def problem49():
choice = xrange(1489, 3340, 2)
for n in choice:
if not prime.hasFactors(n, primes):
m1, strn = n+3330, str(n)
strm1, setn = str(m1), set(strn)
if set(strm1)==setn and not prime.hasFactors(m1, primes):
m2 = m1+3330
if set(str(m2))==setn and not prime.hasFactors(m2, primes):
return strn+strm1+str(m2)
def problem27():
"""http://projecteuler.net/index.php?section=problems&id=27
>>> problem27()
-59231
"""
max_pair = (0,0,0)
primes = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]
for a in xrange(-999, 1000):
for b in xrange(max(2, 1-a), 1000): # b >= 2, a + b + 1 >= 2
n, count = 0, 0
while True:
v = n*n + a*n + b
v = v <=0 and -v or v
if v > primes[-1]:
prime.primesBelow_fast(v, primes)
if prime.isprime_fast(v, primes): count = count + 1
else: break
else:
if not prime.hasFactors(v, primes): count = count + 1
else: break
n = n + 1
if count > max_pair[2]:
max_pair = (a,b,count)
return max_pair[0] * max_pair[1]