) % B != 0:
raise ValueError('segmented_sieve(): B must divide R - L')
# First compute the primes less than sqrt(R).
divisors = sieve_erato(int(sqrt(R)))
Q = [-(L + 1 + (2*i + 3)) / 2 % (2*i + 3) if n != 0 else 0 for i, n in
enumerate(divisors)]
for block in xrange((R - L) / (2 * B)):
lst = bt.bitarray(B)
lst.setall(True)
for i, p in enumerate(divisors):
if p:
lst[Q[i]::2*i+3] = False
Q = [(Q[i] - B) % (2*i + 3) if n != 0 else 0 for i, n in
enumerate(divisors)]
yield lst
