Solution for PRIME1, PRINT using numpy. Times out on PRINT.

sieve.py

from itertools import imap
import numpy


def main():
	limit = 2147483647**.5

	prime = numpy.ones(limit/2, dtype=numpy.bool)
	for i in xrange(3, int(limit**.5) + 1, 2):
		if prime[i/2]:
			prime[i*i/2: : i] = False

	primes = 2*prime.nonzero()[0].astype(int) + 1
	primes = primes[1:].tolist()

	input = imap(int, __import__('sys').stdin.read().split()).next
	out = []
	mapstr = numpy.vectorize(str)

	for _ in xrange(input()):
		l, u = input(), input()

		flag = False
		if l < 3:
			l = 3
			flag = True
		if l%2 == 0:
			l += 1

		cap = u**.5 + 1
		prime = numpy.ones((u - l)/2 + 1, dtype=numpy.bool)
		for p in primes:
			if p > cap:
				break

			if p*p >= l:
				b = p*p
			else:
				b = (l + p - 1)/p*p
				if b%2 == 0:
					b += p

			prime[(b - l)/2: : p] = False

		if flag:
			out.append('2')
		out.append('\n'.join(mapstr(2*prime.nonzero()[0] + l)))

	print '\n'.join(out)


main()